链接
题目传送门:http://www.lydsy.com/JudgeOnline/problem.php?id=1016
优秀题解:https://blog.sengxian.com/solutions/bzoj-1016
题解
考虑最小生成树,如果使用价值相同的非树边边替换树边,得到的效果一定一样
因为不一样的话,用于替换的边就会成为最小生成树的树边
换一句话来说,权值相同的边处理完之后,图的连通性一定一样
于是暴力枚举同一权值的边的组合情况
使用并查集判断一下即可
代码
#include<bits/stdc++.h> #define LL long long using namespace std; const int N = 100+9; const int M = 1000+9; const int MOD = 31011; struct Edge{int u,v,w;}e[M]; vector<Edge> que[M]; int n,m,fa[N],fa_tmp[N],_hash[M],cnt[M],tot,vout=1,vis[N]; inline int read(){ char c=getchar(); int ret=0,f=1; while (c<'0'||c>'9') {if(c=='-')f=-1;c=getchar();} while (c<='9'&&c>='0') {ret=ret*10+c-'0';c=getchar();} return ret*f; } inline int find(int w) { int f=fa[w],tmp; while (fa[f] != f) f = fa[f]; while (w != f) tmp = fa[w], fa[w] = f, w = tmp; return f; } void DFS(int w, int sz, int cur, int id, int &tmp) { if (cur > cnt[id]) { return ; } else if (w == sz + 1) { if (cur == cnt[id]) { memcpy(fa_tmp, fa, sizeof(fa)); int i; for (i=1;i<=sz;i++) if (vis[i]) { if (find(que[id][i-1].u) == find(que[id][i-1].v)) break; fa[find(que[id][i-1].u)] = find(que[id][i-1].v); } tmp += (i == sz + 1); memcpy(fa, fa_tmp, sizeof(fa)); } } else { DFS(w+1, sz, cur, id, tmp); vis[w] = 1; DFS(w+1, sz, cur+1, id, tmp); vis[w] = 0; } } int main(){ n = read(); m = read(); for (int i=1,u,v;i<=m;i++) { e[i].u = u = read(); e[i].v = v = read(); _hash[i] = e[i].w = read(); } sort(_hash+1, _hash+1+m); tot = unique(_hash+1, _hash+1+m) - _hash - 1; for (int i=1,tmp;i<=m;i++) { tmp = lower_bound(_hash+1, _hash+1+tot, e[i].w) - _hash; que[tmp].push_back(e[i]); } for (int i=1;i<=n;i++) fa[i] = i; for (int i=1;i<=tot;i++) { for (int j=que[i].size()-1;~j;j--) { if (find(que[i][j].u) != find(que[i][j].v)) { fa[find(que[i][j].u)] = find(que[i][j].v); cnt[i]++; } } } for (int i=2;i<=n;i++) { if (find(i) != find(1)) { puts("0"); exit(0); } } for (int i=1;i<=n;i++) fa[i] = i; for (int i=1,tmp=0;i<=tot;i++,tmp=0) if (cnt[i]) { DFS(1,que[i].size(),0,i,tmp); for (int j=que[i].size()-1;~j;j--) fa[find(que[i][j].u)] = find(que[i][j].v); (vout *= tmp) %= MOD; } printf("%d\n",vout); return 0; }
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