笛卡尔树1

牛客国庆day2C题

#include<bits/stdc++.h>
using namespace std;
#define int long long
const int N=3e6+10;
int n,a[N],b[N],ls[N],rs[N],sz[N],ans=-1e18,stk[N];
void build(){
    int top=0;
    for(int i=1;i<=n;i++){
        int k=top;
        while(k&&a[i]<=a[stk[k]])k--;
        if(k)rs[stk[k]]=i;
        if(k<top)ls[i]=stk[k+1];
        stk[++k]=i,top=k;
    }
}
int lmax[N],rmax[N];
int lmin[N],rmin[N];
int sum[N];
void dfs(int u){
    if(ls[u])dfs(ls[u]);
    if(rs[u])dfs(rs[u]);
    sum[u]=sum[ls[u]]+b[u]+sum[rs[u]];
    lmax[u]=max(lmax[ls[u]],sum[ls[u]]+b[u]+lmax[rs[u]]);
    lmin[u]=min(lmin[ls[u]],sum[ls[u]]+b[u]+lmin[rs[u]]);
    rmax[u]=max(rmax[rs[u]],sum[rs[u]]+b[u]+rmax[ls[u]]);
    rmin[u]=min(rmin[rs[u]],sum[rs[u]]+b[u]+rmin[ls[u]]);
    if(a[u]>0)ans=max(ans,a[u]*(rmax[ls[u]]+b[u]+lmax[rs[u]]));
    else ans=max(ans,a[u]*(rmin[ls[u]]+b[u]+lmin[rs[u]]));
    
}
signed main(){
    ios::sync_with_stdio(0);cin.tie(0);cout.tie(0);
    cin>>n;
    for(int i=1;i<=n;i++)cin>>a[i];
    for(int i=1;i<=n;i++)cin>>b[i];
    build();
    dfs(stk[1]);
//     cout<<"a["<<stk[1]<<"]="<<a[stk[1]]<<'\n';
    cout<<ans;
}

---

剑指 Offer II 039. 直方图最大矩形面积

这道题确实可以用单调栈，dp写
但是也可以用笛卡尔树写

class Solution {
public:
static const int N=2e5+10;
int w[N],ans,stk[N],ls[N],rs[N],sz[N],n;
void build(){
    for(int i=1;i<=n;i++)ls[i]=rs[i]=sz[i]=0;
    int top=0;
    for(int i=1;i<=n;i++){
        int k=top;
        while(k&&w[i]<=w[stk[k]])k--;
        if(k)rs[stk[k]]=i;
        if(k<top)ls[i]=stk[k+1];
        stk[++k]=i,top=k;
    }
}
void dfs(int u){
    if(ls[u])dfs(ls[u]);
    if(rs[u])dfs(rs[u]);
    sz[u]=sz[ls[u]]+sz[rs[u]]+1;
    ans=max(ans,sz[u]*w[u]);
}

    int largestRectangleArea(vector<int>& h) {
        n=h.size();
        for(int i=1;i<=n;i++)w[i]=h[i-1];
        build();
        dfs(stk[1]);
        return ans;
    }
};