本文主要是介绍P6242 【模板】线段树 3（区间最值操作、区间历史最值），希望对大家解决编程问题提供一定的参考价值，需要的开发者们随着小编来一起学习吧！
文章目录
- 【模板】线段树 3（区间最值操作、区间历史最值）](https://www.luogu.com.cn/problem/P6242)
【模板】线段树 3（区间最值操作、区间历史最值）](https://www.luogu.com.cn/problem/P6242)
用线段树维护一个区间最大值、区间最小值
那个B数组不纯纯来捣乱的吗
那不得建两棵线段树
很显然，第一遍自己打的代码是没有仔细思考pushdown和pushup的
先记住现在过了的模板吧
这道题也是一道模板题，需要学一下思路，然后把板子记住
面向题解学习
#include<bits/stdc++.h>using namespace std;
typedef long long ll;
#define ls (u<<1)
#define rs (u<<1|1)
#define mid ((l+r)>>1)
const int N=1e5+10;
ll a[N];struct Tree
{ll add[N<<2];ll maxn[N<<2];ll minn[N<<2];ll sum[N<<2];Tree(){memset(add,0,sizeof add);memset(maxn,0,sizeof maxn);memset(minn,0,sizeof minn);memset(sum,0,sizeof sum);}void pushup(int u){sum[u]=sum[rs]+sum[ls];maxn[u]=max(maxn[ls],maxn[rs]);minn[u]=min(minn[ls],minn[rs]);}void pushdown(int u,int l, int r){}void build(int u,int l, int r){if(l==r){maxn[u]=a[r];minn[u]=a[r];sum[u]=a[r];return ;}build(ls,l,mid);build(rs,mid+1,r);}void pushdown(int u,int l, int r){if(add[u]){sum[ls]=(sum[ls]+(mid-l+1)*add[u]);sum[rs]=(sum[ls]+(r-mid)*add[u]);add[ls]+=add[u];add[rs]+=add[u];}add[u]=0;}void modify_add(int u, int l, int r, int L, int R,ll d){if(L<=l&&r<=R){add[u]+=d;return;}else{pushdown(u,l,r);if(L<=mid) modify_add(ls,l,mid,L,R,d);if(R>mid) modify_add(rs,mid+1,r,L,R,d);pushup(u);}}void modify_min(int u,int l,int r,int L, int R, ll k){if(L<=l&&r<=R){minn[u]=min(minn[u],k);}pushdown(u,l,r);if(L<=mid) modify_min(ls,l,mid,L,R,k);if(R>mid) modify_min(rs,mid+1,r,L,R,k);pushup(u);}ll query_max(int u,int l,int r,int L, int R){if(L<=l&&r<=R){return maxn[u];}pushdown(u,l,r);ll maxn=-(1<<30);if(L<=mid) maxn=max(maxn,query_max(ls,l,mid,L,R));if(R>mid) maxn=max(maxn,query_max(rs,mid+1,r,L,R));return maxn;}ll query_min(int u,int l,int r,int L, int R){if(L<=l&&r<=R){return maxn[u];}pushdown(u,l,r);ll minn=(1<<30);if(L<=mid) minn=min(minn,query_min(ls,l,mid,L,R));if(R>mid) minn=min(minn,query_min(rs,mid+1,r,L,R));return minn;}ll query_sum(int u,int l,int r,int L, int R){if(L<=l&&r<=R){return sum[u];}pushdown(u,l,r);ll ans=0;if(L<=mid) ans+=query_sum(ls,l,mid,L,R);if(R>mid) ans+=query_sum(rs,mid+1,r,L,R);return ans;}}tr[2];signed main()
{int n,m;cin>>n>>m;for(int i=1;i<=n;i++) cin>>a[i];tr[0].build(1,1,n);tr[1].build(1,1,n);while(m--){int op;ll l,r,k,v;cin>>op>>l>>r;if(op==1){cin>>k;tr[0].modify_add(1,l,r,1,n,k);}else if(op==2){cin>>v;tr[0].modify_min(1,l,r,1,n,v);}else if(op==3){cout<<tr[0].query_sum(1,l,r,1,n)<<endl;}else if(op==4){cout<<tr[0].query_max(1,l,r,1,n)<<endl;}else{cout<<tr[1].query_max(1,l,r,1,n)<<endl;}}return 0;
