308_Range_Sum_Query_2D_Mutable

Range Sum Query 2D - Mutable

Difficulty hard

tags binary_indexed_tree

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
update(3, 2, 2)
sumRegion(2, 1, 4, 3) -> 10

Note:

• The matrix is only modifiable by the update function.
• You may assume the number of calls to update and sumRegion function is distributed evenly.
• You may assume that row1 ≤ row2 and col1 ≤ col2.

思路：

1. 肯定不能暴力写。所以自己写了一个按行来进行累加和的版本，对这道题的case比binary indexed tree都快。

2. 学习了binary indexed tree. 然后写了一篇Blog, 体会到了给别人讲授知识反而可以理清自己的知识。写博客的习惯还是要坚持的， 就是要控制时间利用2333

   注意，这是binary indexed tree的多维应用.

3. segment tree如何实现，需要重新学习下。 上次用的时候最起码是半年前了，完全忘却。

4. 还是老话题需要熟悉下STL的API了， 毕竟这种写法能省很多功夫和时间：

orimatrix = vector<vector<int>>(rlen, vector<int>(clen, 0));

或者考察下实现机制，如果明确知道数组定义之后&未人为初始化时-->里面的值是0的话, 就直接用。

既然折腾了一下binary indexed tree, 那么答案就还是bit版本吧。

solution 1

class NumMatrix {
public:
    NumMatrix(vector<vector<int>> matrix) {
        rlen = matrix.size();
        if (rlen) clen = matrix[0].size();

        orimatrix = vector<vector<int>>(rlen, vector<int>(clen, 0));
        bitmatrix = vector<vector<int>>(rlen, vector<int>(clen, 0));

        for (int i = 0; i < rlen; i++)
            for (int j = 0; j < clen; j++)
                update(i, j, matrix[i][j]);

    }

    void update(int row, int col, int val) {
        int change = val - orimatrix[row][col];
        orimatrix[row][col] = val;
        row++;
        col++;
        for (int i = row; i <= rlen; i += i&(-i))
            for (int j = col; j <= clen; j += j&(-j))
                bitmatrix[i-1][j-1] += change;
    }

    int sum(int row, int col){
        int sum = 0;
        row++;
        col++;
        for (int i = row; i > 0; i -= i&(-i))
            for (int j = col; j > 0; j -= j&(-j))
               sum += bitmatrix[i-1][j-1];
        return sum;
    }

    int sumRegion(int row1, int col1, int row2, int col2) {
        return sum(row2, col2) - sum(row2, col1-1) - sum(row1-1, col2) + sum(row1-1, col1-1);
    }

private:
    vector<vector<int>> bitmatrix;
    vector<vector<int>> orimatrix;
    int rlen, clen;
};