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// 304. Range Sum Query 2D - Immutable
#include "leetcode.h"
/*
* 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 corer '(row2, col2)'.
* you must design an algorithm where 'sumRegion' works on 'O(1)' time
* complexity.
*/
class NumMatrix {
public:
vector<vector<int>> sum;
NumMatrix(vector<vector<int>> &matrix) {
int m = matrix.size(), n = matrix[0].size();
sum = vector<vector<int>>(m + 1, vector<int>(n + 1));
for (int i = 1; i <= m; i++)
for (int j = 1; j <= n; j++)
sum[i][j] = sum[i - 1][j] + sum[i][j - 1] - sum[i - 1][j - 1] +
matrix[i - 1][j - 1];
}
int sumRegion(int row1, int col1, int row2, int col2) {
row1++, col1++, row2++, col2++;
return sum[row2][col2] - sum[row2][col1 - 1] - sum[row1 - 1][col2] +
sum[row1 - 1][col1 - 1];
}
};
int main() {
vvd 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}};
NumMatrix *obj = new NumMatrix(matrix);
printf("%d\n", obj->sumRegion(2, 1, 4, 3)); // expect: 8
printf("%d\n", obj->sumRegion(1, 1, 2, 2)); // expect: 11
printf("%d\n", obj->sumRegion(1, 2, 2, 4)); // expect: 12
}
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