308. Range Sum Query 2D - Mutable

Description

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:

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

Solution

虽然这道题适合用高深的线段树去解（which我不会），但后来发现简单的DP做法也是可以过哒。

DP, constructor O(mn), update O(n), sumRegion O(m), S(mn)

class NumMatrix {
    private int m;
    private int n;
    private int[][] matrix;
    private int[][] rowSum;
    
    public NumMatrix(int[][] matrix) {
        if (matrix == null || matrix.length == 0 || matrix[0].length == 0) {
            return;
        }
        
        m = matrix.length;
        n = matrix[0].length;
        this.matrix = matrix;
        rowSum = new int[m][n + 1];
        
        for (int i = 0; i < m; ++i) {
            for (int j = 0; j < n; ++j) {
                rowSum[i][j + 1] = rowSum[i][j] + matrix[i][j];
            }
        }
    }
    
    public void update(int row, int col, int val) {
        int delta = val - matrix[row][col];
        for (int j = col; j < n; ++j) {
            rowSum[row][j + 1] += delta;
        }
        matrix[row][col] = val;  // don't forget
    }
    
    public int sumRegion(int row1, int col1, int row2, int col2) {
        return getSum(row1, row2, col2) - getSum(row1, row2, col1 - 1);
    }
    
    private int getSum(int row1, int row2, int col) {
        int sum = 0;
        for (int i = row1; i <= row2; ++i) {
            sum += rowSum[i][col + 1];
        }
        return sum;
    }
}

/**
 * Your NumMatrix object will be instantiated and called as such:
 * NumMatrix obj = new NumMatrix(matrix);
 * obj.update(row,col,val);
 * int param_2 = obj.sumRegion(row1,col1,row2,col2);
 */