leetcode 304

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• 基本思路：使用DP维护，算法基本是小学奥数级别。

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C++

class NumMatrix {
public:
    NumMatrix(vector > &matrix) {
        if (matrix.empty() || matrix[0].empty()) 
            return;
        dp.resize(matrix.size() + 1, vector(matrix[0].size() + 1, 0));
        for (int i = 1; i <= matrix.size(); ++i) {
            for (int j = 1; j <= matrix[0].size(); ++j) {
                dp[i][j] = dp[i][j - 1] + dp[i - 1][j] - dp[i - 1][j - 1] + matrix[i - 1][j - 1];
            }
        }
    }
    int sumRegion(int row1, int col1, int row2, int col2) {
        return dp[row2 + 1][col2 + 1] - dp[row1][col2 + 1] - dp[row2 + 1][col1] + dp[row1][col1];
    }

private:
    vector > dp;
};

Java

//faster
class NumMatrix {
    
    private int[][] dp;

    public NumMatrix(int[][] matrix) {
        //this chunk is faster
        if (null == matrix || 0 == matrix.length) {
            return;
        }
        int m = matrix.length;
        int n = matrix[0].length;
        dp = new int[m + 1][n + 1];
        //chunck end
        
        for (int i = 1; i <= m; i++) {
            for (int j = 1; j <= n; j++) {
                dp[i][j] = 
                    matrix[i - 1][j - 1] + dp[i - 1][j] + dp[i][j - 1] - dp[i - 1][j - 1];
            }
        }
    }
    
    public int sumRegion(int row1, int col1, int row2, int col2) {
        return dp[row2 + 1][col2 + 1] - dp[row2 + 1][col1] - dp[row1][col2 + 1] + dp[row1][col1];
    }
}