题目

代码

下面的两个代码的区别在于modify的分类，modify最简单的分类方式是存在性分类，另一种类似某些query采用的三段式分类，详细见代码

存在性

#include <bits/stdc++.h>
using namespace std;
using ll = long long;
const int N = 1e5+10;
int a[N];
struct node
{
    int l, r;
    ll sum;
    ll add;
}tr[4*N];
void pushup(int u)
{
    tr[u].sum = tr[u << 1].sum + tr[u << 1 | 1].sum;
}
void pushdown(int i)
{
    node &u = tr[i], &l = tr[i << 1], &r = tr[i << 1 | 1];
    if(u.add)
    {
        l.add += u.add; r.add += u.add;
        l.sum += (l.r - l.l + 1) * u.add; r.sum += (r.r - r.l + 1) * u.add;
        u.add = 0;
    }
}
void build(int u, int l, int r)
{
    if(l == r) tr[u] = {l, r, a[l], 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 v)
{
    if(l <= tr[u].l && tr[u].r <= r)
    {
        tr[u].add += v;
        tr[u].sum += (ll)(tr[u].r - tr[u].l + 1) * v;
        return;
    }
    pushdown(u);
    int mid = tr[u].l + tr[u].r >> 1;
    if(l <= mid) modify(u << 1, l, r, v);
    if(r > mid) modify(u << 1 | 1, l, r, v);
    pushup(u);
}
ll query(int u, int l, int r)
{
    if(l <= tr[u].l && tr[u].r <= r) return tr[u].sum;
    pushdown(u);
    int mid = tr[u].l + tr[u].r >> 1;
    if(r <= mid) return query(u << 1, l, r);
    else if(l > mid) return query(u << 1 | 1, l, r);
    else
    {
        
        ll ans = 0;
        ans += query(u << 1, l, r);
        ans += query(u << 1 | 1, l, r);
        return ans;
    }
}
int main()
{
    int n, m;
    cin >> n >> m;
    for(int i = 1; i <= n; i++) cin >> a[i];
    
    build(1, 1, n);
    while (m -- )
    {
        char op; int l, r;
        cin >> op >> l >> r;
        if(op == 'C')
        {
            int d;
            cin >> d;
            modify(1, l, r, d);
        }
        else
        {
            cout << query(1, l, r) << '\n';
        }
    }
    
    return 0;
}

三段式

#include <bits/stdc++.h>
using namespace std;
using ll = long long;
const int N = 1e5+10;
int a[N];
struct node
{
    int l, r;
    ll sum;
    ll add;
}tr[4*N];
void pushup(int u)
{
    tr[u].sum = tr[u << 1].sum + tr[u << 1 | 1].sum;
}
void pushdown(int i)
{
    node &u = tr[i], &l = tr[i << 1], &r = tr[i << 1 | 1];
    if(u.add)
    {
        l.add += u.add; r.add += u.add;
        l.sum += (l.r - l.l + 1) * u.add; r.sum += (r.r - r.l + 1) * u.add;
        u.add = 0;
    }
}
void build(int u, int l, int r)
{
    if(l == r) tr[u] = {l, r, a[l], 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 v)
{
    if(l <= tr[u].l && tr[u].r <= r)
    {
        tr[u].add += v;
        tr[u].sum += (ll)(tr[u].r - tr[u].l + 1) * v;
        return;
    }
    pushdown(u);
    int mid = tr[u].l + tr[u].r >> 1;
    if(r <= mid) modify(u << 1, l, r, v);
    else if(l > mid) modify(u << 1 | 1, l, r, v);
    else
    {
        
        modify(u << 1, l, r, v);
        modify(u << 1 | 1, l, r, v);
    }
    pushup(u);
}
ll query(int u, int l, int r)
{
    if(l <= tr[u].l && tr[u].r <= r) return tr[u].sum;
    pushdown(u);
    int mid = tr[u].l + tr[u].r >> 1;
    if(r <= mid) return query(u << 1, l, r);
    else if(l > mid) return query(u << 1 | 1, l, r);
    else
    {
        
        ll ans = 0;
        ans += query(u << 1, l, r);
        ans += query(u << 1 | 1, l, r);
        return ans;
    }
}
int main()
{
    int n, m;
    cin >> n >> m;
    for(int i = 1; i <= n; i++) cin >> a[i];
    
    build(1, 1, n);
    while (m -- )
    {
        char op; int l, r;
        cin >> op >> l >> r;
        if(op == 'C')
        {
            int d;
            cin >> d;
            modify(1, l, r, d);
        }
        else
        {
            cout << query(1, l, r) << '\n';
        }
    }
    
    return 0;
}