package leetcode_1To300;

/**
 * 本代码来自 Cspiration，由 @Cspiration 提供
 * 题目来源：http://leetcode.com
 * - Cspiration 致力于在 CS 领域内帮助中国人找到工作，让更多海外国人受益
 * - 现有课程：Leetcode Java 版本视频讲解（1-900题）（上）（中）（下）三部
 * - 算法基础知识（上）（下）两部；题型技巧讲解（上）（下）两部
 * - 节省刷题时间，效率提高2-3倍，初学者轻松一天10题，入门者轻松一天20题
 * - 讲师：Edward Shi
 * - 官方网站：https://cspiration.com
 * - 版权所有，转发请注明出处
 */
public class _308_RangeSumQuery2DMutable {

    /**
     * 308. Range Sum Query 2D - Mutable
     */
    int[][] tree;
    int[][] nums;
    int m;
    int n;

    // time : O(m * logm * n * logn)
    public _308_RangeSumQuery2DMutable(int[][] matrix) {
        if (matrix.length == 0 || matrix[0].length == 0) return;
        m = matrix.length;
        n = matrix[0].length;
        tree = new int[m + 1][n + 1];
        nums = new int[m][n];
        for (int i = 0; i < m; i ++) {
            for (int j = 0; j < n; j++) {
                update(i, j, matrix[i][j]);
            }
        }
    }

    // time : O(logm * logn)
    public void update(int row, int col, int val) {
        if (m == 0 || n == 0) return;
        int diff = val - nums[row][col];
        nums[row][col] = val;
        for (int i = row + 1; i <= m; i += i & (-i)) {
            for (int j = col + 1; j <= n; j += j & (-j)) {
                tree[i][j] += diff;
            }
        }
    }

    // time : O(logm * logn)
    public int sumRegion(int row1, int col1, int row2, int col2) {
        if (m == 0 || n == 0) return 0;
        return sum(row2 + 1, col2 + 1) + sum(row1, col1)
                - sum(row1, col2 + 1) - sum(row2 + 1, col1);
    }

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