BZOJ 1266 上学路线(最短路+最小割)
给出n个点的无向图,每条边有两个属性,边权和代价。
第一问求1-n的最短路。第二问求用最小的代价删边使得最短路的距离变大。
对于第二问。显然该删除的是出现在最短路径上的边。如果我们将图用最短路跑一遍预处理出所有最短路径。
然后我们要删除的边集一定是这个图的一个割。否则最短路径不会增加。即求此图的最小割。
![](https://images.cnblogs.com/OutliningIndicators/ContractedBlock.gif)
# include <cstdio> # include <cstring> # include <cstdlib> # include <iostream> # include <vector> # include <queue> # include <stack> # include <map> # include <set> # include <cmath> # include <algorithm> using namespace std; # define lowbit(x) ((x)&(-x)) # define pi acos(-1.0) # define eps 1e-9 # define MOD 1000000000 # define INF 1000000000 # define mem(a,b) memset(a,b,sizeof(a)) # define FOR(i,a,n) for(int i=a; i<=n; ++i) # define FO(i,a,n) for(int i=a; i<n; ++i) # define bug puts("H"); # define lch p<<1,l,mid # define rch p<<1|1,mid+1,r # define mp make_pair # define pb push_back typedef pair<int,int> PII; typedef vector<int> VI; # pragma comment(linker, "/STACK:1024000000,1024000000") typedef long long LL; int Scan() { int x=0,f=1;char ch=getchar(); while(ch<'0'||ch>'9'){if(ch=='-')f=-1;ch=getchar();} while(ch>='0'&&ch<='9'){x=x*10+ch-'0';ch=getchar();} return x*f; } void Out(int a) { if(a<0) {putchar('-'); a=-a;} if(a>=10) Out(a/10); putchar(a%10+'0'); } const int N=505; //Code begin... struct Edge{int p, next, w, d;}edge[N*N]; struct Edge1{int p, next, w;}edge1[N*N]; int head[N], head1[N], dist[N], cnt=1, cnt1=2, n, m, s, t; struct qnode{ int v, c; qnode(int _v=0, int _c=0):v(_v),c(_c){} bool operator<(const qnode &r)const{return c>r.c;} }; int vis[N]; priority_queue<qnode>que; queue<int>Q; void add_edge(int u, int v, int d, int w){ edge[cnt].p=v; edge[cnt].w=w; edge[cnt].d=d; edge[cnt].next=head[u]; head[u]=cnt++; edge[cnt].p=u; edge[cnt].w=w; edge[cnt].d=d; edge[cnt].next=head[v]; head[v]=cnt++; } void add_edge1(int u, int v, int w){ edge1[cnt1].p=v; edge1[cnt1].w=w; edge1[cnt1].next=head1[u]; head1[u]=cnt1++; edge1[cnt1].p=u; edge1[cnt1].w=0; edge1[cnt1].next=head1[v]; head1[v]=cnt1++; } void Dijkstra(int n, int start){ mem(vis,0); FOR(i,1,n) dist[i]=INF; dist[start]=0; que.push(qnode(start,0)); qnode tmp; while (!que.empty()) { tmp=que.top(); que.pop(); int u=tmp.v; if (vis[u]) continue; vis[u]=true; for (int i=head[u]; i; i=edge[i].next) { int v=edge[i].p, cost=edge[i].d; if (!vis[v]&&dist[v]>dist[u]+cost) dist[v]=dist[u]+cost, que.push(qnode(v,dist[v])); } } } int bfs(){ int i, v; mem(vis,-1); vis[s]=0; Q.push(s); while (!Q.empty()) { v=Q.front(); Q.pop(); for (i=head1[v]; i; i=edge1[i].next) { if (edge1[i].w>0 && vis[edge1[i].p]==-1) { vis[edge1[i].p]=vis[v] + 1; Q.push(edge1[i].p); } } } return vis[t]!=-1; } int dfs(int x, int low){ int i, a, temp=low; if (x==t) return low; for (i=head1[x]; i; i=edge1[i].next) { if (edge1[i].w>0 && vis[edge1[i].p]==vis[x]+1){ a=dfs(edge1[i].p,min(edge1[i].w,temp)); temp-=a; edge1[i].w-=a; edge1[i^1].w+=a; if (temp==0) break; } } if (temp==low) vis[x]=-1; return low-temp; } int main () { int u, v, d, w; scanf("%d%d",&n,&m); FOR(i,1,m) scanf("%d%d%d%d",&u,&v,&d,&w), add_edge(u,v,d,w); Dijkstra(n,1); printf("%d\n",dist[n]); mem(vis,0); Q.push(n); vis[n]=true; while (!Q.empty()) { int tmp=Q.front(); Q.pop(); for (int i=head[tmp]; i; i=edge[i].next) { int v=edge[i].p; if (dist[v]+edge[i].d!=dist[tmp]) continue; add_edge1(v,tmp,edge[i].w); if (!vis[v]) vis[v]=true, Q.push(v); } } s=1; t=n; int tmp, sum=0; while (bfs()) while (tmp=dfs(s,INF)) sum+=tmp; printf("%d\n",sum); return 0; }