Given a floor of size MxN size and tiles of size 2×1, the task is to find the maximum number of tiles required to cover the floor as much as possible of size MxN size.
Note: A tile can either be placed horizontally or vertically and no two tiles should overlap.
Examples:
Input: M = 2, N = 4
Output: 4
Explanation:
4 tiles are needed to cover the floor.Input: M = 3, N = 3
Output: 4
Explanation:
4 tiles are needed to cover the floor.
Approach:
- If N is even, then the task is to place m rows of (N/2) number of tiles to cover the whole floor.
- Else if N is odd, then cover M rows till N – 1 (even) columns in the same way as discussed in the above point and put (M/2) number of tiles in the last column. If both M and N are odd, then one cell of the floor remains uncovered.
- Therefore, the maximum number of tiles is floor((M * N) / 2).
Below is the implementation of the above approach:
C++
// C++ program for the above approach#include <bits/stdc++.h>using namespace std;// Function to find the maximum number// of tiles required to cover the floor// of size m x n using 2 x 1 size tilesvoid maximumTiles(int n, int m){ // Print the answer cout << (m * n) / 2 << endl;}// Driver Codeint main(){ // Given M and N int M = 3; int N = 4; // Function Call maximumTiles(N, M); return 0;} |
Java
// Java program for the above approach import java.util.*;class GFG{// Function to find the maximum number// of tiles required to cover the floor// of size m x n using 2 x 1 size tilesstatic void maximumTiles(int n, int m){ // Print the answer System.out.println((m * n) / 2);}// Driver codepublic static void main (String[] args){ // Given M and N int M = 3; int N = 4; // Function call maximumTiles(N, M);}}// This code is contributed by offbeat |
Python3
# Python3 program for the above approach # Function to find the maximum number# of tiles required to cover the floor# of size m x n using 2 x 1 size tilesdef maximumTiles(n, m): # Print the answer print(int((m * n) / 2));# Driver codeif __name__ == '__main__': # Given M and N M = 3; N = 4; # Function call maximumTiles(N, M);# This code is contributed by sapnasingh4991 |
C#
// C# program for the above approach using System;class GFG{// Function to find the maximum number// of tiles required to cover the floor// of size m x n using 2 x 1 size tilesstatic void maximumTiles(int n, int m){ // Print the answer Console.WriteLine((m * n) / 2);}// Driver codepublic static void Main(String[] args){ // Given M and N int M = 3; int N = 4; // Function call maximumTiles(N, M);}}// This code is contributed by amal kumar choubey |
Javascript
<script>// JavaScript program for the above approach// Function to find the maximum number// of tiles required to cover the floor// of size m x n using 2 x 1 size tilesfunction maximumTiles(n, m){ // Print the answer document.write((m * n) / 2);} // Driver Code // Given M and N let M = 3; let N = 4; // Function call maximumTiles(N, M); </script> |
Output:
6
Time Complexity: O(1)
Auxiliary Space: O(1)
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