二维区域和检索 - 矩阵不可变

给定一个二维矩阵，计算其子矩形范围内元素的总和，该子矩阵的左上角为 (row1, col1) ，右下角为 (row2, col2) 。

  • 示例：

    给定 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

提示：

  • 你可以假设矩阵不可变。
  • 会多次调用 sumRegion 方法。
  • 你可以假设 row1 ≤ row2 且 col1 ≤ col2 。

Solution

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#include <iostream>
#include <vector>
using namespace std;

class NumMatrix {
public:
    vector<vector<int>> sums;
    NumMatrix(vector<vector<int>>& matrix) {
        for (int i = 0; i < matrix.size(); ++i) {
            vector<int> sum;
            for (int j = 0; j < matrix[i].size(); ++j) {
                if (i == 0) {
                    if (j == 0) {
                        sum.push_back(matrix[0][0]);
                    } else {
                        sum.push_back(matrix[0][j] + sum[j - 1]);
                    }
                } else {
                    if (j == 0) {
                        sum.push_back(matrix[i][0] + sums[i - 1][0]);
                    } else {
                        sum.push_back(matrix[i][j] + sums[i - 1][j] + sum[j - 1] - sums[i - 1][j - 1]);
                    }
                }
            }
            sums.push_back(sum);
        }
    }
    
    int sumRegion(int row1, int col1, int row2, int col2) {
        int result = sums[row2][col2];
        if (row1 > 0) {
            result -= sums[row1 - 1][col2];
        }
        if (col1 > 0) {
            result -= sums[row2][col1 - 1];
        }
        if (row1 > 0 && col1 > 0) {
            result += sums[row1 - 1][col1 - 1];
        }
        return result;
    }
};

/**
 * Your NumMatrix object will be instantiated and called as such:
 * NumMatrix* obj = new NumMatrix(matrix);
 * int param_1 = obj->sumRegion(row1,col1,row2,col2);
 */
int main() {
    vector<vector<int>> 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);
    std::cout << obj->sumRegion(2, 1, 4, 3) << std::endl; //  -> 8
    std::cout << obj->sumRegion(1, 1, 2, 2) << std::endl; //  -> 11
    std::cout << obj->sumRegion(1, 2, 2, 4) << std::endl; //  -> 12
}