304. Range Sum Query 2D

304. Range Sum Query 2D - Immutable

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.

cache sums from (0,0) to (i,j)

class NumMatrix {
    int[][] sums;
    public NumMatrix(int[][] matrix) {
        if(!(matrix == null || matrix.length == 0 || matrix[0] == null || matrix[0].length == 0)) {
            sums = new int[matrix.length][matrix[0].length];
            for(int i = 0 ; i< sums.length; i++) {
                sums[i][0] = matrix[i][0];
                for(int j = 1; j < matrix[0].length; j++) {
                    sums[i][j] = matrix[i][j] + sums[i][j-1];
                }
            }
            for(int i = 1; i < sums.length; i++) {
                for(int j = 0; j < sums[0].length; j++) {
                    sums[i][j] += sums[i-1][j];
                }
            }
        }

    }
    public int sumRegion(int row1, int col1, int row2, int col2) {
        if(sums == null) return -1;
        int total = sums[row2][col2];
        int sub1 = row1 == 0 ? 0 : sums[row1-1][col2];
        int sub2 = col1 == 0 ? 0 : sums[row2][col1-1];
        int sub3 = row1 * col1 == 0 ? 0 : sums[row1-1][col1-1];
        return total - sub1 - sub2 + sub3;
    }
  }

Calculate all sums TLE pass 11/12

class NumMatrix {
    int[][][][] dp;
    int[][] matrix;

    public NumMatrix(int[][] matrix) {
        if(!(matrix == null || matrix.length == 0 || matrix[0] == null || matrix[0].length == 0)) {
            this.matrix = matrix;
            int n = matrix.length, m = matrix[0].length;
            dp = new int[n][m][n][m];
            for(int area = 1; area <= m*n; area++) {
                for(int a = 1; a <= area; a++) {
                    if(area % a != 0) continue;
                    int b = area / a;
                    for(int i = 0; i < n; i++) {
                        for(int j = 0; j < m; j++) {
                            int r = i + a - 1, c = j + b - 1;
                            if(r >= n || c >= m) continue;
                            if(r == i && c == j) dp[i][j][r][c] = matrix[i][j];
                            else if(a==1) {
                                dp[i][j][r][c] = dp[i][j][r][c-1] + matrix[r][c];
                            } else if(b==1) {
                                dp[i][j][r][c] = dp[i][j][r-1][c] + matrix[r][c];
                            } else {
                                dp[i][j][r][c] = dp[i][j][r][c-1] + dp[i][c][r][c];
                            }
                        }
                    }
                }
            }
        }
        System.out.println("fin");
    }
    public int sumRegion(int row1, int col1, int row2, int col2) {
        if(matrix == null) return -1;
        return dp[row1][col1][row2][col2];
    }