# 304. Range Sum Query 2D - Immutable

Given a 2D matrix matrix , find the sum of the elements inside the rectangle defined by its upper left corner ( row 1, col 1) and lower right corner ( row 2, col 2).

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 to sumRegion function.
3. You may assume that row 1 ≤ row 2 and col 1 ≤ col 2.

``````class NumMatrix {
public:
NumMatrix(vector<vector<int> > &matrix) {
if (matrix.empty() || matrix[0].empty()) return;
dp.resize(matrix.size() + 1, vector<int>(matrix[0].size() + 1, 0));
for (int i = 1; i <= matrix.size(); ++i) {
for (int j = 1; j <= matrix[0].size(); ++j) {
dp[i][j] = dp[i][j - 1] + dp[i - 1][j] - dp[i - 1][j - 1] + matrix[i - 1][j - 1];
}
}
}
int sumRegion(int row1, int col1, int row2, int col2) {
return dp[row2 + 1][col2 + 1] - dp[row1][col2 + 1] - dp[row2 + 1][col1] + dp[row1][col1];
}

private:
vector<vector<int> > dp;
};
``````

Range Sum Query 2D - Mutable

Range Sum Query - Immutable

Range Sum Query - Mutable

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