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 (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
To calculate sums, the ideas as below
+-----+-+-------+ +--------+-----+ +-----+---------+ +-----+--------+
| | | | | | | | | | | | |
| | | | | | | | | | | | |
+-----+-+ | +--------+ | | | | +-----+ |
| | | | = | | + | | | - | |
+-----+-+ | | | +-----+ | | |
| | | | | | | |
| | | | | | | |
+---------------+ +--------------+ +---------------+ +--------------+
sums[i][j] = sums[i-1][j] + sums[i][j-1] - sums[i-1][j-1] +
matrix[i-1][j-1]
So, we use the same idea to find the specific area's sum.
+---------------+ +--------------+ +---------------+ +--------------+ +--------------+
| | | | | | | | | | | | | |
| (r1,c1) | | | | | | | | | | | | |
| +------+ | | | | | | | +---------+ | +---+ |
| | | | = | | | - | | | - | (r1,c2) | + | (r1,c1) |
| | | | | | | | | | | | | |
| +------+ | +---------+ | +---+ | | | | |
| (r2,c2)| | (r2,c2)| | (r2,c1) | | | | |
+---------------+ +--------------+ +---------------+ +--------------+ +--------------+
class NumMatrix {
private:
int row, col;
vector<vector<int>> sums;
public:
NumMatrix(vector<vector<int>> &matrix) {
row = matrix.size();
col = row>0 ? matrix[0].size() : 0;
sums = vector<vector<int>>(row+1, vector<int>(col+1, 0));
for(int i = 1; i <= row; i++) {
for(int j = 1; j <= col; j++) {
sums[i][j] = matrix[i-1][j-1] +
sums[i-1][j] + sums[i][j-1] - sums[i-1][j-1] ;
}
}
}
int sumRegion(int row1, int col1, int row2, int col2) {
return sums[row2 + 1][col2 + 1] - sums[row2+1][col1] - sums[row1][col2 + 1] + sums[row1][col1];
}
};
// Your NumMatrix object will be instantiated and called as such:
// NumMatrix numMatrix(matrix);
// numMatrix.sumRegion(0, 1, 2, 3);
// numMatrix.sumRegion(1, 2, 3, 4);