POJ 3723 解题报告

来源：互联网发布：淘宝网店上架宝贝教程编辑：程序博客网时间：2024/06/06 03:23

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。

thestoryofsnow3723Accepted908K344MSC++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;}

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