Leetcode 304. Range Sum Query 2D - Immutable

题目

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.

思路

因为是immutable的，所以我们可以使用prefix sum matrix搞定。这里的技巧叫做overlapping rectangle，sum = dp[i][j] - left - top + topleft。

复杂度

time O(mn), space O(mn)

代码

  public class NumMatrix {
    int[][] prefix;
    int[][] matrix;
    public NumMatrix(int[][] matrix) {
        //init
        if (matrix == null || matrix.length == 0 || matrix[0].length == 0) {
            return;
        }
        int row = matrix.length;
        int col = matrix[0].length;
        this.matrix = matrix;
        prefix = new int[row][col];
        //prefix
        for (int j = 0; j < col; j++) {
            if (j == 0) {
                prefix[0][0] = matrix[0][0];
            } else {
                prefix[0][j] = prefix[0][j - 1] + matrix[0][j];
            }
        }
        for (int i = 1; i < row; i++) {
            int curRow = 0;
            for (int j = 0; j < col; j++) {
                curRow += matrix[i][j];
                prefix[i][j] = prefix[i - 1][j] + curRow;
            }
        }
    }

    public int sumRegion(int row1, int col1, int row2, int col2) {
        int top = row1 - 1 >= 0? prefix[row1 - 1][col2]: 0;
        int left = col1 - 1 >= 0? prefix[row2][col1 - 1]: 0;
        int topLeft = (row1 - 1 >= 0) && (col1 - 1 >= 0)? prefix[row1 - 1][col1 - 1]: 0;
        int sum = prefix[row2][col2] - (top + left - topLeft);

        return sum;
    }
}


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