Total coverage of all zeros in a binary matrix

Given a binary matrix that is, it contains 0s and 1s only, we need to find sum of coverage of all zeros of the matrix where coverage for a particular 0 is defined as total number of ones around a zero in left, right, up and bottom directions. The ones can be anywhere till corner point in a direction. 

Examples:

Input : mat[][] = {0 0 0 0
                   1 0 0 1
                   0 1 1 0
                   0 1 0 0}
Output : 20
First four zeros are surrounded by only 
one 1.  So coverage for zeros in first 
row is 1 + 1 + 1 + 1
Zeros in second row are surrounded by
three 1's. Note that there is no 1 above.
There are 1's in all other three directions.
Coverage of zeros in second row = 3 + 3. 
Similarly counting for others also, we get
overall count as below.
1 + 1 + 1 + 1 + 3 + 3 + 2 + 2 + 2 + 2 + 2 = 20

Input : mat[][] = {1 1 1 0
                   1 0 0 1}
Output : 8
Coverage of first zero is 2
Coverages of other two zeros is 3
Total coverage = 2 + 3 + 3 = 8

A simple solution to solve this problem is by counting ones around zeros independently i.e. we run loop four times in each direction for each cell for the given matrix. Whenever we find a 1 in any loop, we break the loop and increment result by 1.

An efficient solution is to do following. 

1. Traverse all rows from left to right, increment result if a 1 is already seen (in current traversal) and current element is 0.
2. Traverse all rows from right to left, increment result if a 1 is already seen (in current traversal) and current element is 0.
3. Traverse all columns from top to bottom, increment result if a 1 is already seen (in current traversal) and current element is 0.
4. Traverse all columns from bottom to top, increment result if a 1 is already seen (in current traversal) and current element is 0.

In below code a Boolean variable isOne is taken, which is made true as soon as a one is encountered in current traversal, for all zeros after that iteration, result is incremented by one, same procedure is applied in all four directions to get final answer. We reset isOne to false after every traversal.

C++

//  C++ program to get total coverage of all zeros in
// a binary matrix
#include <bits/stdc++.h>
using namespace std;
#define R 4
#define C 4

// Returns total coverage of all zeros in mat[][]
int getTotalCoverageOfMatrix(int mat[R][C])
{
    int res = 0;

    //  looping for all rows of matrix
    for (int i = 0; i < R; i++)
    {
        bool isOne = false;  // 1 is not seen yet

        // looping in columns from left to right
        // direction to get left ones
        for (int j = 0; j < C; j++)
        {
            // If one is found from left
            if (mat[i][j] == 1)
                isOne = true;

            // If 0 is found and we have found
            // a 1 before.
            else if (isOne)
                res++;
        }

        // Repeat the above process for right to
        // left direction.
        isOne = false;
        for (int j = C-1; j >= 0; j--)
        {
            if (mat[i][j] == 1)
                isOne = true;
            else if (isOne)
                res++;
        }
    }

    // Traversing across columns for up and down
    // directions.
    for (int j = 0; j < C; j++)
    {
        bool isOne = false;  // 1 is not seen yet
        for (int i = 0; i < R; i++)
        {
            if (mat[i][j] == 1)
                isOne = true;
            else if (isOne)
                res++;
        }

        isOne = false;
        for (int i = R-1; i >= 0; i--)
        {
            if (mat[i][j] == 1)
                isOne = true;
            else if (isOne)
                res++;
        }
    }
    return res;
}

//  Driver code to test above methods
int main()
{
    int mat[R][C] = {{0, 0, 0, 0},
        {1, 0, 0, 1},
        {0, 1, 1, 0},
        {0, 1, 0, 0}
    };

    cout << getTotalCoverageOfMatrix(mat);

    return 0;
}

Java

// Java program to get total
// coverage of all zeros in
// a binary matrix
import java .io.*;

class GFG
{
static int R = 4;
static int C = 4;

// Returns total coverage
// of all zeros in mat[][]
static int getTotalCoverageOfMatrix(int [][]mat)
{
    int res = 0;

    // looping for all
    // rows of matrix
    for (int i = 0; i < R; i++)
    {
        // 1 is not seen yet
        boolean isOne = false;

        // looping in columns from
        // left to right direction
        // to get left ones
        for (int j = 0; j < C; j++)
        {
            // If one is found
            // from left
            if (mat[i][j] == 1)
                isOne = true;

            // If 0 is found and we
            // have found a 1 before.
            else if (isOne)
                res++;
        }

        // Repeat the above
        // process for right
        // to left direction.
        isOne = false;
        for (int j = C - 1; j >= 0; j--)
        {
            if (mat[i][j] == 1)
                isOne = true;
            else if (isOne)
                res++;
        }
    }

    // Traversing across columns
    // for up and down directions.
    for (int j = 0; j < C; j++)
    {
        // 1 is not seen yet
        boolean isOne = false;
        for (int i = 0; i < R; i++)
        {
            if (mat[i][j] == 1)
                isOne = true;
            else if (isOne)
                res++;
        }

        isOne = false;
        for (int i = R - 1; i >= 0; i--)
        {
            if (mat[i][j] == 1)
                isOne = true;
            else if (isOne)
                res++;
        }
    }
    return res;
}

// Driver code
static public void main (String[] args)
{
    int [][]mat = {{0, 0, 0, 0},
                   {1, 0, 0, 1},
                   {0, 1, 1, 0},
                   {0, 1, 0, 0}};

System.out.println(
           getTotalCoverageOfMatrix(mat));
}
}

// This code is contributed by anuj_67.

