[算法分析与设计] leetcode 每周一题: Range Sum Query 2D - Immutable

题目链接：https://leetcode.com/problems/range-sum-query-2d-immutable/description/

题目意思： 

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

Note:

1. You may assume that the matrix does not change.
2. There are many calls to sumRegion function.
3. You may assume that row1 ≤ row2 and col1 ≤ col2.

思路：

一开始是打算暴力破解，存储matrix，查询时候直接两个for循环，不过貌似会 超时。。。所以干脆就维护一个状态表vmatrix, vmatrix[i][j]表示原表[i][j]左上区域包括matrix[i][j]的总和，然后查询的时候注意边界问题

代码如下；

class NumMatrix {
private:
    vector<vector<int>> vmatrix;
public:
    
    NumMatrix(vector<vector<int>> matrix) {
        if(matrix.size() == 0) return;
        int rows = matrix.size();
        int cols = matrix[0].size();
        
        for(int i = 0; i < rows; i++ ) {
            vector<int> row;
            int sum = 0;
            for(int j = 0; j < cols; j++) {
                sum += matrix[i][j];
                if(i == 0) {
                    row.push_back(sum);

                } else  {
                    row.push_back(vmatrix[i-1][j] + sum);
                }
            }
            vmatrix.push_back(row);
        }
    }
    
    int sumRegion(int r1, int c1, int r2, int c2) {
        if(r1 >= 1 && c1 >= 1 ) {
             return vmatrix[r2][c2] - vmatrix[r1 - 1][c2] - vmatrix[r2][c1 - 1] + vmatrix[r1 - 1][c1 - 1];
        } else if(r1 >= 1 && c1 == 0) {
            return vmatrix[r2][c2] - vmatrix[r1 - 1][c2];
        } else if(r1 == 0 && c1 >= 1) {
            return vmatrix[r2][c2] - vmatrix[r2][c1 - 1];
        } else {
            return vmatrix[r2][c2];
        }
    }
};

/**
 * Your NumMatrix object will be instantiated and called as such:
 * NumMatrix obj = new NumMatrix(matrix);
 * int param_1 = obj.sumRegion(row1,col1,row2,col2);
 */