luogu 5468 [NOI2019]回家路线 最短路/暴力

想写一个 70 pts 算法，结果数据水，直接就切了

最短路：

// luogu-judger-enable-o2
#include<bits/stdc++.h>
using namespace std;
#define setIO(s) freopen(s".in","r",stdin)
#define maxn 300000
#define ll long long
struct Node { int x,y,p,q;  }nd[maxn];
vector<int>G1[maxn],G2[maxn];
map<int,int>date1[maxn],date2[maxn];
int n,m,A,B,C,cnt1,edges,cnt2;
int hd[maxn*10],to[maxn*10],nex[maxn*10];
ll val[maxn*10];
inline void addedge(int u,int v,ll c)
{
    nex[++edges]=hd[u], hd[u]=edges, to[edges]=v,val[edges]=c;
}
inline ll calc(ll u) { return 1ll*A*u*u + 1ll*B*u + 1ll*C; }
int S,T;
int inq[maxn*10];
ll dis[maxn*10];
queue<int>Q;
inline void spfa()
{
    for(int i=1;i<maxn*10;++i) dis[i]=1000000000000;
    Q.push(S);
    inq[S]=1;
    dis[S]=0;
    while(!Q.empty())
    {
        int u=Q.front(); Q.pop();
        inq[u]=0;
        for(int i=hd[u];i;i=nex[i])
        {
            int v=to[i];
            if(dis[u]+val[i] < dis[v])
            {
                dis[v]=dis[u] + val[i];
                if(!inq[v])
                {
                    inq[v]=1;
                    Q.push(v);
                }
            }
        }
    }
    printf("%lld\n",dis[T]);
}
int main()
{
    int i,j;
    // setIO("input");
    scanf("%d%d%d%d%d",&n,&m,&A,&B,&C);
    for(i=1;i<=m;++i)
    {
        scanf("%d%d%d%d",&nd[i].x,&nd[i].y,&nd[i].p,&nd[i].q);
        G1[nd[i].y].push_back(nd[i].q);
        G2[nd[i].x].push_back(nd[i].p);
        if(!date2[nd[i].x][nd[i].p]) date2[nd[i].x][nd[i].p]=++cnt2;
        if(!date1[nd[i].y][nd[i].q]) date1[nd[i].y][nd[i].q]=++cnt1;
    }
    for(i=1;i<=m;++i)
    {
        addedge(date2[nd[i].x][nd[i].p], date1[nd[i].y][nd[i].q] + cnt2, 0);
    }
    int k=0;
    for(i=1;i<=n;++i)
    {
        if(!G1[i].size() || !G2[i].size()) continue;
        for(j=0;j<G1[i].size();++j)
        {
            for(k=0;k<G2[i].size();++k)
            {
                if(G1[i][j]>G2[i][k]) continue;
                addedge(date1[i][G1[i][j]] + cnt2, date2[i][G2[i][k]], calc(G2[i][k] - G1[i][j]));
            }
        }
    }
    S=0,T=cnt1 + cnt2 +100;
    for(i=0;i<=1000;++i)  if(date2[1][i]) addedge(S, date2[1][i], calc(i));
    for(i=0;i<=1000;++i)  if(date1[n][i]) addedge(date1[n][i] + cnt2, T, i);
    spfa();
    return 0;
}

　　

$O(mt)$ DP (网上说这个做法在现场能切题)

#include<bits/stdc++.h>
#define setIO(s) freopen(s".in","r",stdin)
#define maxn 300001
#define inf 1000000000
using namespace std;
int n,m,A,B,C;
int f[maxn][1002];
int calc(int t)
{
    return A*t*t+B*t+C;
}
struct Node{ int x,y,p,q; }nd[maxn];
bool cmp(Node a, Node b)
{
    return a.p < b.p;
}
int main()
{
    //    setIO("input");
    int i,j;
    scanf("%d%d%d%d%d",&n,&m,&A,&B,&C);
    for(i=1;i<=m;++i)
    {
        scanf("%d%d%d%d",&nd[i].x,&nd[i].y,&nd[i].p,&nd[i].q);
    }
    sort(nd+1,nd+1+m,cmp);
    for(i=0;i<=n;++i) for(j=0;j<=1000;++j) f[i][j]=inf;
    f[1][0]=0;
    for(i=1;i<=m;++i)
    {
        for(j=0;j<=nd[i].p;++j)
        {
            if(f[nd[i].x][j]==inf) continue;
            f[nd[i].y][nd[i].q] = min(f[nd[i].y][nd[i].q], f[nd[i].x][j] + calc(nd[i].p - j));
        }
    }
    int ans=inf;
    for(i=0;i<=1000;++i)
    {
        ans=min(ans, f[n][i] + i);
    }
    printf("%d\n",ans);
    return 0;
}