LeetCode -- Range Sum Query 2D - Immutable

public class NumMatrix {        PRivate int[,] _matrix;        private int[,] _sum;        public NumMatrix(int[,] matrix) {            _matrix = matrix;    		CreateCache();        }            public int SumRegion(int row1, int col1, int row2, int col2) {    		// get the all    		var areaTotal = _sum[row2, col2];     		    		// remove the left side sum    		var areaLeft = col1 > 0 ? _sum[row2, col1-1] : 0;    		// remove the top side sum    		var areaTop = row1 > 0 ? _sum[row1-1, col2] : 0;    		    		var result = areaTotal - areaLeft - areaTop;    		// check if there is overlay between top area and left area    		if(row1 > 0 && col1 > 0){    			var common = _sum[row1-1,col1-1];    			result += common;    		}    		return result;        }    	    	private void CreateCache(){    		var rows = _matrix.GetLength(0);    		var columns = _matrix.GetLength(1);    		if(rows == 0 && columns == 0){    			return ;    		}    		    		    		_sum = new int[rows,columns];    		    		// init the first row and column value    		_sum[0,0] = _matrix[0,0];    		for (var i = 1;i < rows;i ++){    			_sum[i,0] = _matrix[i,0] + _sum[i-1,0];    		}    		for (var j = 1;j < columns; j++){    			_sum[0,j] = _matrix[0,j] + _sum[0, j-1];    		}    		    		// from top to bottom , left to right    		// cache the sum value of each rect    		for (var i = 1;i < rows; i++){    			for (var j = 1;j < columns; j++){    				_sum[i,j] = _matrix[i,j]+ _sum[i,j-1] + _sum[i-1, j] - _sum[i-1,j-1];    			}    		}    		    	//	Console.WriteLine(_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);