[hiho 20]线段树的区间修改

题目描述

区间修改有别于单点修改，如果每次都修改到叶子节点，复杂度可以退化到O(n)。

因此为节点引入一个lazy标记，修改时，如果待修改区间与某个节点的区间重合，那么这个节点更新值后标记lazy，不再修改其子节点。

类似于查询操作，这个修改操作的复杂度是O(logn)。

另外，查询或修改时，如果遇到已经标记了lazy的节点，需要先将lazy标记下放到两个子节点，再进行后续处理。

#include <stdio.h>
#include <algorithm>

typedef
struct _seg_tree_ {
    int left, right;
    int val;
    bool lazy_tag;
    _seg_tree_ *lson = NULL, *rson = NULL;
    _seg_tree_(int left_idx, int right_idx, int value)
        : left(left_idx), right(right_idx), val(value), lazy_tag(false) {}
} seg_tree, *pseg_tree;

pseg_tree construct_seg_tree(int left, int right) {
    if (left == right) {
        int val;
        scanf("%d", &val);
        return new seg_tree(left, left, val);
    }
    int mid = left + (right - left) / 2;
    pseg_tree lson = construct_seg_tree(left, mid);
    pseg_tree rson = construct_seg_tree(mid + 1, right);
    int val = lson->val + rson->val;
    pseg_tree ans = new seg_tree(left, right, val);
    ans->lson = lson;
    ans->rson = rson;
    return ans;
}

void lazy_down(pseg_tree proot) {
    int mid = proot->left + (proot->right - proot->left) / 2;
    proot->lazy_tag = false;
    int x = proot->val / (proot->right - proot->left + 1);
    proot->lson->lazy_tag = true;
    proot->lson->val = x * (mid - proot->lson->left + 1);
    proot->rson->lazy_tag = true;
    proot->rson->val = x * (proot->rson->right - mid);
}

int query_seg_tree(pseg_tree proot, int left, int right) {
    if (left == proot->left && right == proot->right) {
        return proot->val;
    }

    int mid = proot->left + (proot->right - proot->left) / 2;
    if (proot->lazy_tag == true) {
        lazy_down(proot);
    }
    if (left > mid) {
        return query_seg_tree(proot->rson, left, right);
    }
    if (right <= mid) {
        return query_seg_tree(proot->lson, left, right);
    }
    return query_seg_tree(proot->lson, left, mid)
        + query_seg_tree(proot->rson, mid + 1, right);
}

void modify_seg_tree(pseg_tree proot, int left, int right, int val) {
    if (left == proot->left && right == proot->right) {
        proot->val = val * (right - left + 1);
        proot->lazy_tag = true;
        return;
    }
    int mid = proot->left + (proot->right - proot->left) / 2;
    if (proot->lazy_tag == true) {
        lazy_down(proot);
    }
    if (left > mid) {
        modify_seg_tree(proot->rson, left, right, val);
    }
    else if (right <= mid) {
        modify_seg_tree(proot->lson, left, right, val);
    }
    else {
        modify_seg_tree(proot->rson, mid + 1, right, val);
        modify_seg_tree(proot->lson, left, mid, val);
    }
    proot->val = proot->lson->val + proot->rson->val;
}

int main(){
    int n, q;
    scanf("%d", &n);
    pseg_tree proot = construct_seg_tree(1, n);
    scanf("%d", &q);
    int op, left, right, value;
    while (q--) {
        scanf("%d%d%d", &op, &left, &right);
        if (op == 0) {
            int ans = query_seg_tree(proot, left, right);
            printf("%d\n", ans);
        } else {
            scanf("%d", &value);
            modify_seg_tree(proot, left, right, value);
        }
    }

    return 0;
}