}
学习5，6测试点思路
#include<bits/stdc++.h>using namespace std;
typedef long long ll;
#define ls (u<<1)
#define rs (u<<1|1)
#define mid ((l+r)>>1)
const int N=1e5+10;
ll a[N];
ll l,r,k,v;struct Tree
{ll maxa[N<<2];ll maxb[N<<2];ll minn[N<<2];ll sum[N<<2];ll tag1[N<<2];ll tag2[N<<2];Tree(){memset(maxa,0,sizeof maxa);memset(maxb,0,sizeof maxb);memset(minn,0,sizeof minn);memset(sum,0,sizeof sum);memset(tag1,0,sizeof tag1);memset(tag2,0,sizeof tag2);}void pushup(int u){sum[u]=sum[rs]+sum[ls];maxa[u]=max(maxa[ls],maxa[rs]);//minn[u]=min(minn[ls],minn[rs]);maxb[u]=max(maxb[ls],maxb[rs]);}void pushdown(int u,int l, int r){ll k1=tag1[u],k2=tag2[u];if(k1&&k2){sum[ls]+=k1,sum[rs]+=k1;maxb[ls]=max(maxb[ls],maxa[ls]+k2);maxb[rs]=max(maxb[rs],maxa[rs]+k2);maxa[ls]+=k1,maxa[rs]+=k1;tag2[ls]=max(tag2[ls],tag1[ls]+k1);tag2[rs]=max(tag2[rs],tag1[rs]+k1);tag1[ls]+=k1,tag1[rs]+=k1;tag1[u]=0,tag2[u]=0;}}void build(int u,int l, int r){if(l==r){maxa[u]=a[r];maxb[u]=a[r];minn[u]=a[r];sum[u]=a[r];return ;}build(ls,l,mid);build(rs,mid+1,r);pushup(u);}void modify_add(int u, int l, int r, int L, int R){if(L<=l&&r<=R){sum[u]+=(r-l+1)*k; tag1[u]+=k;tag2[u]=max(tag1[u],tag2[u]);maxa[u]+=k;maxb[u]=max(maxb[u],maxa[u]);return;}else{pushdown(u,l,r);if(L<=mid) modify_add(ls,l,mid,L,R);if(R>mid) modify_add(rs,mid+1,r,L,R);pushup(u);}}//先不管这个void modify_min(int u,int l,int r,int L, int R){if(L<=l&&r<=R){minn[u]=min(minn[u],v);}pushdown(u,l,r);if(L<=mid) modify_min(ls,l,mid,L,R);if(R>mid) modify_min(rs,mid+1,r,L,R);pushup(u);}ll query_maxa(int u,int l,int r,int L, int R){if(L<=l&&r<=R){return maxa[u];}pushdown(u,l,r);ll maxn=-(1<<30);if(L<=mid) maxn=max(maxn,query_maxa(ls,l,mid,L,R));if(R>mid) maxn=max(maxn,query_maxa(rs,mid+1,r,L,R));return maxn;}ll query_maxb(int u,int l,int r,int L, int R){if(L<=l&&r<=R){return maxb[u];}pushdown(u,l,r);ll maxn=-(1<<30);if(L<=mid) maxn=max(maxn,query_maxb(ls,l,mid,L,R));if(R>mid) maxn=max(maxn,query_maxb(rs,mid+1,r,L,R));return maxn;}ll query_sum(int u,int l,int r,int L, int R){if(L<=l&&r<=R){return sum[u];}pushdown(u,l,r);ll ans=0;if(L<=mid) ans+=query_sum(ls,l,mid,L,R);if(R>mid) ans+=query_sum(rs,mid+1,r,L,R);return ans;}}tr[1];signed main()
