Given three positive integers X, Y, and N, such that Y < X, the task is to find the largest number from the range [0, N] whose modulus with X is equal to Y modulo X.
Examples:
Input: X = 10, Y = 5, N = 15
Output: 15
Explanation:
The value of 15 % 10 (= 5) and 5 % 10 (= 5) are equal.
Therefore, the required output is 15.Input: X = 5, Y = 0, N = 4
Output: 0
Approach: The given problem can be solved based on the following observations:
- Since Y is less than X, then Y % X must be Y. Therefore, the idea is to find the maximum value from the range [0, N] whose modulus with X is Y.
- Assume the maximum number, say num = N, to get the remainder modulo with X as Y.
- Subtract N with the remainder of N % X to get the remainder as 0, and then add Y to it. Then, the remainder of that number with X will be Y.
- Check if the number is less than N. If found to be true, then set num =  (N – N % X + Y).
- Otherwise, again subtract the number with the value of X, i.e., num = (N – N % X – (X – Y)), to get the maximum value from the interval [0, N].
- Mathematically:
- If (N – N % X + Y) ? N, then set num = (N – N % X + Y).
- Otherwise, update num = (N – N % X – (X – Y)).
Follow the steps below to solve the problem:
- Initialize a variable, say num, to store the maximum number that has the remainder Y % X from the range [0, N].
- If (N – N % X + Y) ? N, then update num = (N – N % X + Y).
- Otherwise, update num = (N – N % X – (X – Y)).
- After completing the above steps, print the value of num as the result.
Below is the implementation of the above approach:
C++
// C++ program for the above approach#include <bits/stdc++.h>using namespace std;Â
// Function to print the largest// number upto N whose modulus// with X is same as Y % Xlong long maximumNum(long long X,                     long long Y,                     long long N){    // Stores the required number    long long num = 0;Â
    // Update num as the result    if (N - N % X + Y <= N) {Â
        num = N - N % X + Y;    }    else {        num = N - N % X - (X - Y);    }Â
    // Return the resultant number    return num;}Â
// Driver Codeint main(){Â Â Â Â long long X = 10;Â Â Â Â long long Y = 5;Â Â Â Â long long N = 15;Â
    cout << maximumNum(X, Y, N);Â
    return 0;} |
Java
// Java program for the above approachimport java.io.*;import java.lang.*;import java.util.*;Â
class GFG {Â
  // Function to print the largest  // number upto N whose modulus  // with X is same as Y % X  static long maximumNum(long X, long Y, long N)  {         // Stores the required number    long num = 0;Â
    // Update num as the result    if (N - N % X + Y <= N)     {      num = N - N % X + Y;    }    else    {      num = N - N % X - (X - Y);    }Â
    // Return the resultant number    return num;  }Â
  // Driver Code  public static void main(String[] args)  {Â
    long X = 10;    long Y = 5;    long N = 15;Â
    System.out.println(maximumNum(X, Y, N));  }}Â
// This code is contributed by Kingash. |
Python3
# Python3 program for the above approachÂ
# Function to print the largest# number upto N whose modulus# with X is same as Y % Xdef maximumNum(X, Y, N):       # Stores the required number    num = 0Â
    # Update num as the result    if (N - N % X + Y <= N):        num = N - N % X + Y    else:        num = N - N % X - (X - Y)Â
    # Return the resultant number    return numÂ
# Driver Codeif __name__ == '__main__':Â Â Â Â X = 10Â Â Â Â Y = 5Â Â Â Â N = 15Â
    print (maximumNum(X, Y, N))Â
# This code is contributed by mohit kumar 29. |
C#
// C# program for the above approachusing System;class GFG {Â
  // Function to print the largest  // number upto N whose modulus  // with X is same as Y % X  static long maximumNum(long X, long Y, long N)  {Â
    // Stores the required number    long num = 0;Â
    // Update num as the result    if (N - N % X + Y <= N) {      num = N - N % X + Y;    }    else {      num = N - N % X - (X - Y);    }Â
    // Return the resultant number    return num;  }Â
  // Driver Code  public static void Main(string[] args)  {Â
    long X = 10;    long Y = 5;    long N = 15;Â
    Console.WriteLine(maximumNum(X, Y, N));  }}Â
// This code is contributed by ukasp. |
Javascript
<script>Â
// Javascript program for the above approachÂ
// Function to print the largest// number upto N whose modulus// with X is same as Y % Xfunction maximumNum(X, Y, N){Â
    // Stores the required number    let num = 0;         // Update num as the result    if (N - N % X + Y <= N)     {        num = N - N % X + Y;    }    else    {        num = N - N % X - (X - Y);    }         // Return the resultant number    return num;}Â
// Driver codelet X = 10;let Y = 5;let N = 15;Â
document.write(maximumNum(X, Y, N));Â
// This code is contributed by target_2Â Â
</script> |
Output:Â
15
Â
Time Complexity: O(1)
Auxiliary Space: O(1)
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