Find minimum possible values of A, B and C when two of the (A + B), (A + C) and (B + C) are given

Given two integers X and Y. X and Y represent any two values among (A + B), (A + C) and (B + C). The task is to find A, B and C such that A + B + C is minimum possible.

Examples:

Input: X = 3, Y = 4
Output: 2 1 2
A = 2, B = 1, C = 2.
Then A + B = 3 and A + C = 4.
A + B + C = 5 which is minimum possible.

Input: X = 123, Y = 13
Output: 1 12 111

Approach: Let X = A + B and Y = B + C. If X > Y let’s swap them. Note that A + B + C = A + B + (Y – B) = A + Y. That’s why it’s optimal to minimize the value of A. So the value of A can always be 1. Then B = X – A and C = Y – B.

Below is the implementation of the above approach:

C++

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// C++ implementation of the approach
#include <bits/stdc++.h>
using namespace std;
  
// Function to find A, B and C
void MinimumValue(int x, int y)
{
  
    // Keep minimum number in x
    if (x > y)
        swap(x, y);
  
    // Find the numbers
    int a = 1;
    int b = x - 1;
    int c = y - b;
  
    cout << a << " " << b << " " << c;
}
  
// Driver code
int main()
{
    int x = 123, y = 13;
  
    // Function call
    MinimumValue(x, y);
  
    return 0;
}

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Java

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// Java implementation of the approach
import java.io.*;
  
class GFG 
{
  
// Function to find A, B and C
static void MinimumValue(int x, int y)
{
  
    // Keep minimum number in x
    if (x > y)
    {
        int temp = x;
            x = y;
            y = temp;
    }
  
    // Find the numbers
    int a = 1;
    int b = x - 1;
    int c = y - b;
  
    System.out.print( a + " " + b + " " + c);
}
  
// Driver code
public static void main (String[] args) 
{
    int x = 123, y = 13;
  
    // Function call
    MinimumValue(x, y);
}
}
  
// This code is contributed by anuj_67..

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Python3

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# Python3 implementation of the approach
  
# Function to find A, B and C
def MinimumValue(x, y):
  
    # Keep minimum number in x
    if (x > y):
        x, y = y, x
  
    # Find the numbers
    a = 1
    b = x - 1
    c = y - b
  
    print(a, b, c)
  
# Driver code
x = 123
y = 13
  
# Function call
MinimumValue(x, y)
  
# This code is contributed by Mohit Kumar

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C#

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// C# implementation of the approach
using System;
  
class GFG 
{
  
// Function to find A, B and C
static void MinimumValue(int x, int y)
{
  
    // Keep minimum number in x
    if (x > y)
    {
        int temp = x;
            x = y;
            y = temp;
    }
  
    // Find the numbers
    int a = 1;
    int b = x - 1;
    int c = y - b;
  
    Console.WriteLine( a + " " + b + " " + c);
}
  
// Driver code
public static void Main () 
{
    int x = 123, y = 13;
  
    // Function call
    MinimumValue(x, y);
}
}
  
// This code is contributed by anuj_67..

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Output:

1 12 111


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Improved By : mohit kumar 29, vt_m