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package g0301_0400.s0304_range_sum_query_2d_immutable;

// #Medium #Array #Matrix #Design #Prefix_Sum #Dynamic_Programming_I_Day_14
// #Programming_Skills_II_Day_13 #Udemy_2D_Arrays/Matrix
// #2022_07_07_Time_153_ms_(87.51%)_Space_133.5_MB_(19.29%)

/**
 * 304 - Range Sum Query 2D - Immutable\.
 *
 * Medium
 *
 * Given a 2D matrix `matrix`, handle multiple queries of the following type:
 *
 * *   Calculate the **sum** of the elements of `matrix` inside the rectangle defined by its **upper left corner** `(row1, col1)` and **lower right corner** `(row2, col2)`.
 *
 * Implement the NumMatrix class:
 *
 * *   `NumMatrix(int[][] matrix)` Initializes the object with the integer matrix `matrix`.
 * *   `int sumRegion(int row1, int col1, int row2, int col2)` Returns the **sum** of the elements of `matrix` inside the rectangle defined by its **upper left corner** `(row1, col1)` and **lower right corner** `(row2, col2)`.
 *
 * **Example 1:**
 *
 * ![](https://assets.leetcode.com/uploads/2021/03/14/sum-grid.jpg)
 *
 * **Input**
 *
 *     ["NumMatrix", "sumRegion", "sumRegion", "sumRegion"]
 *     [[[[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]]], [2, 1, 4, 3], [1, 1, 2, 2], [1, 2, 2, 4]]
 *
 * **Output:** [null, 8, 11, 12]
 *
 * **Explanation:**
 *
 *     NumMatrix numMatrix = new NumMatrix([[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]]);
 *     numMatrix.sumRegion(2, 1, 4, 3); // return 8 (i.e sum of the red rectangle)
 *     numMatrix.sumRegion(1, 1, 2, 2); // return 11 (i.e sum of the green rectangle)
 *     numMatrix.sumRegion(1, 2, 2, 4); // return 12 (i.e sum of the blue rectangle) 
 *
 * **Constraints:**
 *
 * *   `m == matrix.length`
 * *   `n == matrix[i].length`
 * *   `1 <= m, n <= 200`
 * *   -10⁵ <= matrix[i][j] <= 10⁵
 * *   `0 <= row1 <= row2 < m`
 * *   `0 <= col1 <= col2 < n`
 * *   At most 10⁴ calls will be made to `sumRegion`.
**/
public class NumMatrix {
    private int[][] tot;

    public NumMatrix(int[][] matrix) {
        if (matrix == null || matrix.length == 0 || matrix[0].length == 0) {
            return;
        }
        // The dimensions of this tot matrix is actually 1 bigger than the given matrix, cool!
        tot = new int[matrix.length + 1][matrix[0].length + 1];
        for (int i = 0; i < matrix.length; i++) {
            for (int j = 0; j < matrix[0].length; j++) {
                tot[i + 1][j + 1] = matrix[i][j] + tot[i + 1][j] + tot[i][j + 1] - tot[i][j];
            }
        }
    }

    public int sumRegion(int row1, int col1, int row2, int col2) {
        return tot[row2 + 1][col2 + 1]
                - tot[row2 + 1][col1]
                - tot[row1][col2 + 1]
                + tot[row1][col1];
    }
}

/*
 * Your NumMatrix object will be instantiated and called as such:
 * NumMatrix obj = new NumMatrix(matrix);
 * int param_1 = obj.sumRegion(row1,col1,row2,col2);
 */