Collection of Number Programs Using Recursion [Second Edition]

RECURSION PROGRAMS RELATED TO NUMBERS

                                                                                                     

Md. Zeeshan Akhtar 

  RECURSION  RECURSION

GUIDE FOR SCHOOL

Study Guide For St Stude udent nts Programs Related to Numbers  ------------------------ -------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------                                                                       

           

                                                            

                                             

  

                              

                                                       

                                            

  

                                        

                                    

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Study Guide For St Stude udent nts Programs Related to Numbers  ------------------------ -------------------------------------------------- --------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------

                                                                  



                                            

                                                              

  

                                               

                                                        

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GUIDE FOR SCHOOL

Study Guide For St Stude udent nts Programs Related to Numbers  ------------------------ -------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------                                                                       

                                                            

                                                    

                                                         

  

    

                      

                    

          

          

                                    

             

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GUIDE FOR SCHOOL

Study Guide For St Stude udent nts Programs Related to Numbers  ------------------------ -------------------------------------------------- --------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------

                                              

                                                     

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                                                    

 



                    

    

 



 



 

 

 

                     



                     

 

 

 

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 



 

 

 

                        

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Study Guide For St Stude udent nts Programs Related to Numbers  ------------------------ -------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------                         

 

 



 

 



 



 



 



 

 

  

  

                  

                

                                         

  

                                              

                                                                              

                                              

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GUIDE FOR SCHOOL

Study Guide For St Stude udent nts Programs Related to Numbers  ------------------------ -------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------                                                                                              

                    

                                          

                           



      

              

                    

              

                  

  

                  

                                                   

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  RECURSION  RECURSION

GUIDE FOR SCHOOL

Study Guide For St Stude udent nts Programs Related to Numbers  ------------------------ -------------------------------------------------- --------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------

                      

                           

      

                                            

     

                                             

  

                                            

  

                                        

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GUIDE FOR SCHOOL

Study Guide For St Stude udent nts Programs Related to Numbers  ------------------------ -------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------  

                                              

  

                                         

                                                        

                            

                                            

                                                          

                                 

                                                         

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Study Guide For St Stude udent nts Programs Related to Numbers  ------------------------ -------------------------------------------------- --------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------

                                                                                                                                                               

                                                                             

                                                                                 

                                                                                                                                               

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  RECURSION  RECURSION

GUIDE FOR SCHOOL

Study Guide For St Stude udent nts Programs Related to Numbers  ------------------------ -------------------------------------------------- --------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------

                         

               Write the operation you want to perform with the digits coming out from the end over here.

Write the operation you want to perform with the digits coming out from the beginning over here.

 

 



                                                                                                                                                                                    

                    

  

                     

                     

                     

                                                         

 

                                                

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GUIDE FOR SCHOOL

Study Guide For St Stude udent nts Programs Related to Numbers  ------------------------ -------------------------------------------------- --------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------

                                                                           

                                        

                                                                                           

                                                                        

                                                                                                                           

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GUIDE FOR SCHOOL

Study Guide For St Stude udent nts Programs Related to Numbers  ------------------------ -------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------                                                          

                                                

                                        

                                                           

                                                            

                   

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GUIDE FOR SCHOOL

Study Guide For St Stude udent nts Programs Related to Numbers  ------------------------ -------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------                                            

                                          

                                                                                       

                                                          

                                                                      



              

                                                                                 

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  RECURSION  RECURSION

GUIDE FOR SCHOOL

Study Guide For St Stude udent nts Programs Related to Numbers  ------------------------ -------------------------------------------------- --------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------

        

  

             

                         

              

  

                       

                      

   

                       

                        

                           

                           

                 

            

               

               



  

 

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GUIDE FOR SCHOOL

Study Guide For St Stude udent nts Programs Related to Numbers  ------------------------ -------------------------------------------------- --------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------

                                 

                  

                             

                                       

                                        

                                    

                                                         

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GUIDE FOR SCHOOL

Study Guide For St Stude udent nts Programs Related to Numbers  ------------------------ -------------------------------------------------- --------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------

                   

                      

                                  

                      

                                

                    

                                                    

                                                 

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GUIDE FOR SCHOOL

Study Guide For St Stude udent nts Programs Related to Numbers  ------------------------ -------------------------------------------------- --------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------

                                            

                             

                                      

                                                   

                                   

                                                                             

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Study Guide For St Stude udent nts Programs Related to Numbers  ------------------------ -------------------------------------------------- --------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------

           

  

  

  

   

              

                       

                                                              

                   

                  

                            

                                                 

     

                                                 

                                     

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GUIDE FOR SCHOOL

Study Guide For St Stude udent nts Programs Related to Numbers  ------------------------ -------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------                                                          

                                     

                  

                                                   

                             

      

                                                 

  

                                                 

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  RECURSION  RECURSION

GUIDE FOR SCHOOL

Study Guide For St Stude udent nts Programs Related to Numbers  ------------------------ -------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------         

  

  

  

   

              

                      

                          

                  

                  

                          

                                       

               

                 

      

                                                  

  

                                                  

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  RECURSION  RECURSION

GUIDE FOR SCHOOL

Study Guide For St Stude udent nts Programs Related to Numbers  ------------------------ -------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------       

  

  

  

   

                

                              

                              

                    

                      

                                           

      

                                                                      

  

                                                             

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GUIDE FOR SCHOOL

  RECURSION  RECURSION

Study Guide For St Stude udent nts Programs Related to Numbers  ------------------------ -------------------------------------------------- --------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------

       

    

                         

Assuming that there is an array A[ ] sorted in ascending order, the below function searches for a value and returns ‘1’ if the search is successful, otherwise returns ‘-1’.

                                                                  

                                                                                

     

     

                                         

                                         

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