304. Range Sum Query 2D - Immutable 【M】【27】

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本文介绍了一种高效求解二维矩阵中任意矩形区域元素之和的方法。通过预处理矩阵，实现了快速查找指定矩形区域内的元素总和，适用于矩阵不变且需频繁查询的情况。

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

Range Sum Query 2D
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

Note:

You may assume that the matrix does not change.
There are many calls to sumRegion function.
You may assume that row1 ≤ row2 and col1 ≤ col2.

class NumMatrix(object):
    def __init__(self, matrix):
        if matrix == []:
            return
        row = len(matrix[0])
        col = len(matrix)

        self.m = matrix

        for i in xrange(0,col):
            for j in xrange(1,row):
                self.m[i][j] += self.m[i][j-1]

        for i in xrange(1,col):
            for j in xrange(0,row):
                self.m[i][j] += self.m[i-1][j]

        self.m = [[0] * row] + self.m
        #print self.m
        for i in xrange(col+1):

            self.m[i] = [0] + self.m[i]

        #print self.m

        """
        initialize your data structure here.
        :type matrix: List[List[int]]
        """

    def sumRegion(self, row1, col1, row2, col2):

        return self.m[row2+1][col2+1] - self.m[row2+1][col1] - self.m[row1][col2+1] + self.m[row1][col1]

        '''
        if row1 + row2 + col1 + col2 == 0:
            return self.m[0][0]

        a = self.m[row2][col2]
        b = self.m[row2][max(0,col1-1)]
        c = self.m[max(0,row1-1)][col2]
        d = self.m[max(0,row1-1)][max(0,col1-1)]

        print a,b,c,d

        if row1 + col1 == 0:
            return self.m[row2][col2]

        if row1 == 0 and row2 != 0:
            return self.m[row2][col2] - self.m[row2][col1]
        if col1 == 0 and col2 != 0:
            return self.m[row2][col2] - self.m[row2][col1]

        if row1==row2 and col1==col2:
            #print '?'
            return a - b - c + d#self.mm[row2][col2]# - self.m[row2-1][col2-1]

        if row1 == row2 :
            return a - b
        if col1 == col2:
            print '~~'
            return a - c

        #print a,b,c,d
        return a - b - c + d
        '''