Range Sum Query 2D - Immutable

题目链接

原题

Given a 2D matrix matrix, find the sum of the elements 
inside the rectangle defined by (row1, col1), (row2, col2).

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.

思路

利用积分图的方法来做, 参考
https://zh.wikipedia.org/wiki/%E7%A7%AF%E5%88%86%E5%9B%BE

code

class NumMatrix {
public:

    NumMatrix(vector<vector<int>> &matrix) {
        clear();
        int m = matrix.size();
        if(m <= 0) return;
        int n = matrix[0].size();
        for(int i = 0; i < m; i++) {
            m_.push_back(vector<int>(n, 0));
            s_.push_back(vector<int>(n, 0));
            for(int j = 0; j < n; j++) {
                m_[i][j] = matrix[i][j];
            }
        }
        s_[0][0] = m_[0][0];
        for(int i = 1; i < m; i++) {
            s_[i][0] = m_[i][0] + s_[i - 1][0];
        }
        for(int j = 1; j < n; j++) {
            s_[0][j] = m_[0][j] + s_[0][j - 1];
        }
        for(int i = 1; i < m; i++) {
            for(int j = 1; j < n; j++) {
                s_[i][j] = m_[i][j] + (s_[i - 1][j] + s_[i][j - 1] - s_[i - 1][j - 1]);
            }
        }
    }

    int sumRegion(int row1, int col1, int row2, int col2) {
        // if(row1 > row2) swap(row1, row2);
        // if(col1 > col2) swap(col1, col2);
        int s1 = s_[row2][col2] + s_[row1][col1] - s_[row1][col2] - s_[row2][col1];
        int s2 = m_[row1][col1];
        for(int i = row1 + 1; i <= row2; i++) s2 += m_[i][col1];
        for(int i = col1 + 1; i <= col2; i++) s2 += m_[row1][i];
        return s1 + s2;
    }
private:
    void clear() {
        if(!m_.empty()) {
            int m = m_.size();
            for(int i = 0; i < m; i++) {
                if(m_[i].empty()) continue;
                m_[i].clear();
            }
        }
        if(!s_.empty()) {
            int m = s_.size();
            for(int i = 0; i < m; i++) {
                if(s_[i].empty()) continue;
                s_[i].clear();
            }
        }
    }
    vector<vector<int> > m_;
    vector<vector<int> > s_;
};


// Your NumMatrix object will be instantiated and called as such:
// NumMatrix numMatrix(matrix);
// numMatrix.sumRegion(0, 1, 2, 3);
// numMatrix.sumRegion(1, 2, 3, 4);