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【数据结构】线段树

news 来源：原创 2024/9/20 12:03:05

最大数

最大数
两种操作：

添加操作：向序列后添加一个数，序列长度变成 $n + 1$ ；
询问操作：询问这个序列中最后 $L$ 个数中最大的数是多少。

#include<iostream>
using namespace std;
#define ll long long
int m,p;
struct Tree{int l,r;ll v;
}tr[800001];void pushup(int id){tr[id].v=max(tr[id*2].v,tr[id*2+1].v);
}void bui(int id,int l,int r){// cout<<l<<" "<<r<<endl;tr[id]={l,r,0};if(l==r){tr[id].v=0;return ;}int mid=l+r>>1;bui(id*2,l,mid);bui(id*2+1,mid+1,r);pushup(id);
}ll query(int id,int x,int y){if(x<=tr[id].l&&tr[id].r<=y){return tr[id].v;}int mid=tr[id].l+tr[id].r>>1;ll res=0;if(x<=mid)res=max(res,query(id*2,x,y));if(y>=mid+1)res=max(res,query(id*2+1,x,y));return res;
}void modify(int id,int x,ll k){if(tr[id].l==x&&tr[id].r==x){tr[id].v=k;return ;}int mid=(tr[id].l+tr[id].r)>>1;if(x<=mid)modify(id*2,x,k);if(x>=mid+1)modify(id*2+1,x,k);pushup(id);
}int main(){cin>>m>>p;ll last =0;int len=0;bui(1,0,200000);while(m--){char a;cin>>a;if(a=='Q'){int l;cin>>l;last=query(1,len-l+1,len);//len-len+l-1+1cout<<last<<endl;}else {ll t;cin>>t;modify(1,len+1,(t+last)%p);len++;}}}

最大连续字段和

#include <cstdio>
#include <cstring>
#include <iostream>
#include <algorithm>using namespace std;const int N = 500010;int n, m;
int w[N];
struct Node
{int l, r;int sum, lmax, rmax, tmax;
}tr[N * 4];void pushup(Node &u, Node &l, Node &r)
{u.sum = l.sum + r.sum;u.lmax = max(l.lmax, l.sum + r.lmax);u.rmax = max(r.rmax, r.sum + l.rmax);u.tmax = max(max(l.tmax, r.tmax), l.rmax + r.lmax);
}void pushup(int u)
{pushup(tr[u], tr[u << 1], tr[u << 1 | 1]);
}void build(int u, int l, int r)
{if (l == r) tr[u] = {l, r, w[r], w[r], w[r], w[r]};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 x, int v)
{if (tr[u].l == x && tr[u].r == x) tr[u] = {x, x, v, v, v, v};else{int mid = tr[u].l + tr[u].r >> 1;if (x <= mid) modify(u << 1, x, v);else modify(u << 1 | 1, x, v);pushup(u);}
}Node query(int u, int l, int r)
{if (tr[u].l >= l && tr[u].r <= r) return tr[u];else{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{auto left = query(u << 1, l, r);auto right = query(u << 1 | 1, l, r);Node res;pushup(res, left, right);return res;}}
}int main()
{scanf("%d%d", &n, &m);for (int i = 1; i <= n; i ++ ) scanf("%d", &w[i]);build(1, 1, n);int k, x, y;while (m -- ){scanf("%d%d%d", &k, &x, &y);if (k == 1){if (x > y) swap(x, y);printf("%d\n", query(1, x, y).tmax);}else modify(1, x, y);}return 0;
}

区间最大公约数差分

d=(a1,a2,a3,…)=(a1,a2-a1,a3-a2,…)

#include <cstdio>
#include <cstring>
#include <iostream>
#include <algorithm>using namespace std;typedef long long LL;const int N = 500010;int n, m;
LL w[N];
struct Node
{int l, r;LL sum, d;
}tr[N * 4];LL gcd(LL a, LL b)
{return b ? gcd(b, a % b) : a;
}void pushup(Node &u, Node &l, Node &r)
{u.sum = l.sum + r.sum;u.d = gcd(l.d, r.d);
}void pushup(int u)
{pushup(tr[u], tr[u << 1], tr[u << 1 | 1]);
}void build(int u, int l, int r)
{if (l == r){LL b = w[r] - w[r - 1];tr[u] = {l, r, b, b};}else{tr[u].l = l, tr[u].r = 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 x, LL v)
{if (tr[u].l == x && tr[u].r == x){LL b = tr[u].sum + v;tr[u] = {x, x, b, b};}else{int mid = tr[u].l + tr[u].r >> 1;if (x <= mid) modify(u << 1, x, v);else modify(u << 1 | 1, x, v);pushup(u);}
}Node query(int u, int l, int r)
{if (tr[u].l >= l && tr[u].r <= r) return tr[u];else{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{auto left = query(u << 1, l, r);auto right = query(u << 1 | 1, l, r);Node res;pushup(res, left, right);return res;}}
}int main()
{scanf("%d%d", &n, &m);for (int i = 1; i <= n; i ++ ) scanf("%lld", &w[i]);build(1, 1, n);int l, r;LL d;char op[2];while (m -- ){scanf("%s%d%d", op, &l, &r);if (*op == 'Q'){auto left = query(1, 1, l);Node right({0, 0, 0, 0});if (l + 1 <= r) right = query(1, l + 1, r);printf("%lld\n", abs(gcd(left.sum, right.d)));}else{scanf("%lld", &d);modify(1, l, d);if (r + 1 <= n) modify(1, r + 1, -d);}}return 0;
}