maximalRectangle.cpp

/* You are given an 'N' * 'M' sized binary-valued matrix 'MAT, where 'N' is the number of rows and 'M' is the number of columns. You need to return the maximum size (area) of the submatrix which consists of all 1’s i.e. the maximum area of a submatrix in which each cell has only the value ‘1’.  */

class Solution {public:
int maximalRectangle(vector<vector<char> > &matrix) {
    if(matrix.empty()) return 0;
    const int m = matrix.size();
    const int n = matrix[0].size();
    int left[n], right[n], height[n];
    fill_n(left,n,0); fill_n(right,n,n); fill_n(height,n,0);
    int maxA = 0;
    for(int i=0; i<m; i++) {
        int cur_left=0, cur_right=n; 
        for(int j=0; j<n; j++) { // compute height (can do this from either side)
            if(matrix[i][j]=='1') height[j]++; 
            else height[j]=0;
        }
        for(int j=0; j<n; j++) { // compute left (from left to right)
            if(matrix[i][j]=='1') left[j]=max(left[j],cur_left);
            else {left[j]=0; cur_left=j+1;}
        }
        // compute right (from right to left)
        for(int j=n-1; j>=0; j--) {
            if(matrix[i][j]=='1') right[j]=min(right[j],cur_right);
            else {right[j]=n; cur_right=j;}    
        }
        // compute the area of rectangle (can do this from either side)
        for(int j=0; j<n; j++)
            maxA = max(maxA,(right[j]-left[j])*height[j]);
    }
    return maxA;
}
};
/*
If you think this algorithm is not easy to understand, you can try this example:

0 0 0 1 0 0 0 
0 0 1 1 1 0 0 
0 1 1 1 1 1 0
The vector "left" and "right" from row 0 to row 2 are as follows

row 0:

l: 0 0 0 3 0 0 0
r: 7 7 7 4 7 7 7
row 1:

l: 0 0 2 3 2 0 0
r: 7 7 5 4 5 7 7 
row 2:

l: 0 1 2 3 2 1 0
r: 7 6 5 4 5 6 7
The vector "left" is computing the left boundary. Take (i,j)=(1,3) for example. On current row 1, the left boundary is at j=2. However, because matrix[1][3] is 1, you need to consider the left boundary on previous row as well, which is 3. So the real left boundary at (1,3) is 3.

I hope this additional explanation makes things clearer. */