【数据结构】线段树算法总结（区间修改）

知识概览

线段树一般有5个操作：

1. pushup：用子节点更新当前节点信息
2. pushdown：把懒标记往下传
3. build：初始化一棵树
4. modify：修改一个区间
5. query：查询一个区间

不带懒标记（支持单点修改）的线段树算法见本人博客：

【数据结构】线段树算法总结（单点修改）-CSDN博客文章浏览阅读81次，点赞2次，收藏3次。【代码总结】线段树算法总结（单点修改）https://blog.csdn.net/u012181348/article/details/135119627?spm=1001.2014.3001.5501

例题展示

题目链接

243. 一个简单的整数问题2 - AcWing题库https://www.acwing.com/problem/content/244/

代码

#include 
#include 
#include 
#include 

using namespace std;

typedef long long LL;

const int N = 100010;

int n, m;
int w[N];
struct Node
{
    int l, r;
    LL sum, add;
} tr[N * 4];

void pushup(int u)
{
    tr[u].sum = tr[u << 1].sum + tr[u << 1 | 1].sum;
}

void pushdown(int u)
{
    auto &root = tr[u], &left = tr[u << 1], &right = tr[u << 1 | 1];
    if (root.add)
    {
        left.add += root.add, left.sum += (LL)(left.r - left.l + 1) * root.add;
        right.add += root.add, right.sum += (LL)(right.r - right.l + 1) * root.add;
        root.add = 0;
    }
}

void build(int u, int l, int r)
{
    if (l == r) tr[u] = {l, r, w[r], 0};
    else
    {
        tr[u] = {l, r};
        int mid = l + r >> 1;
        build(u << 1, l, mid), build(u << 1 | 1, mid + 1, r);
        pushup(u);
    }
}

void modify(int u, int l, int r, int d)
{
    if (tr[u].l >= l && tr[u].r <= r)
    {
        tr[u].sum += (LL)(tr[u].r - tr[u].l + 1) * d;
        tr[u].add += d;
    }
    else    // 一定要分裂
    {
        pushdown(u);
        int mid = tr[u].l + tr[u].r >> 1;
        if (l <= mid) modify(u << 1, l, r, d);
        if (r > mid) modify(u << 1 | 1, l, r, d);
        pushup(u);
    }
}

LL query(int u, int l, int r)
{
    if (tr[u].l >= l && tr[u].r <= r) return tr[u].sum;

    pushdown(u);
    int mid = tr[u].l + tr[u].r >> 1;
    LL sum = 0;
    if (l <= mid) sum = query(u << 1, l, r);
    if (r > mid) sum += query(u << 1 | 1, l, r);
    return sum;
}

int main()
{
    scanf("%d%d", &n, &m);
    for (int i = 1; i <= n; i++) scanf("%d", &w[i]);
    build(1, 1, n);

    char op[2];
    int l, r, d;
    while (m--)
    {
        scanf("%s%d%d", op, &l, &r);
        if (*op == 'C')
        {
            scanf("%d", &d);
            modify(1, l, r, d);
        }
        else printf("%lld\n", query(1, l, r));
    }

    return 0;
}

参考资料

1. AcWing算法提高课