304. Range Sum Query 2D - Immutable

class NumMatrix {

    private final int[][] sumMatrix; // 从左上角至当前节点形成矩形的和

    public NumMatrix(int[][] matrix) {
        int m = matrix.length, n = matrix[0].length;
        this.sumMatrix = new int[m + 1][n + 1]; // 多申请一个是避免处理索引越界的情况

        for (int i = 1; i <= m; i++) {
            for (int j = 1; j <= n; j++) {
                this.sumMatrix[i][j] = this.sumMatrix[i - 1][j] + this.sumMatrix[i][j - 1] - this.sumMatrix[i - 1][j - 1] + matrix[i - 1][j - 1];
            }
        }
    }

    public int sumRegion(int row1, int col1, int row2, int col2) {
        // 对齐为 sumMatrix 中的下标
        row1++;
        col1++;
        row2++;
        col2++;

        return sumMatrix[row2][col2] - sumMatrix[row2][col1 - 1] - sumMatrix[row1 - 1][col2] + sumMatrix[row1 - 1][col1 - 1];
    }

}

References

304. Range Sum Query 2D - Immutable
剑指 Offer II 013. 二维子矩阵的和