Given five integers X, Y, A, B, and N, the task is to find the maximum possible absolute difference between X and Y by performing the following operations exactly N times:
- Decrement the value of X by 1 up to A.
- Decrement the value of Y by 1 up to B.
Note: The value of (X – A + Y – B) must be greater than or equal to N
Examples:
Input: X = 12, Y = 8, A = 8, B = 7, N = 2Â
Output: 4Â
Explanation:Â
Decrementing the value of X by 1. Therefore, X = X – 1 = 11Â
Decrementing the value of Y by 1. Therefore, Y = Y – 1 = 7Â
Therefore, the maximum absolute difference between X and Y = abs(X – Y) = abs(11 – 7) = 4Input: X = 10, Y = 10, A = 8, B = 5, N = 3Â
Output: 3Â
Explanation:Â
Decrementing the value of Y by 1 three times. Therefore, Y = Y – 3 = 7Â
Therefore, the maximum absolute difference between X and Y = abs(X – Y) = abs(10 – 7) = 3
Approach: The problem can be solved using the Greedy technique. Follow the steps below to solve the problem:
- Initialize a variable, say n1 to store the maximum count of operations performed on X.
- Update n1 = min(N, X – A).
- Initialize a variable, say n2 to store the maximum count of operations performed on Y.
- Update n2 = min(N, Y – B).
- Initialize a variable say, diff_X_Y_1 to store the absolute difference of X and Y by first decrementing the value of X by 1 exactly min(N, n1) times then decrement the value of Y by the remaining times of operations.
- Initialize a variable say, diff_X_Y_2 to store the absolute difference of X and Y by first decrementing the value of Y by 1 exactly min(N, n2) times then decrement the value of X by the remaining times of operations.
- Finally, print the value of max(diff_X_Y_1, diff_X_Y_2).
Below is the implementation of the above approach :
C++
// C++ program to implement// the above approachÂ
#include <bits/stdc++.h>using namespace std;Â
// Function to find the absolute difference// between X and Y with given operationsint AbsDiff(int X, int Y, int A, int B, int N){    // Stores maximum absolute difference    // between X and Y with given operations    int maxDiff = 0;Â
    // Stores maximum number of operations    // performed on X    int n1 = X - A;Â
    // Update X    X = X - min(N, n1);Â
    // Decrementing N at most N times    N = N - min(N, n1);Â
    // Stores maximum number of operations    // performed on Y    int n2 = Y - B;Â
    // Update Y    Y = Y - min(N, n2);Â
    // Update maxDiff    maxDiff = abs(X - Y);Â
    return maxDiff;}Â
// Function to find the max absolute difference// between X and Y with given operationsint maxAbsDiff(int X, int Y, int A, int B, int N){    // Stores absolute difference between    // X and Y by first decrementing X and then Y    int diffX_Y_1;Â
    // Stores absolute difference between X    // and Y first decrementing Y and then X    int diffX_Y_2;Â
    // Update diffX_Y_1    diffX_Y_1 = AbsDiff(X, Y, A, B, N);Â
    // Swap X, Y and A, B    swap(X, Y);    swap(A, B);Â
    // Update diffX_Y_2    diffX_Y_2 = AbsDiff(X, Y, A, B, N);Â
    return max(diffX_Y_1, diffX_Y_2);}Â
// Driver Codeint main(){Â Â Â Â int X = 10;Â Â Â Â int Y = 10;Â Â Â Â int A = 8;Â Â Â Â int B = 5;Â Â Â Â int N = 3;Â Â Â Â cout << maxAbsDiff(X, Y, A, B, N);} |
Java
// Java program to implement // the above approach import java.util.*;Â
class GFG{     // Function to find the absolute difference // between X and Y with given operations public static int AbsDiff(int X, int Y, int A,                           int B, int N) {          // Stores maximum absolute difference     // between X and Y with given operations     int maxDiff = 0;        // Stores maximum number of operations     // performed on X     int n1 = X - A;        // Update X     X = X - Math.min(N, n1);        // Decrementing N at most N times     N = N - Math.min(N, n1);        // Stores maximum number of operations     // performed on Y     int n2 = Y - B;        // Update Y     Y = Y - Math.min(N, n2);        // Update maxDiff     maxDiff = Math.abs(X - Y);        return maxDiff; }    // Function to find the max absolute difference // between X and Y with given operations public static int maxAbsDiff(int X, int Y, int A,                              int B, int N) {          // Stores absolute difference between     // X and Y by first decrementing X and then Y     int diffX_Y_1;        // Stores absolute difference between X     // and Y first decrementing Y and then X     int diffX_Y_2;        // Update diffX_Y_1     diffX_Y_1 = AbsDiff(X, Y, A, B, N);        // Swap X, Y and A, B     int temp1 = X;    X = Y;    Y = temp1;         int temp2 = A;    A = B;    B = temp2;       // Update diffX_Y_2     diffX_Y_2 = AbsDiff(X, Y, A, B, N);        return Math.max(diffX_Y_1, diffX_Y_2); }Â
// Driver codepublic static void main(String[] args){Â Â Â Â int X = 10; Â Â Â Â int Y = 10; Â Â Â Â int A = 8; Â Â Â Â int B = 5; Â Â Â Â int N = 3; Â Â Â Â Â Â Â Â Â System.out.println(maxAbsDiff(X, Y, A, B, N));}}Â
