Given two integers M and N, the task is to find the minimum number of tiles of size 2 * 1 that can be placed on an M * N grid such that the following conditions are satisfied:
- Each tile must completely cover 2 squares of the board.
- No pair of tiles may overlap.
- Each tile lies must be placed entirely inside the board. It is allowed to touch the edges of the board.
If it is not possible to cover the entire board, print -1
Input: N = 2, M = 4
Output: 4
Explanation: 4 tiles of dimension 2 * 1. Place each tile in one column.Input: N = 3, M = 3
Output: -1
Approach: Follow the steps below to solve the problem
- If N is even, (N / 2) * M tiles can be placed to cover the entire board.
- If N is odd, tiles of 2 * 1 tiles, since the length is odd which can not be expressed as a multiple of 2
Below is the implementation of the above approach:
C++
// C++ Program to implement// the above approach#include <bits/stdc++.h>using namespace std;// Function to count tiles of dimensions// 2 x 1 that can be placed in a grid of// dimensions M * N as per given conditionsint numberOfTiles(int N, int M){ if (N % 2 == 1) { return -1; } // Number of tiles required return (N * 1LL * M) / 2;}// Driver Codeint main(){ int N = 2, M = 4; cout << numberOfTiles(N, M); return 0;} |
Java
// Java Program to implement// the above approachimport java.io.*;class GFG { // Function to count tiles of dimensions // 2 x 1 that can be placed in a grid of // dimensions M * N as per given conditions static int numberOfTiles(int n, int m) { if (n % 2 == 1) { return -1; } // Number of tiles required return (m * n) / 2; } // Driver Code public static void main(String[] args) { int n = 2, m = 4; System.out.println( numberOfTiles(n, m)); }} |
Python
# Python Program to implement# the above approach# Function to count tiles of dimensions# 2 x 1 that can be placed in a grid of# dimensions M * N as per given conditionsdef numberOfTiles(N, M): if (N % 2 == 1): return -1 # Number of tiles required return (N * M) // 2# Driver CodeN = 2M = 4print(numberOfTiles(N, M))# This code is contributed by shubhamsingh10 |
C#
// C# Program to implement// the above approachusing System;public class GFG { // Function to tiles of size 2 x 1 // find the number of tiles that can // be placed as per the given conditions static int numberOfTiles(int n, int m) { if (n % 2 == 1) { return -1; } // Number of tiles required return (m * n) / 2; } // Driver Code static public void Main() { int n = 2, m = 4; Console.WriteLine( numberOfTiles(n, m)); }} |
Javascript
<script>// Javascript Program to implement// the above approach// Function to count tiles of dimensions// 2 x 1 that can be placed in a grid of// dimensions M * N as per given conditionsfunction numberOfTiles(n, m){ if (n % 2 == 1) { return -1; } // Number of tiles required return (m * n) / 2;}// Driver Codevar n = 2, m = 4;document.write(numberOfTiles(n, m));// This code is contributed by kirti</script> |
Output:
4
Time Complexity: O(1)
Auxiliary Space: O(1)
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