## 304. Range Sum Query 2D - Immutable

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
``````

Note:

1. You may assume that the matrix does not change.
2. There are many calls tosumRegion function.
3. You may assume that row1 ≤ row2 and col1 ≤ col2.

Thoughts:

1. Having a 2D dp arrays (m + 1, n + 1)
2. When building: dp[i][i] = matrix[i -1][j-1] + dp[i-1][j] + dp[i][j-1] - dp[i-1][j-1] for i, j in [1,m] and [1,n]
3. When calculating the query: res = dp[row2 + 1][col2 + 1] - dp[row2 + 1][col1] - dp[row1][col2 + 1] + dp[row1][col1]
4. In Python: Initialize 2D list needs to be initialized as [ * m] for _ in range(n)) instead of [ * m]*n] since this would create n identical lists with the same reference.

Code

``````class NumMatrix(object):

def __init__(self, matrix):
"""
:type matrix: List[List[int]]
"""
self.m, self.n = len(matrix), len(matrix) if len(matrix) else 0
self.dp = [ * (self.n + 1) for _ in range(self.m + 1)] # cannot do [ * (self.n + 1)] *  (self.m + 1)
for i in range(1, self.m + 1):
for j in range(1, self.n + 1):
self.dp[i][j] =  matrix[i - 1][j - 1] + self.dp[i - 1][j] + self.dp[i][j-1] - self.dp[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.dp[row2 + 1][col2 + 1] -self.dp[row2 + 1][col1] -self.dp[row1][col2 + 1] + self.dp[row1][col1]

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