[網路流24題] 18 分配問題(二分圖最佳匹配,最小費用最大流)
阿新 • • 發佈:2019-01-05
題目大意:
有n個工作要分配給n個人做,給出每個人做每件工作所產生的效益, 求出最小總效益和最大總效益;
思路分析:
這道題 和17題的思路是一樣的;
①:設立一個源點s,從s向每個人連一條邊,容量為1, 費用為0;
②:從每個人向每個工作連一條邊,容量為INF,費用為這個人做該工作產生的效益;
③:設立一個匯點,從每個工作向匯點連一條邊,容量為1,費用為0;
程式碼實現:
#include<cstdio> #include<cstring> #include<queue> #include<iostream> #define Min(a,b) ((a)<(b)?(a):(b)) #define Max(a,b) ((a)>(b)?(a):(b)) using namespace std; const int N=210, M=20410, INF=0x3f3f3f3f; int n, m, s, t ,top, sum_cost; int head[N], vis[N], dis[N], minflow[N], pre[N], path[N], cost[110][110]; struct Edge{ int to, next, flow, cost; Edge(int _to=0,int _next=0,int _flow=0,int _cost=0):to(_to),next(_next),flow(_flow),cost(_cost){} }edge[M]; void Addedge(int from, int to, int flow, int cost){ edge[top] = Edge(to, head[from], flow, cost); head[from] = top++; edge[top] = Edge(from, head[to], 0, -cost); head[to] = top++; } int Spfa(){ queue<int> q; memset(dis, 0x3f, sizeof(dis)); memset(minflow, 0x3f, sizeof(minflow)); memset(path, -1, sizeof(path)); memset(vis, 0, sizeof(vis)); dis[s]=0; q.push(s); while(!q.empty()){ int u = q.front(); q.pop(); vis[u] = 0; for(int i = head[u]; i + 1; i = edge[i].next){ if(edge[i].flow && dis[edge[i].to] > dis[u] + edge[i].cost){ dis[edge[i].to] = dis[u] + edge[i].cost; pre[edge[i].to] = u; path[edge[i].to] = i; minflow[edge[i].to] = Min(minflow[u], edge[i].flow); if(!vis[edge[i].to]){ vis[edge[i].to] = 1; q.push(edge[i].to); } } } } if(dis[t] == INF) return 0; sum_cost += minflow[t]*dis[t]; int u = t; while(u!=s){ edge[path[u]].flow -= minflow[t]; edge[path[u]^1].flow += minflow[t]; u = pre[u]; } return 1; } int main(){ freopen("job.in", "r", stdin); freopen("job.out", "w", stdout); scanf("%d", &n); memset(head, -1, sizeof(head)); top = s = sum_cost = 0; t = n * 2 + 1; int va; for(int i = 1; i <= n; ++i){ Addedge(s, i, 1, 0); for(int j = 1; j <= n; ++j){ scanf("%d", &cost[i][j]); Addedge(i, j+n, INF, cost[i][j]); } Addedge(i+n, t, 1, 0); } while(Spfa()); printf("%d\n", sum_cost); memset(head, -1, sizeof(head)); top = s = sum_cost = 0; t = n * 2 + 1; for(int i = 1; i <= n; ++i){ Addedge(s, i, 1, 0); for(int j = 1; j <= n; ++j) Addedge(i, j+n, INF, -cost[i][j]); Addedge(i+n, t, 1, 0); } while(Spfa()); printf("%d\n", -sum_cost); }