Count the number of ways to tile the floor of size n x m using 1 x m size tiles in C++

Given two numbers n and m representing the length and breadth of the floor of a room. The goal is to count the number of ways in which this floor can be tiled using the tiles of size 1Xm.

For Example

Input

n=3 m=2

Output

Count the number of ways to tile the floor of size n x m using 1 x m size tiles
are: 3

Explanation

The ways will be three 1x2 tiles arranged as shown below −

Input

n=3 m=3

Output

Count the number of ways to tile the floor of size n x m using 1 x m size tiles
are: 2

Explanation

The ways will be three 1x3 tiles arranged vertically and horizontally. Only
two ways.

Approach used in the below program is as follows −

In this approach we check the value of n. If n is less than m and has value 1 then there will be only one tile to be placed all over the floor of size 1Xm.

If n is equal to m then there will be 2 ways, placing n 1xm tiles all vertically and all horizontally. If n is greater than m then we will calculate ways using previous ways − ways[n−1]+ways[m−1].

• Take integers m and n for the dimensions of the floor and tiles.

• Function ways_tile_floor(int N, int M) takes the dimensions and returns the number of ways to tile the floor of size n x m using 1 x m size tiles.

• Take an array arr[ ] of length N+1 to store count of tiles for index i=current value of N.

• For arr[0] tiles will be 0. So arr[0]=0.

• Traverse arr[] using for loop from i=1 to i=N. For each arr[i], if i>M then calculate count using previous values. arr[i]=arr[i − 1] + arr[i − M].

• In case i=1 and or i<M, set arr[i] with 1.

• In case i=M, set arr[i]=2.

• At the end of the for loop, arr[N] will have a count of ways of arranging tiles.

• Return arr[N] as result.

Example

 Live Demo

#include <bits/stdc++.h>
using namespace std;
int ways_tile_floor(int N, int M){
   int arr[N + 1];
   arr[0] = 0;
   for (int i = 1; i <= N; i++){
      if (i > M){
         arr[i] = arr[i − 1] + arr[i − M];
      }
      else if (i < M || i == 1){
         arr[i] = 1;
      } else {
         arr[i] = 2;
      }
   }
   return arr[N];
}
int main(){
   int n = 3, m = 2;
   cout<<"Count the number of ways to tile the floor of size n x m using 1 x m size tiles are: "<<ways_tile_floor(n, m);
   return 0;
}

Output

If we run the above code it will generate the following output −

Count the number of ways to tile the floor of size n x m using 1 x m size tiles are: 3