【POJ 1679】 The Unique MST

【题目链接】

             点击打开链接

【算法】

           先求出图的最小生成树

           枚举不在最小生成树上的边，若加入这条边，则形成了一个环，如果在环上且在最小生成树上的权值最大的边等于

           这条边的权值，那么，显然最小生成树不唯一

           树上倍增可以解决这个问题

【代码】

           

#include <algorithm>
#include <bitset>
#include <cctype>
#include <cerrno>
#include <clocale>
#include <cmath>
#include <complex>
#include <cstdio>
#include <cstdlib>
#include <cstring>
#include <ctime>
#include <deque>
#include <exception>
#include <fstream>
#include <functional>
#include <limits>
#include <list>
#include <map>
#include <iomanip>
#include <ios>
#include <iosfwd>
#include <iostream>
#include <istream>
#include <ostream>
#include <queue>
#include <set>
#include <sstream>
#include <stdexcept>
#include <streambuf>
#include <string>
#include <utility>
#include <vector>
#include <cwchar>
#include <cwctype>
#include <stack>
#include <limits.h>
using namespace std;
#define MAXN 110
#define MAXM 1000010
#define MAXLOG 20

struct Edge
{
        int x,y;
        long long w;
} edge[MAXM];

int T,n,m,i;
long long val;
vector< pair<int,long long> > e[MAXN];
bool on_mst[MAXM];
int fa[MAXN],anc[MAXN][MAXLOG],dep[MAXN];
long long mx[MAXN][MAXLOG];
bool not_unique;

inline bool cmp(Edge a,Edge b) { return a.w < b.w; }
inline int get_root(int x)
{
        if (fa[x] == x) return x;
        return fa[x] = get_root(fa[x]);
}
inline void kruskal()
{
        int i,x,y,sx,sy;
        long long w;
        for (i = 1; i <= n; i++) fa[i] = i;
        for (i = 1; i <= m; i++) on_mst[i] = false;
        sort(edge+1,edge+m+1,cmp);
        for (i = 1; i <= m; i++)
        {
                x = edge[i].x;
                y = edge[i].y;
                w = edge[i].w;
                sx = get_root(x); 
                sy = get_root(y);
                if (sx != sy)
                {
                        on_mst[i] = true;
                        val += w;
                        fa[sx] = sy;
                        e[x].push_back(make_pair(y,w));
                        e[y].push_back(make_pair(x,w));    
                }    
        }    
}
inline void build(int u)
{
        int i,v;
        for (i = 1; i < MAXLOG; i++) 
        {
                anc[u][i] = anc[anc[u][i-1]][i-1];
                mx[u][i] = max(mx[u][i-1],mx[anc[u][i-1]][i-1]);
        }
        for (i = 0; i < e[u].size(); i++)
        {
                v = e[u][i].first;
                if (anc[u][0] != v)
                {
                        dep[v] = dep[u] + 1;
                        anc[v][0] = u;
                        mx[v][0] = e[u][i].second;
                        build(v);                        
                }
        }
}
inline long long get(int x,int y)
{
        int i,t;
        long long ans = 0;
        if (dep[x] > dep[y]) swap(x,y);
        t = dep[y] - dep[x];
        for (i = 0; i < MAXLOG; i++)
        {
                if (t & (1 << i))
                {
                        ans = max(ans,mx[y][i]);
                        y = anc[y][i];
                }
        }
        if (x == y) return ans;
        for (i = MAXLOG - 1; i >= 0; i--)
        {
                if (anc[x][i] != anc[y][i])
                {
                        ans = max(ans,max(mx[x][i],mx[y][i]));
                        x = anc[x][i];
                        y = anc[y][i];
                }
        }
        return max(ans,max(mx[x][0],mx[y][0]));
}
int main() 
{
        
        scanf("%d",&T);
        while (T--)
        {
                scanf("%d%d",&n,&m);
                val = 0;
                not_unique = false;
                for (i = 1; i <= n; i++) 
                {
                        dep[i] = 0;
                        e[i].clear();
                        memset(anc[i],0,sizeof(anc[i]));
                        memset(mx[i],0,sizeof(mx[i]));
                }
                for (i = 1; i <= m; i++) scanf("%d%d%lld",&edge[i].x,&edge[i].y,&edge[i].w);
                kruskal();
                build(1);
                for (i = 1; i <= m; i++) 
                {
                        if (!on_mst[i]) 
                                not_unique |= (get(edge[i].x,edge[i].y) == edge[i].w);
                }
                if (not_unique) printf("Not Unique!
"); 
                else printf("%lld
",val);
        }
        
        return 0;
    
}