UVA 11354 Bond(MST + LCA)

n<=50000, m<=100000的无向图,对于Q<=50000个询问,每次求q->p的瓶颈路。

其实求瓶颈路数组maxcost[u][v]有用邻接矩阵prim的方法。但是对于这个题的n,邻接矩阵是存不下的。。。所以默默的抄了一遍大白书上的算法。。。先用kruskal求MST,然后对于MST树,每次询问求p和q的LCA,在求LCA的过程中顺便求出瓶颈路。。。

#include<algorithm>
#include<iostream>
#include<cstring>
#include<cstdlib>
#include<fstream>
#include<sstream>
#include<bitset>
#include<vector>
#include<string>
#include<cstdio>
#include<cmath>
#include<stack>
#include<queue>
#include<stack>
#include<map>
#include<set>
#define FF(i, a, b) for(int i=a; i<b; i++)
#define FD(i, a, b) for(int i=a; i>=b; i--)
#define REP(i, n) for(int i=0; i<n; i++)
#define CLR(a, b) memset(a, b, sizeof(a))
#define debug puts("**debug**")
#define LL long long
#define PB push_back
using namespace std; const int maxn = 50005;
const int maxm = 100010;
const int INF = 1e9;
int n, m;
int fa[maxn], pa[maxn], cost[maxn], L[maxn], anc[maxn][100], maxcost[maxn][100];
struct Edge
{
int to, dist;
};
vector<Edge> edges;
vector<int> G[maxn];
inline void add(int a, int b, int c)
{
edges.PB((Edge){b, c});
edges.PB((Edge){a, c});
int nc = edges.size();
G[a].PB(nc-2); G[b].PB(nc-1);
} inline void init()
{
L[1] = cost[1] = 0;
REP(i, n+1) pa[i] = i;
REP(i, n+1) G[i].clear(); edges.clear();
} int findset(int x) { return x == pa[x] ? x : pa[x] = findset(pa[x]); } struct E
{
int u, v, w;
bool operator < (const E rhs) const
{
return w < rhs.w;
}
}e[maxm]; void MST()
{
sort(e, e+m);
int cnt = 0;
REP(i, m)
{
int x = findset(e[i].u), y = findset(e[i].v);
if(x != y)
{
pa[x] = y;
cnt++;
add(e[i].u, e[i].v, e[i].w);
}
if(cnt == n-1) return ;
}
} void dfs(int u, int f)
{
fa[u] = f;
int nc = G[u].size();
REP(i, nc)
{
int v = edges[G[u][i]].to, w = edges[G[u][i]].dist;
if(v != f)
{
cost[v] = w;
L[v] = L[u] + 1;
dfs(v, u);
}
}
} void progress()
{
FF(i, 1, n+1)
{
anc[i][0] = fa[i], maxcost[i][0] = cost[i];
for(int j=1; (1 << j) < n; j++) anc[i][j] = -1;
}
for(int j=1; (1 << j) < n; j++) FF(i, 1, n+1)
if(anc[i][j-1] != -1)
{
int a = anc[i][j-1];
anc[i][j] = anc[a][j-1];
maxcost[i][j] = max(maxcost[i][j-1], maxcost[a][j-1]);
}
} int query(int p, int q)
{
int lo;
if(L[p] < L[q]) swap(p, q);
for(lo = 1; (1 << lo) <= L[p]; lo++); lo--; int ans = -INF;
FD(i, lo, 0)
if(L[p] - (1<<i) >= L[q]) ans = max(ans, maxcost[p][i]), p = anc[p][i]; if(p == q) return ans; //LCA -> p FD(i, lo, 0)
if(anc[p][i] != -1 && anc[p][i] != anc[q][i])
{
ans = max(ans, maxcost[p][i]), p = anc[p][i];
ans = max(ans, maxcost[q][i]), q = anc[q][i];
} ans = max(ans, cost[p]);
ans = max(ans, cost[q]);
return ans; //LCA -> fa[q] fa[p]
} int main()
{
int flag = 0;
while(~scanf("%d%d", &n, &m))
{
if(flag++) puts(""); init();
REP(i, m) scanf("%d%d%d", &e[i].u, &e[i].v, &e[i].w); MST();
dfs(1, -1);
progress(); int Q, p, q;
scanf("%d", &Q);
while(Q--)
{
scanf("%d%d", &p, &q);
printf("%d\n", query(p, q));
}
}
return 0;
}
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