{int n,m;cin>>n>>m;for(int i=1;i<=n;i++) cin>>a[i];tr[0].build(1,1,n);while(m--){int op;cin>>op>>l>>r;if(op==1){cin>>k;tr[0].modify_add(1,1,n,l,r);}else if(op==2){cin>>v;//tr[0].modify_min(1,1,n,l,r);}else if(op==3){cout<<tr[0].query_sum(1,1,n,l,r)<<endl;}else if(op==4){cout<<tr[0].query_maxa(1,1,n,l,r)<<endl;}else{cout<<tr[0].query_maxb(1,1,n,l,r)<<endl;}}return 0;
}
过了1，5，6
#include<bits/stdc++.h>using namespace std;
#define int long long
typedef long long ll;
#define ls (u<<1)
#define rs (u<<1|1)
#define mid ((l+r)>>1)
const int N=1e5+10;
ll a[N];
ll l,r,k,v;struct Tree
{ll maxa[N<<4];ll maxb[N<<4];ll minn[N<<4];ll sum[N<<4];ll tag1[N<<4];ll tag2[N<<4];ll tag3[N<<4];ll tag4[N<<4];ll se[N<<4];ll cnt[N<<4];Tree(){}void pushup(int u){sum[u]=sum[rs]+sum[ls];maxa[u]=max(maxa[ls],maxa[rs]);//minn[u]=min(minn[ls],minn[rs]);maxb[u]=max(maxb[ls],maxb[rs]);if(maxa[ls]==maxa[rs]){se[u]=max(se[ls],se[rs]);cnt[u]=cnt[ls]+cnt[rs];}else if(maxa[ls]>maxa[rs]){se[u]=max(se[ls],maxa[rs]);cnt[u]=cnt[ls];}else{se[u]=max(se[rs],maxa[ls]);cnt[u]=cnt[rs];}}void change(int k1,int k2,int k3,int k4,int u,int l,int r){sum[u]+=cnt[u]*k1+k3*(ll)(r-l+1-cnt[u]);maxb[u]=max(maxb[u],maxa[u]+k2);maxa[u]+=k1;if(se[u]!=-2e9) se[u]+=k3;tag2[u]=max(tag2[u],tag1[u]+k2);tag4[u]=max(tag4[u],tag3[u]+k4);tag1[u]+=k1;tag3[u]+=k3;}void pushdown(int u,int l, int r){ll maxn=max(maxa[ls],maxa[rs]);if(maxa[ls]==maxn)change(tag1[u],tag2[u],tag3[u],tag4[u],ls,l,mid);elsechange(tag3[u],tag4[u],tag3[u],tag4[u],ls,l,mid);if(maxa[rs]==maxn)change(tag1[u],tag2[u],tag3[u],tag4[u],rs,mid+1,r);elsechange(tag3[u],tag4[u],tag3[u],tag4[u],rs,mid+1,r);tag1[u]=tag2[u]=tag3[u]=tag4[u]=0;}void build(int u,int l, int r){if(l==r){maxa[u]=a[r];maxb[u]=a[r];sum[u]=a[r];cnt[u]=1;se[u]=-2e9;return ;}build(ls,l,mid);build(rs,mid+1,r);pushup(u);}void modify_add(int u, int l, int r, int L, int R){if(L<=l&&r<=R){sum[u]+=cnt[u]*k+k*(ll)(r-l+1-cnt[u]);maxa[u]+=k;maxb[u]=max(maxb[u],maxa[u]);if(se[u]!=-2e9) se[u]+=k;tag1[u]+=k;tag2[u]=max(tag1[u],tag2[u]);tag3[u]+=k;tag4[u]=max(tag4[u],tag3[u]);return;}else{pushdown(u,l,r);if(L<=mid) modify_add(ls,l,mid,L,R);if(R>mid) modify_add(rs,mid+1,r,L,R);pushup(u);}}//先不管这个void modify_min(int u,int l,int r,int L, int R){if(L<=l&&r<=R&&se[u]<v){ll x=maxa[u]-v;sum[u]-=cnt[u]*x;maxa[u]=v,tag1[u]-=x;return;}pushdown(u,l,r);if(L<=mid) modify_min(ls,l,mid,L,R);if(R>mid) modify_min(rs,mid+1,r,L,R);pushup(u);}ll query_maxa(int u,int