# Find number formed by K times alternatively reducing X and adding Y to 0

• Last Updated : 06 Sep, 2021

Given three positive integers K, X, and Y, the task is to find the number formed by alternatively subtracting X and adding Y to 0 total K number of times.

Examples:

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Input: X = 2, Y = 5, K = 3
Output: 1
Explanation:
Following are the operations perform K(= 3) number of times on 0:
Operation 1: Reduce the value 0 by X(= 2) modifies it to 0 – 2 = 2.
Operation 2: Increment the value -2 by Y(= 5) modifies it to -2 + 5 = 3.
Operation 3: Reduce the value 3 by X(= 2) modifies it to 3 – 2 = 1.
The value obtained after modifying the value is 1.

Input: X = 1, Y = 100, K = 4
Output: 198

Naive Approach: The given problem can be solved by performing the given operations K number of times and print the result obtained.

Time Complexity: O(K)
Auxiliary Space: O(1)

Efficient Approach: The above approach can also be optimized by finding the total value that is decremented(using the value of X) and incremented(using the value of Y) in K number of moves and then print the sum of these values as the result.

The value that must be added to the result is calculated by:

where, K/2 number of times addition operation is performed.

The value that must be subtracted to the result is calculated by:

where, K/2 number of times subtraction operation is performed if the number of operation is odd, then additional subtraction is performed.

Below is the implementation of the above approach:

## C++

 `// C++ program for the above approach``#include ``using` `namespace` `std;` `// Function to find the value obtained``// after alternatively reducing X and``// adding Y to 0 total K number of times``int` `positionAfterKJumps(``int` `X, ``int` `Y, ``int` `K)``{``    ``// Stores the final result after``    ``// adding only Y to 0``    ``int` `addY = Y * (K / 2);` `    ``// Stores the final number after``    ``// reducing only X from 0``    ``int` `reduceX = -1 * X * (K / 2 + K % 2);` `    ``// Return the result obtained``    ``return` `addY + reduceX;``}` `// Driver Code``int` `main()``{``    ``int` `X = 2, Y = 5, K = 3;``    ``cout << positionAfterKJumps(X, Y, K);` `    ``return` `0;``}`

## Java

 `// Java program for the above approach``import` `java.util.*;` `class` `GFG {` `    ``// Function to find the value obtained``    ``// after alternatively reducing X and``    ``// adding Y to 0 total K number of times``    ``static` `int` `positionAfterKJumps(``int` `X, ``int` `Y, ``int` `K)``    ``{``      ` `        ``// Stores the final result after``        ``// adding only Y to 0``        ``int` `addY = Y * (K / ``2``);` `        ``// Stores the final number after``        ``// reducing only X from 0``        ``int` `reduceX = -``1` `* X * (K / ``2` `+ K % ``2``);` `        ``// Return the result obtained``        ``return` `addY + reduceX;``    ``}` `    ``// Driver Code``    ``public` `static` `void` `main(String[] args) {``        ` `        ``int` `X = ``2``, Y = ``5``, K = ``3``;``        ``System.out.print(positionAfterKJumps(X, Y, K));``    ``}``}` `// This code is contributed by code_hunt.`

## Python3

 `# Python program for the above approach` `# Function to find the value obtained``# after alternatively reducing X and``# adding Y to 0 total K number of times``def` `positionAfterKJumps(X, Y, K):``  ` `    ``# Stores the final result after``    ``# adding only Y to 0``    ``addY ``=` `Y ``*` `(K ``/``/` `2``)` `    ``# Stores the final number after``    ``# reducing only X from 0``    ``reduceX ``=` `-``1` `*` `X ``*` `(K ``/``/` `2` `+` `K ``%` `2``)` `   ``# Return the result obtained``    ``return` `addY ``+` `reduceX` `# Driver Code``X ``=` `2``Y ``=` `5``K ``=` `3``print``(positionAfterKJumps(X, Y, K))` `# This code is contributed by subhammahato348.`

## C#

 `// C# program for the above approach``using` `System;``class` `GFG {` `    ``// Function to find the value obtained``    ``// after alternatively reducing X and``    ``// adding Y to 0 total K number of times``    ``static` `int` `positionAfterKJumps(``int` `X, ``int` `Y, ``int` `K)``    ``{``      ` `        ``// Stores the final result after``        ``// adding only Y to 0``        ``int` `addY = Y * (K / 2);` `        ``// Stores the final number after``        ``// reducing only X from 0``        ``int` `reduceX = -1 * X * (K / 2 + K % 2);` `        ``// Return the result obtained``        ``return` `addY + reduceX;``    ``}` `    ``// Driver Code``    ``public` `static` `void` `Main(String[] args)``    ``{``        ``int` `X = 2, Y = 5, K = 3;``        ``Console.WriteLine(positionAfterKJumps(X, Y, K));``    ``}``}` `// This code is contributed by ukasp.`

## Javascript

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Output:
`1`

Time Complexity: O(1)
Auxiliary Space: O(1)

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