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Minimum number of flips required such that the last cell of matrix can be reached from any other cell

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  • Difficulty Level : Easy
  • Last Updated : 28 May, 2022

Given a matrix arr[][] of dimensions N * M where each cell consists of characters ‘R’ or ‘D’ except the cell arr[N][M] which contains ‘F’. ‘R’ and ‘D’ denotes that the player can move in the right and down direction respectively from the current cell. The task is to find the minimum number of characters required to be flipped from ‘R’ to ‘D’ or ‘D’ to ‘R’ such that it is possible to reach the finishing cell i.e., arr[N][M] from every cell.

Examples:

Input: N = 2, M = 3, arr[][] = {{D, D, R}, {R, R, F}}
Output: 1
Explanation: After changing the direction of (1, 3) to ‘D’, each cell can reach the finishing point.

Input: N = 1, M = 3, arr[1][3] = {{D, D, F}}
Output: 2

Approach: The problem can be solved by observing that each cell can reach the finishing point after changing the following cells:

  • Change all the ‘D’s to ‘R’ in the last row.
  • Change all the ‘R’ to ‘D’ in the last column.

Follow the steps below to solve the problem:

  1. Initialize a variable, say ans, to store the minimum number of flips.
  2. Traverse from i = 0 to N – 1 and count the number of cells arr[i][M-1] which contains ‘R’.
  3. Traverse from i = 0 to M – 1 and count the number of cells arr[N – 1][i] which contains ‘D’.
  4. Print the sum of the two counts obtained in the above step as the required answer.

Below is the implementation of the above approach:

C++




// C++ program for the above approach
 
#include <bits/stdc++.h>
using namespace std;
 
// Function to calculate the minimum
// number of flips required
int countChanges(vector<vector<char> > mat)
{
    // Dimensions of mat[][]
    int n = mat.size();
    int m = mat[0].size();
 
    // Initialize answer
    int ans = 0;
 
    // Count all 'D's in the last row
    for (int j = 0; j < m - 1; j++) {
        if (mat[n - 1][j] != 'R')
            ans++;
    }
 
    // Count all 'R's in the last column
    for (int i = 0; i < n - 1; i++) {
        if (mat[i][m - 1] != 'D')
            ans++;
    }
 
    // Print answer
    return ans;
}
 
// Driver Code
int main()
{
    // Given matrix
    vector<vector<char> > arr = { { 'R', 'R', 'R', 'D' },
                                  { 'D', 'D', 'D', 'R' },
                                  { 'R', 'D', 'R', 'F' } };
 
    // Function call
    int cnt = countChanges(arr);
 
    // Print answer
    cout << cnt << endl;
 
    return 0;
}

Java




// Java program for the above approach
import java.io.*;
 
class GFG{
     
// Function to calculate the minimum
// number of flips required    
public static int countChanges(char mat[][])
{
     
    // Dimensions of mat[][]
    int n = mat.length;
    int m = mat[0].length;
 
    // Initialize answer
    int ans = 0;
 
    // Count all 'D's in the last row
    for(int j = 0; j < m - 1; j++)
    {
        if (mat[n - 1][j] != 'R')
            ans++;
    }
 
    // Count all 'R's in the last column
    for(int i = 0; i < n - 1; i++)
    {
        if (mat[i][m - 1] != 'D')
            ans++;
    }
     
    // Print answer
    return ans;
}
 
// Driver Code
public static void main(String[] args)
{
    char arr[][] = { { 'R', 'R', 'R', 'D' },
                     { 'D', 'D', 'D', 'R' },
                     { 'R', 'D', 'R', 'F' } };
 
    // Function call
    int cnt = countChanges(arr);
 
    // Print answer
    System.out.println(cnt);
}
}
 
// This code is contributed by Manu Pathria

Python3




# Python3 program for the above approach
  
# Function to calculate the minimum
# number of flips required
def countChanges(mat):
     
    # Dimensions of mat[][]
    n = len(mat)
    m = len(mat[0])
  
    # Initialize answer
    ans = 0
  
    # Count all 'D's in the last row
    for j in range(m - 1):
        if (mat[n - 1][j] != 'R'):
            ans += 1
             
    # Count all 'R's in the last column
    for i in range(n - 1):
        if (mat[i][m - 1] != 'D'):
            ans += 1
 
    # Print answer
    return ans
 
# Driver Code
 
# Given matrix
arr = [ [ 'R', 'R', 'R', 'D' ] ,
        [ 'D', 'D', 'D', 'R' ],
        [ 'R', 'D', 'R', 'F' ] ]
  
# Function call
cnt = countChanges(arr)
  
# Print answer   
print(cnt)
 
# This code is contributed by susmitakundugoaldanga

C#




// C# program for the above approach
using System;
 
class GFG{
     
// Function to calculate the minimum
// number of flips required    
public static int countChanges(char [,]mat)
{
     
    // Dimensions of [,]mat
    int n = mat.GetLength(0);
    int m = mat.GetLength(1);
     
    // Initialize answer
    int ans = 0;
     
    // Count all 'D's in the last row
    for(int j = 0; j < m - 1; j++)
    {
        if (mat[n - 1,j] != 'R')
            ans++;
    }
 
    // Count all 'R's in the last column
    for(int i = 0; i < n - 1; i++)
    {
        if (mat[i,m - 1] != 'D')
            ans++;
    }
     
    // Print answer
    return ans;
}
 
// Driver Code
public static void Main(String[] args)
{
    char [,]arr = { { 'R', 'R', 'R', 'D' },
                    { 'D', 'D', 'D', 'R' },
                    { 'R', 'D', 'R', 'F' } };
 
    // Function call
    int cnt = countChanges(arr);
 
    // Print answer
    Console.WriteLine(cnt);
}
}
 
// This code is contributed by Princi Singh

Javascript




<script>
 
// Javascript program for the above approach
 
// Function to calculate the minimum
// number of flips required   
function countChanges(mat)
{
     
    // Dimensions of mat[][]
    let n = mat.length;
    let m = mat[0].length;
  
    // Initialize answer
    let ans = 0;
  
    // Count all 'D's in the last row
    for(let j = 0; j < m - 1; j++)
    {
        if (mat[n - 1][j] != 'R')
            ans++;
    }
  
    // Count all 'R's in the last column
    for(let i = 0; i < n - 1; i++)
    {
        if (mat[i][m - 1] != 'D')
            ans++;
    }
      
    // Print let answer
    return ans;
}
 
// Driver code
let arr = [ [ 'R', 'R', 'R', 'D' ],
            [ 'D', 'D', 'D', 'R' ],
            [ 'R', 'D', 'R', 'F' ] ];
 
// Function call
let cnt = countChanges(arr);
 
// Print let answer
document.write(cnt);
 
// This code is contributed by code_hunt
  
</script>

Output: 

2

 

Time Complexity: O(N+M), where N and M are matrix dimensions.
Auxiliary Space: O(1) , since there is no extra space involved.


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