l,int r,int L, int R){if(L<=l&&r<=R){return maxa[u];}pushdown(u,l,r);ll maxn=-2e9;if(L<=mid) maxn=max(maxn,query_maxa(ls,l,mid,L,R));if(R>mid) maxn=max(maxn,query_maxa(rs,mid+1,r,L,R));return maxn;}ll query_maxb(int u,int l,int r,int L, int R){if(L<=l&&r<=R){return maxb[u];}pushdown(u,l,r);ll maxn=-2e9;if(L<=mid) maxn=max(maxn,query_maxb(ls,l,mid,L,R));if(R>mid) maxn=max(maxn,query_maxb(rs,mid+1,r,L,R));return maxn;}ll query_sum(int u,int l,int r,int L, int R){if(L<=l&&r<=R){return sum[u];}pushdown(u,l,r);ll ans=0;if(L<=mid) ans+=query_sum(ls,l,mid,L,R);if(R>mid) ans+=query_sum(rs,mid+1,r,L,R);return ans;}}tr[1];signed main()
{ll n,m;cin>>n>>m;for(int i=1;i<=n;i++) cin>>a[i];tr[0].build(1,1,n);while(m--){int op;cin>>op>>l>>r;if(op==1){cin>>k;tr[0].modify_add(1,1,n,l,r);}else if(op==2){cin>>v;tr[0].modify_min(1,1,n,l,r);}else if(op==3){cout<<tr[0].query_sum(1,1,n,l,r)<<endl;}else if(op==4){cout<<tr[0].query_maxa(1,1,n,l,r)<<endl;}else{cout<<tr[0].query_maxb(1,1,n,l,r)<<endl;}}return 0;
}
尝试用题解代码写
#include<bits/stdc++.h>using namespace std;
#define int long long
typedef long long ll;
#define ls (u<<1)
#define rs (u<<1|1)
#define mid ((l+r)>>1)
const int N=1e5+10;
ll a[N];
ll l,r,k,v;struct Tree
{ll maxa[N<<4];ll maxb[N<<4];ll minn[N<<4];ll sum[N<<4];ll tag1[N<<4];ll tag2[N<<4];ll tag3[N<<4];ll tag4[N<<4];ll se[N<<4];ll cnt[N<<4];Tree(){}void pushup(int u){sum[u]=sum[rs]+sum[ls];maxa[u]=max(maxa[ls],maxa[rs]);//minn[u]=min(minn[ls],minn[rs]);maxb[u]=max(maxb[ls],maxb[rs]);if(maxa[ls]==maxa[rs]){se[u]=max(se[ls],se[rs]);cnt[u]=cnt[ls]+cnt[rs];}else if(maxa[ls]>maxa[rs]){se[u]=max(se[ls],maxa[rs]);cnt[u]=cnt[ls];}else{se[u]=max(se[rs],maxa[ls]);cnt[u]=cnt[rs];}}void build(int u,int l, int r){if(l==r){maxa[u]=a[r];maxb[u]=a[r];sum[u]=a[r];cnt[u]=1;se[u]=-2e9;return ;}build(ls,l,mid);build(rs,mid+1,r);pushup(u);}void change(int k1,int k2,int k3,int k4,int u,int l,int r){sum[u]+=cnt[u]*k1+k3*(ll)(r-l+1-cnt[u]);maxb[u]=max(maxb[u],maxa[u]+k2);maxa[u]+=k1;if(se[u]!=-2e9) se[u]+=k3;tag2[u]=max(tag2[u],tag1[u]+k2);tag4[u]=max(tag4[u],tag3[u]+k4);tag1[u]+=k1;tag3[u]+=k3;}void pushdown(int u,int l, int r){ll maxn=max(maxa[ls],maxa[rs]);if(maxa[ls]==maxn)change(tag1[u],tag2[u],tag3[u],tag4[u],ls,l,mid);elsechange(tag3[u],tag4[u],tag3[u],tag4[u],ls,l,mid);if(maxa[rs]==maxn)change(tag1[u],tag2[u],tag3[u],tag4[u],rs,mid+1,r);elsechange(tag3[u],tag4[u],tag3[u],tag4[u],rs,mid+1,r);tag1[u]=tag2[u]=tag3[u]=tag4[u]=0;}void modify_add(int u, int l, int r, int L, int R){if(L>l||r>R) return;if(L<=l&&r<=R){sum[u]+=cnt[u]*k+k*(ll)(r-l+1-cnt[u]);maxa[u]+=k;maxb[u]=max(maxb[u],maxa[u]);if(se[u]!