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).

Range Sum Query 2D
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:
You may assume that the matrix does not change.
There are many calls to sumRegion function.
You may assume that row1 ≤ row2 and col1 ≤ col2.

s思路:
1. 从1d变成2d，方法并没变，仍然通过o(m*n)预处理得到所有从[0,0]到[i,j]的所有元素之和！
2. bug:加括号，尤其是问号表达式！不然运算顺序就不保证了。

class NumMatrix {private:    vector<vector<int>> res;public:    NumMatrix(vector<vector<int>> matrix) {        res=matrix;        for(int i=0;i<res.size();i++){            for(int j=0;j<res[0].size();j++){                res[i][j]=res[i][j]+(i>0?res[i-1][j]:0)+(j>0?res[i][j-1]:0)-(i>0&&j>0?res[i-1][j-1]:0);//bug:加括号，尤其是问号表达式！不然运算顺序就不保证了。            }            }    }    int sumRegion(int row1, int col1, int row2, int col2) {        return res[row2][col2]-(col1>0?res[row2][col1-1]:0)-(row1>0?res[row1-1][col2]:0)+(col1>0&&row1>0?res[row1-1][col1-1]:0);//bug:加括号，尤其是问号表达式！不然运算顺序就不保证了。    }};/** * Your NumMatrix object will be instantiated and called as such: * NumMatrix obj = new NumMatrix(matrix); * int param_1 = obj.sumRegion(row1,col1,row2,col2); */