线段树模板

合集 - 学习笔记/模板(11)

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8.线段树模板2024-02-20

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开局宏定义：

#include<bits/stdc++.h>
#define int long long
#define lson (now << 1)//现结点的左孩子
#define rson (now << 1 | 1)//右孩子
using namespace std;

结构体定义：

struct Node{
    int l ,r;  //表示左右区间
    int max, sum; //其他数据域
}tree[N << 2] //=N*4，N指节点个数

常规操作

• 向上回溯：

void push_up(int now){
    tree[now].sum = tree[lson].sum + tree[rson].sum;
    tree[now].max = max(tree[lson].max, tree[rson].max);
}

• 建树：

void build(int now, int l, int r) {
    tree[now].left = l; tree[now].right = r;

    if(l == r){
        tree[now].sum = a[l];
        return;
    }

    int mid = (l + r) >> 1;
    build(lson, l, mid),build(rson, mid+1, r);

    push_up(now);
}

• 单点更新:

void update(int now, int pos, int key){
    if(l == r){
        tree[now].sum = tree[now].max = key;
        return;        
    }

    int mid = (tree[now].left + tree[now].right) >> 1;

    if(pos <= mid) update(lson, pos, key);
    else update(rson, pos, key);

    push_up(now);
}

• 查询区间和：

 int query(int now, int l, int r){
    int s = 0;
    if( l <= tree[now].left and tree[now].right <= r)
          return tree[now],sum;
    
    int mid = (tree[now].left + tree[now].rigth) >> 1;

    if(l <= mid) s += query(lson, l, r);
    if(r > mid) s += query(rson, l, r);
    return s;
}

区间更新操作

• 区间更新:

 int update (int now, int l, int r, int val){
    if(l <= tree[now].left and tree[now].right <= r){
        tree[now].lazy += val;
        tree[now].sum += val * (tree[now].right - tree[now].left + 1);
        return;
    }

    push_down(now);
    int mid = (tree[now].left + tree[now].right) >> 1;
    if(l <= mid) update(lson, l, r, val);
    if(r > mid) update(rson, l, r, val);

    push_up(now);
}

• 延迟标记：

void push_down(int now){
    if(tree[now].lazy){
        int lz = tree[now].lazy;
        tree[now].lazy = 0;
        tree[lson].lazy += lz;
        tree[rson].lazy += lz;
        tree[lson].sum += lz * (tree[lson].right - tree[lson].left + 1);
        tree[rson].sum += lz * (tree[rson].right - tree[rson].left + 1); 
     }
}

• 查询区间和（区间更新版）：

int query(int now, int l, int r){
    int sum = 0;
    if(l <= tree[now].left and tree[now].right <= r)
        return tree[now].sum;

    push_down(now);
    int mid = (tree[now].left + tree[now].right) >> 1;
    if(l <= mid) sum += query(lson, l, r);
    if(r > mid)  sum += query(rson, l, r);

    return sum;
}