Leetcode 307.区域和检索 - 数组可修改（线段树）

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这篇博客详细介绍了线段树的数据结构，用于高效地进行区间求和与单点更新操作。`NumArray` 类实现了线段树，并提供了`buildTree`、`update`和`sumRange`等方法，适用于动态维护数组区间和的问题。

307.区域和检索 - 数组可修改（线段树）

在这里插入图片描述
b站视频详解线段树

class NumArray {

    private int[] tree;
    private int[] nums;
    private int n;

    private void buildTree(int node, int start, int end){
        if(start == end){
            tree[node] = nums[start];
            return;
        }
        int mid = (start + end) / 2;
        int left = node * 2 + 1;
        int right = node * 2 + 2;
        buildTree(left, start, mid);
        buildTree(right, mid + 1, end);
        tree[node] = tree[left] + tree[right];
    }

    private void updateTree(int node, int start, int end, int idx, int val){
        if(start > end) return;
        if(start == end){
            nums[idx] = val;
            tree[node] = val;
        }else{
            int mid = (start + end) / 2;
            int left = node * 2 + 1;
            int right = node * 2 + 2;
            if(idx >= start && idx <= mid){
                updateTree(left, start, mid, idx, val);
            }else{
                updateTree(right, mid + 1, end, idx, val);
            }
            tree[node] = tree[left] + tree[right];
        }
    }

    private int query(int node, int start, int end, int L, int R){
        if(L > end || R < start) return 0;
        if(start == end) return tree[node];
        if(L <= start && end <= R){
            return tree[node];
        }else{
            int mid = (start + end) / 2;
            int left = node * 2 + 1;
            int right = node * 2 + 2;
            int ls = query(left, start, mid, L, R);
            int rs = query(right, mid + 1, end, L, R);
            return ls + rs;
        }
    }

    public NumArray(int[] nums) {
        this.n = nums.length;
        tree = new int[n * 4];
        this.nums = nums;
        buildTree(0, 0, n - 1);
    }
    
    public void update(int index, int val) {
        updateTree(0, 0, n - 1, index, val);
    }
    
    public int sumRange(int left, int right) {
        return query(0, 0, n - 1, left, right);
    }
}

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