// This code is contributed by divyeshrabadiya07 |
Python3
# Python3 program to implement# the above approach  # Function to find the absolute difference# between X and Y with given operationsdef AbsDiff(X, Y, A, B, N):         # Stores maximum absolute difference    # between X and Y with given operations    maxDiff = 0      # Stores maximum number of operations    # performed on X    n1 = X - A      # Update X    X = X - min(N, n1)      # Decrementing N at most N times    N = N - min(N, n1)      # Stores maximum number of operations    # performed on Y    n2 = Y - B      # Update Y    Y = Y - min(N, n2)      # Update maxDiff    maxDiff = abs(X - Y)      return maxDiffÂ
# Function to find the max absolute difference# between X and Y with given operationsdef maxAbsDiff(X, Y, A, B, N):      # Stores absolute difference between    # X and Y by first decrementing X and then Y    diffX_Y_1 = AbsDiff(X, Y, A, B, N)      # Swap X, Y and A, B    temp1 = X    X = Y    Y = temp1      temp2 = A    A = B    B = temp2Â
    # Stores absolute difference between X    # and Y first decrementing Y and then X    diffX_Y_2 = AbsDiff(X, Y, A, B, N)      return max(diffX_Y_1, diffX_Y_2)Â
# Driver CodeX = 10Y = 10A = 8B = 5N = 3Â
print(maxAbsDiff(X, Y, A, B, N))Â
# This code is contributed by sanjoy_62 |
C#
// C# program to implement // the above approach using System;Â
class GFG{     // Function to find the absolute difference // between X and Y with given operations public static int AbsDiff(int X, int Y, int A,                           int B, int N) {          // Stores maximum absolute difference     // between X and Y with given operations     int maxDiff = 0;        // Stores maximum number of operations     // performed on X     int n1 = X - A;        // Update X     X = X - Math.Min(N, n1);        // Decrementing N at most N times     N = N - Math.Min(N, n1);          // Stores maximum number of operations     // performed on Y     int n2 = Y - B;        // Update Y     Y = Y - Math.Min(N, n2);        // Update maxDiff     maxDiff = Math.Abs(X - Y);        return maxDiff; }    // Function to find the max absolute difference // between X and Y with given operations public static int maxAbsDiff(int X, int Y, int A,                              int B, int N) {          // Stores absolute difference between     // X and Y by first decrementing X and then Y     int diffX_Y_1;        // Stores absolute difference between X     // and Y first decrementing Y and then X     int diffX_Y_2;        // Update diffX_Y_1     diffX_Y_1 = AbsDiff(X, Y, A, B, N);          // Swap X, Y and A, B     int temp1 = X;    X = Y;    Y = temp1;         int temp2 = A;    A = B;    B = temp2;       // Update diffX_Y_2     diffX_Y_2 = AbsDiff(X, Y, A, B, N);        return Math.Max(diffX_Y_1, diffX_Y_2); }Â
// Driver codepublic static void Main(String[] args){Â Â Â Â int X = 10; Â Â Â Â int Y = 10; Â Â Â Â int A = 8; Â Â Â Â int B = 5; Â Â Â Â int N = 3; Â Â Â Â Â Â Â Â Â Console.WriteLine(maxAbsDiff(X, Y, A, B, N));}}Â
// This code is contributed by Amit Katiyar |
Javascript
<script>// Javascript program to implement// the above approachÂ
// Function to find the absolute difference// between X and Y with given operationsfunction AbsDiff(X, Y, A, B, N){          // Stores maximum absolute difference    // between X and Y with given operations    let maxDiff = 0;        // Stores maximum number of operations    // performed on X    let n1 = X - A;        // Update X    X = X - Math.min(N, n1);        // Decrementing N at most N times    N = N - Math.min(N, n1);        // Stores maximum number of operations    // performed on Y    let n2 = Y - B;        // Update Y    Y = Y - Math.min(N, n2);        // Update maxDiff    maxDiff = Math.abs(X - Y);        return maxDiff;}    // Function to find the max absolute difference// between X and Y with given operationsfunction maxAbsDiff(X, Y, A, B, N){          // Stores absolute difference between    // X and Y by first decrementing X and then Y    let diffX_Y_1;        // Stores absolute difference between X    // and Y first decrementing Y and then X    let diffX_Y_2;        // Update diffX_Y_1    diffX_Y_1 = AbsDiff(X, Y, A, B, N);        // Swap X, Y and A, B    let temp1 = X;    X = Y;    Y = temp1;          let temp2 = A;    A = B;    B = temp2;        // Update diffX_Y_2    diffX_Y_2 = AbsDiff(X, Y, A, B, N);        return Math.max(diffX_Y_1, diffX_Y_2);}    // Driver Code          let X = 10;    let Y = 10;    let A = 8;    let B = 5;    let N = 3;          document.write(maxAbsDiff(X, Y, A, B, N));      </script> |
Output:Â
3
Â
Time complexity: O(1)
Auxiliary Space:O(1)
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