Leetcode Range Sum Query 2d-immutable

Given a 2D matrix matrix, find the sum of the elements inside the rectangle defined by it upper left corner ( row1, Col1) and lower right corner ( row2, Col2).

The above rectangle (with the red border) are defined by (row1, col1) = (2, 1) and (Row2, col2) = (4, 3), which contains Su m = 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), 8sumRegion (1, 1, 2, 2), 11sumRegion (1, 2, 2, 4), 12

Note:

1. Assume that the matrix does not a change.
2. There is many calls to sumregion function.
3. Assume that row1≤ row2 and Col1≤ Col2.

Problem Solving Ideas:

Dynamic programming m is the matrix row, and n is the matrix column where the matrix is empty.

Establish ACCU = new Int[m+1][n+1], first row and first column 0

Value of each coordinate recurrence formula:accu[i][j] = Accu[i-1][j] + accu[i][j-1]-accu[i-1][j-1] + matrix[i-1][j-1]

The selected rectangle interval drawing indicates that the values are determined by 4 vertices,

Formula: Accu[row2+1][col2+1]-accu[row2+1][col1]-accu[row1][col2+1] + accu[row1][col1]

Java Code:

 Public classNummatrix {Private int[] accu;  PublicNummatrix (int[] matrix) {        if(Matrix = =NULL|| Matrix.length = = 0) {            return; }        intm =matrix.length; intn = matrix[0].length; Accu=New int[M+1] [N+1]; //base Case first Row/column are 0 default is 0         for(inti = 1; i<= m; i++){             for(intj = 1; J <= N; J + +) {Accu[i][j]= Accu[i-1][j] + accu[i][j-1]-accu[i-1][j-1] + matrix[i-1][j-1]; }         }    }     Public intSumregion (intRow1,intCol1,intRow2,intcol2) {        returnACCU[ROW2+1][COL2+1]-accu[row2+1][col1]-accu[row1][col2+1] +Accu[row1][col1]; }}//Your Nummatrix object would be instantiated and called as such://Nummatrix Nummatrix = new Nummatrix (matrix);//nummatrix.sumregion (0, 1, 2, 3);//nummatrix.sumregion (1, 2, 3, 4);

Reference:

1. Https://leetcode.com/discuss/69054/dp-java-solution

2. Https://leetcode.com/discuss/69315/an-easy-c-dp-solution-with-simple-explanation

Leetcode Range Sum Query 2d-immutable