Range Sum Query 2D - Immutable(matrix)

Given a 2D matrixmatrix, find the sum of the elements inside the rectangle defined by its upper left corner (row1,col1) and lower right corner (row2,col2).

The above rectangle (with the red border) is defined by (row1, col1) =(2, 1)and (row2, col2) =(4, 3), which contains sum =8.

Example:

Given 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]
]

sumRegion(2, 1, 4, 3) -
>
 8
sumRegion(1, 1, 2, 2) -
>
 11
sumRegion(1, 2, 2, 4) -
>
 12

分析

+-----+-+-------+     +--------+-----+     +-----+---------+     +-----+--------+
|     | |       |     |        |     |     |     |         |     |     |        |
|     | |       |     |        |     |     |     |         |     |     |        |
+-----+-+       |     +--------+     |     |     |         |     +-----+        |
|     | |       |  =  |              |  +  |     |         |  -  |              |
+-----+-+       |     |              |     +-----+         |     |              |
|               |     |              |     |               |     |              |
|               |     |              |     |               |     |              |
+---------------+     +--------------+     +---------------+     +--------------+

   sums[i][j]      =    sums[i-1][j]    +     sums[i][j-1]    -   sums[i-1][j-1]   +  

                        matrix[i-1][j-1]

别忘了最后index 是 r2+1 c2+1

class NumMatrix:

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

            n = len(matrix)
            m = len(matrix[0])
            f = [[0]*(m+1) for _ in range(n+1)]
            for i in range(1,n+1):
                for j in range(1,m+1):
                    f[i][j] = f[i][j-1]+f[i-1][j]-f[i-1][j-1]+matrix[i-1][j-1]

            self.f = f
        else:
            self.f= None




    def sumRegion(self, row1, col1, row2, col2):
        """
        :type row1: int
        :type col1: int
        :type row2: int
        :type col2: int
        :rtype: int
        """
        if not self.f:
            return 0
        return self.f[row2+1][col2+1]-self.f[row1][col2+1]-self.f[row2+1][col1]+self.f[row1][col1]

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