count-submatrices-with-equal-frequency-of-x-and-y.py

# Time:  O(n * m)
# Space: O(n * m)

# dp
class Solution(object):
    def numberOfSubmatrices(self, grid):
        """
        :type grid: List[List[str]]
        :rtype: int
        """
        result = 0
        dp1 = [[0]*(len(grid[0])+1) for _ in xrange(len(grid)+1)]
        dp2 = [[0]*(len(grid[0])+1) for _ in xrange(len(grid)+1)]
        for i in xrange(len(grid)):
            for j in xrange(len(grid[0])):
                dp1[i+1][j+1] = dp1[i][j+1]+dp1[i+1][j]-dp1[i][j]+int(grid[i][j] == 'X')
                dp2[i+1][j+1] = dp2[i][j+1]+dp2[i+1][j]-dp2[i][j]+int(grid[i][j] == 'Y')
                result += int(dp1[i+1][j+1] == dp2[i+1][j+1] != 0)
        return result


# Time:  O(n * m)
# Space: O(n * m)
# dp
class Solution2(object):
    def numberOfSubmatrices(self, grid):
        """
        :type grid: List[List[str]]
        :rtype: int
        """
        result = 0
        dp1 = [[0]*len(grid[0]) for _ in xrange(len(grid))]
        dp2 = [[0]*len(grid[0]) for _ in xrange(len(grid))]
        for i in xrange(len(grid)):
            for j in xrange(len(grid[0])):
                if i-1 >= 0:
                    dp1[i][j] += dp1[i-1][j]
                    dp2[i][j] += dp2[i-1][j]
                if j-1 >= 0:
                    dp1[i][j] += dp1[i][j-1]
                    dp2[i][j] += dp2[i][j-1]
                if i-1 >= 0 and j-1 >= 0:
                    dp1[i][j] -= dp1[i-1][j-1]
                    dp2[i][j] -= dp2[i-1][j-1]
                dp1[i][j] += int(grid[i][j] == 'X')
                dp2[i][j] += int(grid[i][j] == 'Y')
                result += int(dp1[i][j] == dp2[i][j] != 0)
        return result