zoj 2676 最小割+0-1规划 ***
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1 #include <iostream> 2 #include <algorithm> 3 #include <cstring> 4 #include <string> 5 #include <cstdio> 6 #include <cmath> 7 #include <queue> 8 #include <map> 9 #include <set> 10 #define eps 1e-5 11 #define MAXN 222 12 #define MAXM 5555 13 #define INF 100000007 14 using namespace std; 15 typedef double type; 16 struct node 17 { 18 int v; 19 type c, f; 20 int next, r; 21 }edge[MAXM]; 22 int dist[MAXN], nm[MAXN], src, des, n; 23 int head[MAXN], e; 24 void add(int x, int y, type c) 25 { 26 edge[e].v = y; 27 edge[e].c = c; 28 edge[e].f = 0; 29 edge[e].r = e + 1; 30 edge[e].next = head[x]; 31 head[x] = e++; 32 edge[e].v = x; 33 edge[e].c = 0; 34 edge[e].f = 0; 35 edge[e].r = e - 1; 36 edge[e].next = head[y]; 37 head[y] = e++; 38 } 39 void rev_BFS() 40 { 41 int Q[MAXN], h = 0, t = 0; 42 for(int i = 1; i <= n; ++i) 43 { 44 dist[i] = MAXN; 45 nm[i] = 0; 46 } 47 Q[t++] = des; 48 dist[des] = 0; 49 nm[0] = 1; 50 while(h != t) 51 { 52 int v = Q[h++]; 53 for(int i = head[v]; i != -1; i = edge[i].next) 54 { 55 if(edge[edge[i].r].c == 0 || dist[edge[i].v] < MAXN)continue; 56 dist[edge[i].v] = dist[v] + 1; 57 ++nm[dist[edge[i].v]]; 58 Q[t++] = edge[i].v; 59 } 60 } 61 } 62 void init() 63 { 64 e = 0; 65 memset(head, -1, sizeof(head)); 66 } 67 type maxflow() 68 { 69 rev_BFS(); 70 int u; 71 type total = 0; 72 int cur[MAXN], rpath[MAXN]; 73 for(int i = 1; i <= n; ++i)cur[i] = head[i]; 74 u = src; 75 while(dist[src] < n) 76 { 77 if(u == des) // find an augmenting path 78 { 79 type tf = INF; 80 for(int i = src; i != des; i = edge[cur[i]].v) 81 tf = min(tf, edge[cur[i]].c); 82 for(int i = src; i != des; i = edge[cur[i]].v) 83 { 84 edge[cur[i]].c -= tf; 85 edge[edge[cur[i]].r].c += tf; 86 edge[cur[i]].f += tf; 87 edge[edge[cur[i]].r].f -= tf; 88 } 89 total += tf; 90 u = src; 91 } 92 int i; 93 for(i = cur[u]; i != -1; i = edge[i].next) 94 if(edge[i].c > 0 && dist[u] == dist[edge[i].v] + 1)break; 95 if(i != -1) // find an admissible arc, then Advance 96 { 97 cur[u] = i; 98 rpath[edge[i].v] = edge[i].r; 99 u = edge[i].v; 100 } 101 else // no admissible arc, then relabel this vtex 102 { 103 if(0 == (--nm[dist[u]]))break; // GAP cut, Important! 104 cur[u] = head[u]; 105 int mindist = n; 106 for(int j = head[u]; j != -1; j = edge[j].next) 107 if(edge[j].c > 0)mindist = min(mindist, dist[edge[j].v]); 108 dist[u] = mindist + 1; 109 ++nm[dist[u]]; 110 if(u != src) 111 u = edge[rpath[u]].v; // Backtrack 112 } 113 } 114 return total; 115 } 116 int nt, m; 117 int xx[MAXM], yy[MAXM], vis[MAXN], out[MAXM]; 118 type cc[MAXM]; 119 bool ok(double mid) 120 { 121 init(); 122 double flow = 0; 123 for(int i = 1; i <= m; i++) 124 { 125 if(cc[i] > mid) 126 add(xx[i], yy[i], cc[i] - mid), add(yy[i], xx[i], cc[i] - mid); 127 else flow += cc[i] - mid; 128 } 129 flow += maxflow(); 130 if(flow < eps) return true; 131 else return false; 132 } 133 void dfs(int u) 134 { 135 vis[u] = 1; 136 for(int i = head[u]; i != -1; i = edge[i].next) 137 if(edge[i].c > 0 && !vis[edge[i].v]) 138 dfs(edge[i].v); 139 } 140 int main() 141 { 142 int cas = 0; 143 while(scanf("%d%d", &nt, &m) != EOF) 144 { 145 if(cas++) printf("\n"); 146 src = 1; 147 des = nt; 148 n = nt; 149 double low = INF, high = 0; 150 for(int i = 1; i <= m; i++) 151 { 152 scanf("%d%d%lf", &xx[i], &yy[i], &cc[i]); 153 low = min(low, cc[i]); 154 high = max(high, cc[i]); 155 } 156 while(high - low > eps) 157 { 158 double mid = (low + high) / 2; 159 if(ok(mid)) high = mid; 160 else low = mid; 161 } 162 ok(low); 163 memset(vis, 0, sizeof(vis)); 164 dfs(src); 165 int cnt = 0; 166 for(int i = 1; i <= m; i++) 167 if(vis[xx[i]] + vis[yy[i]] == 1 || cc[i] <= low) 168 out[cnt++] = i; 169 printf("%d\n", cnt); 170 for(int i = 0; i < cnt; i++) 171 { 172 printf("%d", out[i]); 173 if(i < cnt - 1) putchar(' '); 174 else putchar('\n'); 175 } 176 } 177 return 0; 178 }
