POJ 3723 解题报告

这道题是最小生成树问题。由于“收集”每个人只能用一次“关系”，所以利用的关系不能形成环。贪心从最小的关系开始，只要不能形成环就收集。这就是kruskal用并查集的算法。最后没收集的人每人按最大代价加入总代价就可以了。

thestoryofsnow

3723

Accepted

908K

344MS

C++

2132B

/*
ID: thestor1
LANG: C++
TASK: poj3723
*/
#include <iostream>
#include <fstream>
#include <cmath>
#include <cstdio>
#include <cstring>
#include <limits>
#include <string>
#include <vector>
#include <list>
#include <set>
#include <map>
#include <queue>
#include <stack>
#include <algorithm>
#include <cassert>

using namespace std;

const int MAXR = 50000;
const int MAXN = 10000;
const int MAXM = 10000;

void makeset(const int N, int parent[], int rank[])
{
for (int u = 0; u < N; ++u)
{
parent[u] = u;
rank[u] = 0;
}
}

int find(int u, int parent[])
{
if (parent[u] != u)
{
parent[u] = find(parent[u], parent);
}
return parent[u];
}

void union_set(int u, int v, int parent[], int rank[])
{
int ru = find(u, parent);
int rv = find(v, parent);
if (ru == rv)
{
return;
}

if (rank[ru] < rank[rv])
{
parent[ru] = rv;
}
else if (rank[rv] < rank[ru])
{
parent[rv] = ru;
}
else
{
parent[ru] = rv;
rank[rv]++;
}
}

class Edge
{
public:
int u, v, w;
Edge() {}
Edge(int u, int v, int w) : u(u), v(v), w(w) {}

bool operator< (const Edge &rhs) const
{
if (this->w != rhs.w)
{
return this->w < rhs.w;
}
return this->u < rhs.u || (this->u == rhs.u && this->v < rhs.v);
}
};

int kruskal(int parent[], int rank[], const int N, Edge edges[], const int M, int &collected)
{
makeset(N, parent, rank);

sort(edges, edges + M);

int mst = 0;
for (int i = 0; i < M; ++i)
{
Edge edge = edges[i];
if (find(edge.u, parent) != find(edge.v, parent))
{
collected++;
mst += edge.w;
union_set(edge.u, edge.v, parent, rank);
}
}
return mst;
}

int main()
{
int parent[MAXN + MAXM];
int rank[MAXN + MAXM];
Edge edges[MAXR];

int T;
scanf("%d", &T);
int N, M, R;
int xi, yi, di;
for (int t = 0; t < T; ++t) {
scanf("%d%d%d", &N, &M, &R);
for (int r = 0; r < R; ++r) {
scanf("%d%d%d", &xi, &yi, &di);
edges[r].u = xi;
edges[r].v = N + yi;
edges[r].w = 10000 - di;
}
int collected = 0;
int mst = kruskal(parent, rank, N + M, edges, R, collected);

int minimumPay = mst + (N + M - collected) * 10000;
printf("%d\n", minimumPay);
}
return 0;
}