segment tree线段树 Range Sum Query - Mutable

最新推荐文章于 2021-07-06 17:43:54 发布

原创最新推荐文章于 2021-07-06 17:43:54 发布 · 207 阅读

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本文介绍了一种高效的数据结构——段树，用于快速处理区间查询和更新操作。段树是一种二叉树，每个节点包含数组子范围的聚合信息，如最小值、最大值或总和等。文章详细解释了如何自底向上构建段树，以及如何更新段树中特定位置的值，并提供了一个范围求和查询的方法。

The segment tree for array a[0,1,…,n−1] is a binary tree in which each node contains aggregate information (min, max, sum, etc.) for a subrange [i…j]of the array, as its left and right child hold information for range [i…(i+j)/2]and [(i+j)/2+1,j].

bottom-up approach

Build segment tree

int[] tree;
int n;
public NumArray(int[] nums) {
    if (nums.length > 0) {
        n = nums.length;
        tree = new int[n * 2];
        buildTree(nums);
    }
}
private void buildTree(int[] nums) {
    for (int i = n, j = 0;  i < 2 * n; i++,  j++)
        tree[i] = nums[j];
    for (int i = n - 1; i > 0; --i)
        tree[i] = tree[i * 2] + tree[i * 2 + 1];
}

Update segment tree

void update(int pos, int val) {
    pos += n;
    tree[pos] = val;
    while (pos > 0) {
        int left = pos;
        int right = pos;
        if (pos % 2 == 0) {
            right = pos + 1;
        } else {
            left = pos - 1;
        }
        // parent is updated after child is updated
        tree[pos / 2] = tree[left] + tree[right];
        pos /= 2;
    }
}

Range Sum Query

public int sumRange(int l, int r) {
    // get leaf with value 'l'
    l += n;
    // get leaf with value 'r'
    r += n;
    int sum = 0;
    while (l <= r) {
        if ((l % 2) == 1) {
           sum += tree[l];
           l++;
        }
        if ((r % 2) == 0) {
           sum += tree[r];
           r--;
        }
        l /= 2;
        r /= 2;
    }
    return sum;
}