# Area of plot remaining at the end

Given two integers N and M that represent the length and breadth of a rectangular plot and another integer K that represent the number of persons. Each person will divide the plot into two parts such that it will be the largest possible square from the plot and will leave the second part for others, it continues until the plot is over or every person gets the plot. Now, The task is to determine the area of the plot left in the end.
Examples:

Input: N = 5, M = 3, K = 2
Output:
1st person divides the 5×3 plot into 2 parts i.e 3×3 and 2×3
and will get the plot having dimension 3×3. The other person divides the 2×3 plot again into
two parts i.e 2×2 and 1×2 and will get the plot having dimension 2×2. Now, the remaining
part of plot is having dimension 1×2 and area as 2 units.
Input: N = 4, M = 8, K = 4
Output:

Approach:

1. If Length is greater than breadth then subtract breadth from length.
2. If breadth is greater than length then subtract length from breadth.
3. Repeat the above steps for all the persons while there area of the remaining plot is greater than 0.
4. Print the area of the remaining plot in the end i.e. length * breadth.

Below is the implementation of the above approach:

## C++

 `// C++ implementation of the approach` `#include ` `using` `namespace` `std;`   `// Function to return the area` `// of the remaining plot` `int` `remainingArea(``int` `N, ``int` `M, ``int` `K)` `{`   `    ``// Continue while plot has positive area` `    ``// and there are persons left` `    ``while` `(K-- && N && M) {`   `        ``// If length > breadth` `        ``// then subtract breadth from length` `        ``if` `(N > M)` `            ``N = N - M;`   `        ``// Else subtract length from breadth` `        ``else` `            ``M = M - N;` `    ``}`   `    ``if` `(N > 0 && M > 0)` `        ``return` `N * M;` `    ``else` `        ``return` `0;` `}`   `// Driver code` `int` `main()` `{` `    ``int` `N = 5, M = 3, K = 2;`   `    ``cout << remainingArea(N, M, K);`   `    ``return` `0;` `}`

## Java

 `// Java implementation of the approach` `class` `GFG {`   `    ``// Function to return the area` `    ``// of the remaining plot` `    ``static` `int` `remainingArea(``int` `N, ``int` `M, ``int` `K)` `    ``{`   `        ``// Continue while plot has positive area` `        ``// and there are persons left` `        ``while` `(K-- > ``0` `&& N > ``0` `&& M > ``0``) {`   `            ``// If length > breadth` `            ``// then subtract breadth from length` `            ``if` `(N > M)` `                ``N = N - M;`   `            ``// Else subtract length from breadth` `            ``else` `                ``M = M - N;` `        ``}`   `        ``if` `(N > ``0` `&& M > ``0``)` `            ``return` `N * M;` `        ``else` `            ``return` `0``;` `    ``}`   `    ``// Driver code` `    ``public` `static` `void` `main(String[] args)` `    ``{` `        ``int` `N = ``5``, M = ``3``, K = ``2``;`   `        ``System.out.println(remainingArea(N, M, K));` `    ``}` `}`   `/* This code contributed by PrinciRaj1992 */`

## Python3

 `# Python3 implementation of the approach `   `# Function to return the area ` `# of the remaining plot ` `def` `remainingArea(N, M, K):`   `    ``# Continue while plot has positive area ` `    ``# and there are persons left ` `    ``while` `(K > ``0` `and` `N > ``0` `and` `M > ``0``):`   `        ``# If length > breadth ` `        ``# then subtract breadth from length ` `        ``if` `(N > M): ` `            ``N ``=` `N ``-` `M; `   `        ``# Else subtract length from breadth ` `        ``else``:` `            ``M ``=` `M ``-` `N; ` `        ``K ``=` `K ``-` `1``;` `    ``if` `(N > ``0` `and` `M > ``0``): ` `        ``return` `N ``*` `M; ` `    ``else``:` `        ``return` `0``; `   `# Driver code ` `N ``=` `5``;` `M ``=` `3``;` `K ``=` `2``; `   `print``(remainingArea(N, M, K)); `   `# This code contributed by Rajput-Ji`

## C#

 `// C# implementation of the approach` `using` `System;`   `class` `GFG {`   `    ``// Function to return the area` `    ``// of the remaining plot` `    ``static` `int` `remainingArea(``int` `N, ``int` `M, ``int` `K)` `    ``{`   `        ``// Continue while plot has positive area` `        ``// and there are persons left` `        ``while` `(K-- > 0 && N > 0 && M > 0) {`   `            ``// If length > breadth` `            ``// then subtract breadth from length` `            ``if` `(N > M)` `                ``N = N - M;`   `            ``// Else subtract length from breadth` `            ``else` `                ``M = M - N;` `        ``}`   `        ``if` `(N > 0 && M > 0)` `            ``return` `N * M;` `        ``else` `            ``return` `0;` `    ``}`   `    ``// Driver code` `    ``static` `public` `void` `Main()` `    ``{` `        ``int` `N = 5, M = 3, K = 2;`   `        ``Console.WriteLine(remainingArea(N, M, K));` `    ``}` `}`   `/* This code contributed by ajit */`

## PHP

 ` breadth ` `        ``// then subtract breadth from length ` `        ``if` `(``\$N` `> ``\$M``) ` `            ``\$N` `= ``\$N` `- ``\$M``; `   `        ``// Else subtract length from breadth ` `        ``else` `            ``\$M` `= ``\$M` `- ``\$N``; ` `    ``} `   `    ``if` `(``\$N` `> 0 && ``\$M` `> 0) ` `        ``return` `\$N` `* ``\$M``; ` `    ``else` `        ``return` `0; ` `} `   `// Driver code ` `\$N` `= 5;` `\$M` `= 3;` `\$K` `= 2; `   `echo` `remainingArea(``\$N``, ``\$M``, ``\$K``); `   `// This code is contributed by AnkitRai01`   `?>`

## Javascript

 ``

Output:

`2`

Time Complexity: O(K)

Auxiliary Space: O(1)

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