• 所有题， Immutable的题用prefix sum，Mutable的题用Segment Tree
  303. Range Sum Query - Immutable
  304. Range Sum Query 2D - Immutable
  307. Range Sum Query - Mutable
  308. Range Sum Query 2D - Mutable

303. Range Sum Query - Immutable

1-D prefix sum

304. Range Sum Query 2D - Immutable

2D_range_sum.jpeg

class NumMatrix {
    //pre[i][j] is the sum of rectangle from (0, 0) to (i-1, j-1)
    int[][] pre;
    public NumMatrix(int[][] matrix) {
        if (matrix.length == 0 || matrix[0].length == 0) return;
        int m = matrix.length, n = matrix[0].length;
        pre = new int[m+1][n+1];
        for (int i = 1; i <= m; i++) {
            for (int j = 1; j <= n; j++) {
                pre[i][j] = pre[i-1][j] + pre[i][j-1] - pre[i-1][j-1] + matrix[i-1][j-1];
            }
        }
    }
    
    public int sumRegion(int r1, int c1, int r2, int c2) {
        //(r1, c1)     (r1, c2)
        //(r2, c1)     (r2, c2)
        return pre[r2+1][c2+1] - pre[r1][c2+1] - pre[r2+1][c1] + pre[r1][c1];    
    }
}

307. Range Sum Query - Mutable

SegmentTree_1.jpeg

SegmentTree_2.jpeg

class NumArray {
    class STNode {
        int begin, end, sum;
        STNode left, right;
        public STNode(int begin, int end, int sum) {
            this.begin = begin;
            this.end = end;
            this.sum = sum;
        }
    }
    class SegmentTree {
        STNode root;
        public SegmentTree(int[] nums) {
            root = build(0, nums.length-1, nums);
        }
        public STNode build(int begin, int end, int[] nums) {
            if (begin == end) {
                return new STNode(begin, end, nums[begin]);
            } 
            int mid = begin + (end - begin) / 2;
            STNode left = build(begin, mid, nums);
            STNode right = build(mid + 1, end, nums);
            STNode root = new STNode(begin, end, left.sum + right.sum);
            root.left = left;
            root.right = right;
            return root;
        } 
        public void update(STNode root, int index, int val) { //update a leave
            if (root.begin == root.end && root.begin == index) {
                root.sum = val;
                return;
            }
            int mid = root.begin + (root.end - root.begin) / 2;
            //如果index小于等于mid，leaf to be updated is in the left sub tree
            //else, it is in the right sub tree
            if (index <= mid) {
                update(root.left, index, val);
            } else {
                update(root.right, index, val);
            }
            root.sum = (root.left == null ? 0 : root.left.sum) + 
                    (root.right == null ? 0 : root.right.sum);
        } 
        public int query(STNode root, int i, int j) {
            if (root.begin == i && root.end == j) {
                return root.sum;
            }
            int mid = root.begin + (root.end - root.begin) / 2;
            if (j <= mid) {
                return query(root.left, i, j);
            } else if (i >= mid+1) {
                return query(root.right, i, j);
            } else {
                return query(root.left, i, mid) + query(root.right, mid + 1, j);
            }
        }
    }
    
    SegmentTree st;
    public NumArray(int[] nums) {
        if (nums == null || nums.length == 0) return;
        st = new SegmentTree(nums);    
    }
    
    public void update(int i, int val) {
        st.update(st.root, i, val);
    }
    
    public int sumRange(int i, int j) {
        return st.query(st.root, i, j);
    }
}

/**
 * Your NumArray object will be instantiated and called as such:
 * NumArray obj = new NumArray(nums);
 * obj.update(i,val);
 * int param_2 = obj.sumRange(i,j);
 */