题目描述：
题解：
矩阵前缀和
1.求坐标(0,0)到(i,j)的matrix对应位置之和。
图中红色部分=两个绿色部分相加-蓝色部分+[i,j]
用thesum[i][j]表示坐标[i,j]到[0,0]的和，thessum[i][j] = thesum[i-1][j]+thesum[i][j-1]-thesum[i-1][j-1]+,matrix[i][j]
2.求坐标[i,j]到[m,n]值之和。
[m][n]到[i][j]矩阵值之和=红色部分-两个绿色部分+蓝色部分
=thesum[i][j]=thesum[i][n]-thesum[m][j]+thesum[m][n]
class NumMatrix:
def __init__(self, matrix: List[List[int]]):
if not matrix or not matrix[0]:
m, n = 0, 0
else:
m = len(matrix)
n = len(matrix[0])
self.thesum = [[0 for i in range(n+1)]for j in range(m+1)]
for i in range(m):
for j in range(n):
self.thesum[i+1][j+1] = self.thesum[i][j+1]+self.thesum[i+1][j]-self.thesum[i][j]+matrix[i][j]
def sumRegion(self, row1: int, col1: int, row2: int, col2: int) -> int:
return self.thesum[row2+1][col2+1]-self.thesum[row2+1][col1]-self.thesum[row1][col2+1]+self.thesum[row1][col1]