=-2e9) se[u]+=k;tag1[u]+=k;tag2[u]=max(tag1[u],tag2[u]);tag3[u]+=k;tag4[u]=max(tag4[u],tag3[u]);return;}pushdown(u,l,r);modify_add(ls,l,mid,L,R);modify_add(rs,mid+1,r,L,R);pushup(u);}void modify_min(int u,int l,int r,int L, int R){if(L>l||r>R||v>=maxa[u]) return; if(L<=l&&r<=R&&se[u]<v){ll x=maxa[u]-v;sum[u]-=cnt[u]*x;maxa[u]=v;tag1[u]-=x;return;}pushdown(u,l,r);modify_min(ls,l,mid,L,R);modify_min(rs,mid+1,r,L,R);pushup(u);}ll query_sum(int u,int l,int r,int L, int R){if(L>l||r>R) return 0;if(L<=l&&r<=R){return sum[u];}pushdown(u,l,r);return query_sum(ls,l,mid,L,R)+query_sum(rs,mid+1,r,L,R);}ll query_maxa(int u,int l,int r,int L, int R){if(L>l||r>R) return -2e9;if(L<=l&&r<=R){return maxa[u];}pushdown(u,l,r);return max(query_maxa(ls,l,mid,L,R),query_maxa(rs,mid+1,r,L,R));}ll query_maxb(int u,int l,int r,int L, int R){if(L>l||r>R) return -2e9;if(L<=l&&r<=R){return maxb[u];}pushdown(u,l,r);return max(query_maxa(ls,l,mid,L,R),query_maxa(rs,mid+1,r,L,R));}}tr[1];signed main()
{ll n,m;cin>>n>>m;for(int i=1;i<=n;i++) cin>>a[i];tr[0].build(1,1,n);while(m--){int op;cin>>op>>l>>r;if(op==1){cin>>k;tr[0].modify_add(1,1,n,l,r);}else if(op==2){cin>>v;tr[0].modify_min(1,1,n,l,r);}else if(op==3){cout<<tr[0].query_sum(1,1,n,l,r)<<endl;}else if(op==4){cout<<tr[0].query_maxa(1,1,n,l,r)<<endl;}else{cout<<tr[0].query_maxb(1,1,n,l,r)<<endl;}}return 0;
}
ac代码
#include<bits/stdc++.h>using namespace std;
#define int long long
typedef long long ll;
#define ls (u<<1)
#define rs (u<<1|1)
#define mid ((l+r)>>1)
const int N=1e7+10;
ll a[N];
ll k,v;struct Tree
{ll maxa[N<<4];ll maxb[N<<4];ll minn[N<<4];ll sum[N<<4];ll tag1[N<<4];ll tag2[N<<4];ll tag3[N<<4];ll tag4[N<<4];ll se[N<<4];ll cnt[N<<4];Tree(){//memset(maxa,0,sizeof maxa);}void pushup(int u){sum[u]=sum[rs]+sum[ls];maxa[u]=max(maxa[ls],maxa[rs]);//minn[u]=min(minn[ls],minn[rs]);maxb[u]=max(maxb[ls],maxb[rs]);if(maxa[ls]==maxa[rs]){se[u]=max(se[ls],se[rs]);cnt[u]=cnt[ls]+cnt[rs];}else if(maxa[ls]>maxa[rs]){se[u]=max(se[ls],maxa[rs]);cnt[u]=cnt[ls];}else{se[u]=max(se[rs],maxa[ls]);cnt[u]=cnt[rs];}}void build(int u,int l, int r){if(l==r){maxa[u]=a[r];maxb[u]=a[r];sum[u]=a[r];cnt[u]=1;se[u]=-2e9;return ;}build(ls,l,mid);build(rs,mid+1,r);pushup(u);}void change(int k1,int k2,int k3,int k4,int u,int l,int r){sum[u]+=cnt[u]*k1+k3*(ll)(r-l+1-cnt[u]);maxb[u]=max(maxb[u],maxa[u]+k2);maxa[u]+=k1;if(se[u]!