Arithmetic Progression containing X and Y with least possible first term | C ++ program for the approach ; Function that finds the minimum positive first term including X with given common difference and the number of terms ; Stores the first term ; Initialize the low and high ; Perform binary search ; Find the mid ; Check if first term is greater than 0 ; Store the possible first term ; Search between mid + 1 to high ; Search between low to mid - 1 ; Return the minimum first term ; Function that finds the Arithmetic Progression with minimum possible first term containing X and Y ; Considering X to be smaller than Y always ; Stores the max common difference ; Stores the minimum first term and the corresponding common difference of the resultant AP ; Iterate over all the common difference ; Check if X and Y is included for current common difference ; Store the possible common difference ; Number of terms from X to Y with diff1 common difference ; Number of terms from X to Y with diff2 common difference ; Find the corresponding first terms with diff1 and diff2 ; Store the minimum first term and the corresponding common difference ; Print the resultant AP ; Driver Code ; Given length of AP and the two terms ; Function Call
#include <bits/stdc++.h> NEW_LINE using namespace std ; int minFirstTerm ( int X , int diff , int N ) { int first_term ; int low = 0 , high = N ; while ( low <= high ) { int mid = ( low + high ) / 2 ; if ( X - mid * diff > 0 ) { first_term = X - mid * diff ; low = mid + 1 ; } else high = mid - 1 ; } return first_term ; } void printAP ( int N , int X , int Y ) { if ( X > Y ) swap ( X , Y ) ; int maxDiff = Y - X ; int first_term = INT_MAX , diff ; for ( int i = 1 ; i * i <= maxDiff ; i ++ ) { if ( maxDiff % i == 0 ) { int diff1 = i ; int diff2 = maxDiff / diff1 ; int terms1 = diff2 + 1 ; int terms2 = diff1 + 1 ; int first_term1 = minFirstTerm ( X , diff1 , N - terms1 ) ; int first_term2 = minFirstTerm ( X , diff2 , N - terms2 ) ; if ( first_term1 < first_term ) { first_term = first_term1 ; diff = diff1 ; } if ( first_term2 < first_term ) { first_term = first_term2 ; diff = diff2 ; } } } for ( int i = 0 ; i < N ; i ++ ) { cout << first_term << " ▁ " ; first_term += diff ; } } int main ( ) { int N = 5 , X = 10 , Y = 15 ; printAP ( N , X , Y ) ; return 0 ; }