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).
The above rectangle (with the red border) is defined by (row1, col1) = (2, 1) and (row2, col2) = (4, 3), which contains sum = 8.
class NumMatrix(object):
def __init__(self, matrix):
"""
:type matrix: List[List[int]]
"""
if len(matrix) == 0 or len(matrix[0]) == 0:
m = n = 0
else:
m, n = len(matrix), len(matrix[0])
self.prefix = [[0] * (n + 1) for _ in xrange(m + 1)]
for i in xrange(1, m + 1):
for j in xrange(1, n + 1):
self.prefix[i][j] = self.prefix[i-1][j] + self.prefix[i][j-1] \
- self.prefix[i-1][j-1] + matrix[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
"""
return self.prefix[row2 + 1][col2 + 1] + self.prefix[row1][col1] \
- self.prefix[row1][col2 + 1] - self.prefix[row2 + 1][col1]
