'''
Level: Medium   Tag: [Design], [DP]

Given a 2D matrix matrix, handle multiple queries of the following type:

Calculate the sum of the elements of matrix inside the rectangle defined by its upper left corner (row1, col1) and lower right corner (row2, col2).
Implement the NumMatrix class:

NumMatrix(int[][] matrix) Initializes the object with the integer matrix matrix.
int sumRegion(int row1, int col1, int row2, int col2)
Returns the sum of the elements of matrix inside the rectangle defined by its upper left corner (row1, col1) and lower right corner (row2, col2).


Example 1:

"../../../Material/sum-grid.jpg"

Input
["NumMatrix", "sumRegion", "sumRegion", "sumRegion"]
[[[[3, 0, 1, 4, 2],
   [5, 6, 3, 2, 1],
   [1, 2, 0, 1, 5],
   [4, 1, 0, 1, 7],
   [1, 0, 3, 0, 5]]], [2, 1, 4, 3], [1, 1, 2, 2], [1, 2, 2, 4]]
Output
[null, 8, 11, 12]

Explanation
NumMatrix numMatrix = new NumMatrix([[3, 0, 1, 4, 2], [5, 6, 3, 2, 1], [1, 2, 0, 1, 5], [4, 1, 0, 1, 7], [1, 0, 3, 0, 5]]);
numMatrix.sumRegion(2, 1, 4, 3); // return 8 (i.e sum of the red rectangle)
numMatrix.sumRegion(1, 1, 2, 2); // return 11 (i.e sum of the green rectangle)
numMatrix.sumRegion(1, 2, 2, 4); // return 12 (i.e sum of the blue rectangle)


Constraints:

m == matrix.length
n == matrix[i].length
1 <= m, n <= 200
-10^5 <= matrix[i][j] <= 10^5
0 <= row1 <= row2 < m
0 <= col1 <= col2 < n
At most 10^4 calls will be made to sumRegion.

'''

class NumMatrix(object):

    def __init__(self, matrix):
        """
        :type matrix: List[List[int]]
        """
        self.matrix = matrix


    def sumRegion(self, row1, col1, row2, col2):
        """
        :type row1: int
        :type col1: int
        :type row2: int
        :type col2: int
        :rtype: int
        """
        ans = 0
        for i in range(row1, row2+1):
            ans += sum(self.matrix[i][col1: col2+1])

        print(ans)

        return ans




class NumMatrix_DP(object):

    def __init__(self, matrix):
        """
        :type matrix: List[List[int]]
        """
        m = len(matrix)
        n = len(matrix[0])
        self.prefix_sum = [[0] * (n+1) for _ in range(m+1)]

        # prefix_sum[i-1][j-1]被減去
        # 是因為prefix_sum[i-1][j] + prefix_sum[i][j-1]本身就有包含prefix_sum[i-1][j-1]
        # 所以要減去多加的部分
        for i in range(1, m+1):
            for j in range(1, n+1):
                self.prefix_sum[i][j] = matrix[i-1][j-1] + self.prefix_sum[i-1][j] + self.prefix_sum[i][j-1] \
                                        - self.prefix_sum[i-1][j-1]



    def sumRegion(self, row1, col1, row2, col2):
        """
        :type row1: int
        :type col1: int
        :type row2: int
        :type col2: int
        :rtype: int
        """
        row2 += 1
        col2 += 1

        # prefix_sum[row1][col2] 和 prefix_sum[row2][col1] 被重複加到
        # 所以要扣掉
        ans = self.prefix_sum[row2][col2] + self.prefix_sum[row1][col1] \
            - self.prefix_sum[row1][col2] - self.prefix_sum[row2][col1]

        print(ans)
        return ans

# Your NumMatrix object will be instantiated and called as such:
# obj = NumMatrix(matrix)
# param_1 = obj.sumRegion(row1,col1,row2,col2)

matrix = [
    [3, 0, 1, 4, 2],
    [5, 6, 3, 2, 1],
    [1, 2, 0, 1, 5],
    [4, 1, 0, 1, 7],
    [1, 0, 3, 0, 5]
]
obj = NumMatrix(matrix)
obj.sumRegion(2, 1, 4, 3)
obj.sumRegion(1, 1, 2, 2)
obj.sumRegion(1, 2, 2, 4)


obj2 = NumMatrix_DP(matrix)
obj2.sumRegion(2, 1, 4, 3)
obj2.sumRegion(1, 1, 2, 2)
obj2.sumRegion(1, 2, 2, 4)