Python3

# Python3 program to get total coverage of all zeros in
# a binary matrix
R = 4
C = 4

# Returns total coverage of all zeros in mat[][]
def getTotalCoverageOfMatrix(mat):
    res = 0

    # looping for all rows of matrix
    for i in range(R):

        isOne = False # 1 is not seen yet

        # looping in columns from left to right
        # direction to get left ones
        for j in range(C):

            # If one is found from left
            if (mat[i][j] == 1):
                isOne = True

            # If 0 is found and we have found
            # a 1 before.
            else if (isOne):
                res += 1

        # Repeat the above process for right to
        # left direction.
        isOne = False
        for j in range(C - 1, -1, -1):
            if (mat[i][j] == 1):
                isOne = True
            else if (isOne):
                res += 1

    # Traversing across columns for up and down
    # directions.
    for j in range(C):
        isOne = False # 1 is not seen yet
        for i in range(R):

            if (mat[i][j] == 1):
                isOne = True
            else if (isOne):
                res += 1

        isOne = False
        for i in range(R - 1, -1, -1):
            if (mat[i][j] == 1):
                isOne = True
            else if (isOne):
                res += 1

    return res

# Driver code
mat = [[0, 0, 0, 0],[1, 0, 0, 1],[0, 1, 1, 0],[0, 1, 0, 0]]
print(getTotalCoverageOfMatrix(mat))

# This code is contributed by shubhamsingh10

C#

// C# program to get total coverage
// of all zeros in a binary matrix
using System;

class GFG {

static int R = 4;
static int C = 4;

// Returns total coverage of all zeros in mat[][]
static int getTotalCoverageOfMatrix(int [,]mat)
{
    int res = 0;

    // looping for all rows of matrix
    for (int i = 0; i < R; i++)
    {
        // 1 is not seen yet
        bool isOne = false;

        // looping in columns from left to
        // right direction to get left ones
        for (int j = 0; j < C; j++)
        {
            // If one is found from left
            if (mat[i,j] == 1)
                isOne = true;

            // If 0 is found and we
            // have found a 1 before.
            else if (isOne)
                res++;
        }

        // Repeat the above process for
        // right to left direction.
        isOne = false;
        for (int j = C-1; j >= 0; j--)
        {
            if (mat[i,j] == 1)
                isOne = true;
            else if (isOne)
                res++;
        }
    }

    // Traversing across columns
    // for up and down directions.
    for (int j = 0; j < C; j++)
    {
        // 1 is not seen yet
        bool isOne = false;
        for (int i = 0; i < R; i++)
        {
            if (mat[i,j] == 1)
                isOne = true;
            else if (isOne)
                res++;
        }

        isOne = false;
        for (int i = R-1; i >= 0; i--)
        {
            if (mat[i,j] == 1)
                isOne = true;
            else if (isOne)
                res++;
        }
    }
    return res;
}

// Driver code to test above methods
    static public void Main ()
    {
        int [,]mat = {{0, 0, 0, 0},
                      {1, 0, 0, 1},
                      {0, 1, 1, 0},
                      {0, 1, 0, 0}};

    Console.WriteLine(getTotalCoverageOfMatrix(mat));
    }
}

// This code is contributed by vt_m.

Javascript

<script>
    // Javascript program to get total
    // coverage of all zeros in
    // a binary matrix

    let R = 4;
    let C = 4;

    // Returns total coverage
    // of all zeros in mat[][]
    function getTotalCoverageOfMatrix(mat)
    {
        let res = 0;

        // looping for all
        // rows of matrix
        for (let i = 0; i < R; i++)
        {
            // 1 is not seen yet
            let isOne = false;

            // looping in columns from
            // left to right direction
            // to get left ones
            for (let j = 0; j < C; j++)
            {
                // If one is found
                // from left
                if (mat[i][j] == 1)
                    isOne = true;

                // If 0 is found and we
                // have found a 1 before.
                else if (isOne)
                    res++;
            }

            // Repeat the above
            // process for right
            // to left direction.
            isOne = false;
            for (let j = C - 1; j >= 0; j--)
            {
                if (mat[i][j] == 1)
                    isOne = true;
                else if (isOne)
                    res++;
            }
        }

        // Traversing across columns
        // for up and down directions.
        for (let j = 0; j < C; j++)
        {
            // 1 is not seen yet
            let isOne = false;
            for (let i = 0; i < R; i++)
            {
                if (mat[i][j] == 1)
                    isOne = true;
                else if (isOne)
                    res++;
            }

            isOne = false;
            for (let i = R - 1; i >= 0; i--)
            {
                if (mat[i][j] == 1)
                    isOne = true;
                else if (isOne)
                    res++;
            }
        }
        return res;
    }

    let mat = [[0, 0, 0, 0],
               [1, 0, 0, 1],
               [0, 1, 1, 0],
               [0, 1, 0, 0]];

    document.write(getTotalCoverageOfMatrix(mat));

</script>

Output

20

Time Complexity: O(n²) 
Auxiliary Space: O(1)