斜率DP模板

斜率dp 線性裸題 3507

#include<stdio.h>
#define N  500010
int dp[N];
int q[N];
int head,tail;
int sum[N];
int a[N];
int n,m;
int getDP(int i,int j)
{
    return dp[j]+(sum[i]-sum[j])*(sum[i]-sum[j])+m;
}
int getUP(int j,int k)
{
    return dp[j]+sum[j]*sum[j]-(dp[k]+sum[k]*sum[k]);
}
int getDOWN(int j,int k)
{
   return  2*(sum[j]-sum[k]);
}
int main()
{
	int i;
	while(scanf("%d%d",&n,&m)!=-1)
	{
       sum[0]=0;
	   for(i=1;i<=n;i++)
	   {
		   scanf("%d",&a[i]);
		   sum[i]=sum[i-1]+a[i];
	   }
       head=tail=0;
	   q[tail++]=0;
	   dp[0]=0;
	   for(i=1;i<=n;i++)
	   {
	      while(head+1<tail&&getUP(q[head+1],q[head])<=sum[i]*getDOWN(q[head+1],q[head]))
			  head++;
		  dp[i]=getDP(i,q[head]);
		  while(head+1<tail&&getUP(q[tail-1],q[tail-2])*getDOWN(i,q[tail-1])>=getUP(i,q[tail-1])*getDOWN(q[tail-1],q[tail-2]))
		  tail--;
		  q[tail++]=i;
	   }
	   printf("%d\n",dp[n]);
	}
    return 0;
}

樹上的斜率dp
2016瀋陽I

#include <bits/stdc++.h>

using namespace std;
typedef long long ll;
const int maxn=200005;
int head[maxn];
int tot;
struct Edge
{
    int to;
    int next;
    ll w;
}edge[maxn];
void add(int u,int v,ll w)
{
    edge[tot].to=v; edge[tot].next=head[u];  edge[tot].w=w;
    head[u]=tot++;
}
const ll inf=0x3f3f3f3f3f;
ll ans=0;
int n;
ll p;
ll dp[maxn],sum[maxn];
ll q[maxn];
ll getup(int j,int k)
{
    return (dp[j]+sum[j]*sum[j])-(dp[k]+sum[k]*sum[k]);
}
ll getdown(int j,int k)
{
    return 2*(sum[j]-sum[k]);
}
ll getdp(int i,int j)
{
    return dp[j]+(sum[i]-sum[j])*(sum[i]-sum[j])+p;
}
void dis(int u,int fa)
{
    for(int i=head[u];i!=-1;i=edge[i].next)
    {
        int v=edge[i].to;
        ll  w=edge[i].w;
        if(v==fa) continue;
        sum[v]=sum[u]+w;
        dis(v,u);
    }
}
void dfs(int u,int fa,int s,int t)
{
   int pre=-1;
    if(u!=1)
    {
        while(s<t&&getup(q[s+1],q[s])<=sum[u]*getdown(q[s+1],q[s])) s++;
        dp[u]=min(dp[u],getdp(u,q[s]));
        while(s<t&&getup(q[t],q[t-1])*getdown(u,q[t])>=getup(u,q[t])*getdown(q[t],q[t-1])) t--;
        pre=q[++t];
        q[t]=u;
    }
    ans=max(ans,dp[u]);

    for(int i=head[u];i!=-1;i=edge[i].next)
    {
        int v=edge[i].to;
        if(v==fa) continue;
        dfs(v,u,s,t);
    }
    if(pre!=-1) q[t]=pre;
}
int main()
{
    int T;
    scanf("%d",&T);
    while(T--)
    {
        scanf("%d %I64d",&n,&p);
        memset(head,-1,sizeof(head));
        tot=0;
        ans=0;
        for(int i=1;i<n;++i)
        {
            int u,v;
            ll w;
            scanf("%d %d %I64d",&u,&v,&w);
            add(u,v,w);
            add(v,u,w);
        }
        sum[0]=0;
        dis(1,0);

        for(int i=1;i<=n;++i) dp[i]=sum[i]*sum[i];
        q[0]=0;
        dfs(1,0,1,0);
        printf("%I64d\n",ans);

    }
    return 0;
}