=-2e9) se[u]+=k3;tag2[u]=max(tag2[u],tag1[u]+k2);tag4[u]=max(tag4[u],tag3[u]+k4);tag1[u]+=k1;tag3[u]+=k3;}void pushdown(int u,int l, int r){ll maxn=max(maxa[ls],maxa[rs]);if(maxa[ls]==maxn)change(tag1[u],tag2[u],tag3[u],tag4[u],ls,l,mid);elsechange(tag3[u],tag4[u],tag3[u],tag4[u],ls,l,mid);if(maxa[rs]==maxn)change(tag1[u],tag2[u],tag3[u],tag4[u],rs,mid+1,r);elsechange(tag3[u],tag4[u],tag3[u],tag4[u],rs,mid+1,r);tag1[u]=tag2[u]=tag3[u]=tag4[u]=0;}void modify_add(int u, int l, int r, int L, int R){if(L<=l&&r<=R){sum[u]+=cnt[u]*k+k*(ll)(r-l+1-cnt[u]);maxa[u]+=k;maxb[u]=max(maxb[u],maxa[u]);if(se[u]!=-2e9) se[u]+=k;tag1[u]+=k;tag2[u]=max(tag1[u],tag2[u]);tag3[u]+=k;tag4[u]=max(tag4[u],tag3[u]);return;}else{pushdown(u,l,r);if(L<=mid) modify_add(ls,l,mid,L,R);if(R>mid) modify_add(rs,mid+1,r,L,R);pushup(u);}}void modify_min(int u,int l,int r,int L, int R){// woc为什么？，为什么加上L>l||r>R就是wa一片if(maxa[u]<=v) return;if(L<=l&&r<=R&&se[u]<v){ll x=maxa[u]-v;sum[u]-=cnt[u]*x;maxa[u]=v;tag1[u]-=x;return;}pushdown(u,l,r);if(L<=mid) modify_min(ls,l,mid,L,R);if(R>mid) modify_min(rs,mid+1,r,L,R);pushup(u);}ll query_sum(int u,int l,int r,int L, int R){if(L<=l&&r<=R){return sum[u];}pushdown(u,l,r);ll ans=0;if(L<=mid) ans+=query_sum(ls,l,mid,L,R);if(R>mid) ans+=query_sum(rs,mid+1,r,L,R);return ans;}ll query_maxa(int u,int l,int r,int L, int R){if(L<=l&&r<=R){return maxa[u];}pushdown(u,l,r);ll maxn=-2e9;if(L<=mid) maxn=max(maxn,query_maxa(ls,l,mid,L,R));if(R>mid) maxn=max(maxn,query_maxa(rs,mid+1,r,L,R));return maxn;}ll query_maxb(int u,int l,int r,int L, int R){if(L<=l&&r<=R){return maxb[u];}pushdown(u,l,r);ll maxn=-2e9;if(L<=mid) maxn=max(maxn,query_maxb(ls,l,mid,L,R));if(R>mid) maxn=max(maxn,query_maxb(rs,mid+1,r,L,R));return maxn;}}tr[1];signed main()
{ll n,m;cin>>n>>m;ll l,r;for(int i=1;i<=n;i++) cin>>a[i];tr[0].build(1,1,n);while(m--){int op;cin>>op>>l>>r;if(op==1){cin>>k;tr[0].modify_add(1,1,n,l,r);}else if(op==2){cin>>v;tr[0].modify_min(1,1,n,l,r);}else if(op==3){cout<<tr[0].query_sum(1,1,n,l,r)<<endl;}else if(op==4){cout<<tr[0].query_maxa(1,1,n,l,r)<<endl;}else{cout<<tr[0].query_maxb(1,1,n,l,r)<<endl;}}return 0;
}
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