HDU 5294 Tricks Device 最短路+最小割

来源:互联网 发布:js 箭头函数作用域 编辑:程序博客网 时间:2024/05/22 17:20

题意:给你一个无向图 问你 至少和至多 删除多少条边 可以使从起点到终点的最短路变长(并不一定不可到达)

思路:比赛的时候想的方法是费用流+二分 无限超时 水的不行- - 正解是先用最短路预处理出所有的最短路径 建图后求最小割即为至少删除的边数 因为删除了最小割上的边 最短路上的起点和终点就不连通了 放在原图上最短路必然增大 而原图所有边数减去最短路径上边数最少的那条路径的值就是至多删除的边数 代码写得很糟乱 懂了思想就好。。

#include <cstdio>#include <cstring>#include <algorithm>#include <queue>using namespace std;#define REP( i, a, b ) for( int i = a; i < b; i++ )#define FOR( i, a, b ) for( int i = a; i <= b; i++ )#define CLR( a, x ) memset( a, x, sizeof a )#define CPY( a, x ) memcpy( a, x, sizeof a )const int maxn = 2000 + 10;const int maxe  = 240000 + 10;const int INF = 1e9;struct Edge{          int v, c, f;          int next;          Edge() {}          Edge(int v, int c, int f, int next) : v(v), c(c), f(f), next(next) {}};struct ISAP{          int n, s, t;          int num[maxn], cur[maxn], d[maxn], p[maxn];          int Head[maxn], cntE;          int Q[maxn], head, tail;          Edge edge[maxe];          void Init(int n){                    this -> n = n;                    cntE = 0;                    CLR(Head, -1);          }          void Add(int u, int v, int c){                    edge[cntE] = Edge(v, c, 0, Head[u]);                    Head[u] = cntE++;                    edge[cntE] = Edge(u, 0, 0, Head[v]);                    Head[v] = cntE++;          }          void Bfs(){                    CLR(d, -1);                    CLR(num, 0);                    d[t] = 0;                    head = tail = 0;                    Q[tail++] = t;                    num[0] = 1;                    while(head != tail){                              int u = Q[head++];                              for(int i = Head[u]; ~i; i = edge[i].next){                                        Edge &e = edge[i];                                        if(~d[e.v]) continue;                                        d[e.v] = d[u] + 1;                                        Q[tail++] = e.v;                                        num[d[e.v]] ++;                              }                    }          }          int Maxflow(int s, int t){                    this -> s = s;                    this -> t = t;                    CPY(cur, Head);                    Bfs();                    int flow = 0, u = p[s] = s;                    while(d[s] < n){                              if(u == t){                                        int f = INF, neck;                                        for(int i = s; i != t; i = edge[cur[i]].v){                                                  if(f > edge[cur[i]].c - edge[cur[i]].f){                                                            f = edge[cur[i]].c - edge[cur[i]].f;                                                            neck = i;                                                  }                                        }                                        for(int i = s; i != t; i = edge[cur[i]].v){                                                  edge[cur[i]].f += f;                                                  edge[cur[i]^1].f -= f;                                        }                                        flow += f;                                        u = neck;                              }                              int ok = 0;                              for(int i = cur[u]; ~i; i = edge[i].next){                                        Edge &e = edge[i];                                        if(e.c > e.f && d[e.v] + 1 == d[u]){                                                  ok = 1;                                                  cur[u] = i;                                                  p[e.v] = u;                                                  u = e.v;                                                  break;                                        }                              }                              if(!ok){                                        int m = n - 1;                                        if(--num[d[u]] == 0) break;                                        for(int i = Head[u]; ~i; i = edge[i].next){                                                  Edge &e = edge[i];                                                  if(e.c - e.f > 0 && m > d[e.v]){                                                            cur[u] = i;                                                            m = d[e.v];                                                  }                                        }                                        ++num[d[u] = m + 1];                                        u = p[u];                              }                    }                    return flow;          }}solver;struct SPFA{          int top, cntE, n;          int Head[maxn], vis[maxn], cnt[maxn], STACK[maxn], dist[maxn];          Edge edge[maxe];          void init(int n){                    this -> n = n;                    CLR(Head, -1);                    CLR(vis, 0);                    cntE = top = 0;          }          void add(int u, int v, int d){                    edge[cntE] = Edge(v, d, 0, Head[u]);                    Head[u] = cntE++;          }          bool spfa(int s){                    CLR(vis, 0);                    CLR(cnt, 0);                    vis[s] = cnt[s] = 1;                    STACK[top++] = s;                    REP(i, 0, n) dist[i] = INF;                    dist[s] = 0;                    while(top){                              int u = STACK[--top];                              vis[u] = 0;                              for(int i = Head[u]; ~i; i = edge[i].next){                                        int v = edge[i].v;                                        if(dist[v] > dist[u] + edge[i].c){                                                  dist[v] = dist[u] + edge[i].c;                                                  if(!vis[v]){                                                            vis[v] = 1;                                                            STACK[top++] = v;                                                            if(++cnt[v] > n) return false;                                                  }                                        }                              }                    }                    return true;          }}Spfa, Spfa2;int n, m;int vis[maxn];void bfs(){          memset(vis, 0, sizeof(vis));          vis[n-1] = 1;          queue<int> Q;          Q.push(n-1);          while(!Q.empty()){                    int u = Q.front(); Q.pop();                    for(int i = Spfa.Head[u]; ~i; i = Spfa.edge[i].next){                              int v = Spfa.edge[i].v;                              if(Spfa.dist[v] + Spfa.edge[i].c == Spfa.dist[u]){                                        solver.Add(u, v, 1);                                        Spfa2.add(u, v, 1);//                                        printf(".. %d %d\n", u+1, v+1);                                        if(!vis[v]) Q.push(v);                                        vis[v] = 1;                              }                    }          }          Spfa2.spfa(n-1);          printf("%d %d\n", solver.Maxflow(n-1, 0), m - Spfa2.dist[0]);}void solve(){          Spfa.init(n);          Spfa2.init(n);          solver.Init(n);          REP(i, 0, m){                    int u, v, d;                    scanf("%d%d%d", &u, &v, &d);                    --u; --v;                    Spfa.add(u, v, d);                    Spfa.add(v, u, d);          }          Spfa.spfa(0);          bfs();}int main(){//          freopen("in.txt", "r", stdin);          while(~scanf("%d%d", &n, &m)) solve();          return 0;}


0 0
原创粉丝点击