线段树学习笔记

让我们来一步一步理解！

1.向上更新

void push_up(int rt){//向上更新
    sum[rt] = sum[rt << 1] + sum[rt << 1 | 1];
}

2.向下更新

void push_down(int rt, int m){
    if(add[rt]){//若有标记,则将标记向下移动一层
        add[rt << 1] += add[rt];
        add[rt << 1 | 1] += add[rt];
        sum[rt << 1] += (m - (m >> 1)) * add[rt];
        sum[rt << 1 | 1] += (m >> 1) * add[rt];
        add[rt] = 0;//取消本层标记
    }
}

3.开始建树

void build(int l, int r, int rt){//建树
    add[rt] = 0;
    if(l == r){
        scanf("%lld", &sum[rt]);
        return;
    }
    int mid = (l + r) >> 1;
    build(lson);
    build(rson);
    push_up(rt);//向上更新
}

4.区间更新

void update(int L, int R, ll key, int l, int r, int rt){//区间更新
    if(L <= l && R >= r){
　　//该区间是完整的
        sum[rt] += (r - l + 1) * key;
        add[rt] += key;
        return;
    }
    push_down(rt, r - l + 1);//向下更新,下传标记
    int mid = (l + r) >> 1;
    if(L <= mid) update(L, R, key, lson);
    if(R > mid) update(L, R, key, rson);
    push_up(rt);//向上更新
}

5.区间求和

int query(int L, int R, int l, int r, int rt){//区间求和
    if(L <= l && R >= r) return sum[rt];
    push_down(rt, r - l + 1);//向下更新
    int mid = (l + r) >> 1;
    int ans = 0;
    if(L <= mid) ans += query(L, R, lson);
    if(R > mid) ans += query(L, R, rson);
    return ans;
}

例题：poj 3468 3468 -- A Simple Problem with Integers (poj.org)

线段树裸题！

#include<bits/stdc++.h>
#define ll long long
#define lson l, mid, rt << 1
#define rson mid + 1, r, rt << 1 | 1

using namespace std;

const int MAXN = 1e5 + 10;
ll sum[MAXN << 2];
ll add[MAXN << 2];

void push_up(int rt){//向上更新
    sum[rt] = sum[rt << 1] + sum[rt << 1 | 1];
}

void push_down(int rt, int m){
    if(add[rt]){//若有标记,则将标记向下移动一层
        add[rt << 1] += add[rt];
        add[rt << 1 | 1] += add[rt];
        sum[rt << 1] += (m - (m >> 1)) * add[rt];
        sum[rt << 1 | 1] += (m >> 1) * add[rt];
        add[rt] = 0;//取消本层标记
    }
}

void build(int l, int r, int rt){//建树
    add[rt] = 0;
    if(l == r){
        scanf("%lld", &sum[rt]);
        return;
    }
    int mid = (l + r) >> 1;
    build(lson);
    build(rson);
    push_up(rt);//向上更新
}

void update(int L, int R, ll key, int l, int r, int rt){//区间更新
    if(L <= l && R >= r){
        sum[rt] += (r - l + 1) * key;
        add[rt] += key;
        return;
    }
    push_down(rt, r - l + 1);//向下更新
    int mid = (l + r) >> 1;
    if(L <= mid) update(L, R, key, lson);
    if(R > mid) update(L, R, key, rson);
    push_up(rt);//向上更新
}

ll query(int L, int R, int l, int r, int rt){//区间求和
    if(L <= l && R >= r) return sum[rt];//该区间完整
    push_down(rt, r - l + 1);//向下更新
    int mid = (l + r) >> 1;
    ll ans = 0;
    if(L <= mid) ans += query(L, R, lson);
    if(R > mid) ans += query(L, R, rson);
    return ans;
}

int main(void){
    int n, m;
    scanf("%d%d", &n, &m);
    build(1, n, 1);
    while(m--){
        char op[3];
        int x, y;
        ll z;
        scanf("%s", op);
        if(op[0] == 'C'){
            cin>>x>>y>>z;
            update(x, y, z, 1, n, 1);
        }else{
            cin>>x>>y;
            printf("%lld\n", query(x, y, 1, n, 1));
        }
    }
}