Given a 2D matrix matrix
, handle multiple queries of the following type:
- Calculate the sum of the elements of
matrix
inside the rectangle defined by its upper left corner(row1, col1)
and lower right corner(row2, col2)
.
Implement the NumMatrix
class:
-
NumMatrix(int[][] matrix)
Initializes the object with the integer matrixmatrix
. -
int sumRegion(int row1, int col1, int row2, int col2)
Returns the sum of the elements ofmatrix
inside the rectangle defined by its upper left corner(row1, col1)
and lower right corner(row2, col2)
.
Example 1:
Input
["NumMatrix", "sumRegion", "sumRegion", "sumRegion"]
[[[[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]]], [2, 1, 4, 3], [1, 1, 2, 2], [1, 2, 2, 4]]
Output
[null, 8, 11, 12]
Explanation
NumMatrix numMatrix = new NumMatrix([[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]]);
numMatrix.sumRegion(2, 1, 4, 3); // return 8 (i.e sum of the red rectangle)
numMatrix.sumRegion(1, 1, 2, 2); // return 11 (i.e sum of the green rectangle)
numMatrix.sumRegion(1, 2, 2, 4); // return 12 (i.e sum of the blue rectangle)
Constraints:
-
m == matrix.length
-
n == matrix[i].length
-
1 <= m, n <= 200
-
-104 <= matrix[i][j] <= 104
-
0 <= row1 <= row2 < m
-
0 <= col1 <= col2 < n
- At most
104
calls will be made tosumRegion
.
SOLUTION:
class NumMatrix:
def __init__(self, matrix: List[List[int]]):
m = len(matrix)
n = len(matrix[0])
self.matrix = matrix
self.qsum = [[None for i in range(n)] for j in range(m)]
def getSum(self, i, j):
if i < 0 or j < 0:
return 0
if self.qsum[i][j] != None:
return self.qsum[i][j]
prev = self.getSum(i - 1, j - 1)
row = self.getSum(i - 1, j)
col = self.getSum(i, j - 1)
res = row + col + self.matrix[i][j] - prev
self.qsum[i][j] = res
return res
def sumRegion(self, row1: int, col1: int, row2: int, col2: int) -> int:
c = self.getSum(row2, col2)
l = self.getSum(row2, col1 - 1)
t = self.getSum(row1 - 1, col2)
s = self.getSum(row1 - 1, col1 - 1)
return c - l - t + s
# Your NumMatrix object will be instantiated and called as such:
# obj = NumMatrix(matrix)
# param_1 = obj.sumRegion(row1,col1,row2,col2)
Top comments (0)