题意:n个池塘，m条水渠，求从第一个池塘到第m个池塘能运送的最大流量；
思路：裸最大流dicnic算法。建分层图并不断找增广路，直到找不到增广路即为最大流。
邻接表实现：
#include <cstdio> #include <cstring> #include <queue> using namespace std; #define MAXN 210 #define INF 0x3f3f3f3f struct Edge { int st, ed; int c; int next; }edge[MAXN << 1]; int n, m; int s, t; int ans; int e = 0; int head[MAXN]; int d[MAXN]; int min(int a, int b) { return a < b ? a : b; } void init() { int i, j; int a, b, c; s = 1; //源点 t = m; //汇点 e = 0; //边数 ans = 0; memset(head, -1, sizeof(head)); for(i = 1; i <= n; i++) { scanf("%d%d%d", &a, &b, &c); edge[e].st = a; edge[e].ed = b; edge[e].c = c; edge[e].next = head[a]; head[a]= e++; edge[e].st = b; edge[e].ed = a; edge[e].next = head[b]; head[b] = e++; } } int bfs() { memset(d, -1, sizeof(d)); queue<int> q; d[s] = 0; q.push(s); int i; int cur; while(!q.empty()) { cur = q.front(); q.pop(); for(i = head[cur]; i != -1; i = edge[i].next) { if(d[edge[i].ed] == -1 && edge[i].c > 0) { d[edge[i].ed] = d[cur] + 1; q.push(edge[i].ed); } } } if(d[t] < 0) return 0; return 1; } int dinic(int x, int flow) { if(x == t) return flow; int i, a; for(i = head[x]; i != -1; i = edge[i].next) { if(d[edge[i].ed] == d[x] + 1 && edge[i].c > 0 && (a = dinic(edge[i].ed, min(flow, edge[i].c)))) { edge[i].c -= a; edge[i ^ 1].c += a; return a; } } return 0; } void solve() { while(scanf("%d%d", &n, &m) != EOF) { init(); while(bfs()) //建图，增广 { int increment; increment = dinic(1, INF); ans += increment; } printf("%d ", ans); } } int main() { solve(); return 0; }
邻接矩阵实现：
#include <cstdio> #include <cstring> #include <cstdlib> #include <iostream> #define min(x,y) ((x<y)?(x):(y)) using namespace std; const int MAX=0x5fffffff;// int tab[250][250];//邻接矩阵 int dis[250];//距源点距离,分层图 int q[2000],h,r;//BFS队列 ,首,尾 int N,M,ANS;//N:点数;M,边数 int BFS() //建分层图 { int i,j; memset(dis,0xff,sizeof(dis));//以-1填充 dis[1]=0; h=0;r=1; q[1]=1; while (h<r) { j=q[++h]; for (i=1;i<=N;i++) if (dis[i]<0 && tab[j][i]>0) { dis[i]=dis[j]+1; q[++r]=i; } } if (dis[N]>0) return 1; else return 0;//汇点的DIS小于零,表明BFS不到汇点 } //Find代表一次增广,函数返回本次增广的流量,返回0表示无法增广 int find(int x,int low)//Low是源点到现在最窄的(剩余流量最小)的边的剩余流量 { int i,a=0; if (x==N)return low;//是汇点 for (i=1;i<=N;i++) if (tab[x][i] >0 //联通 && dis[i]==dis[x]+1 //是分层图的下一层 &&(a=find(i,min(low,tab[x][i]))))//能到汇点(a != 0) { tab[x][i]-=a; tab[i][x]+=a; return a; } return 0; } int main() { //freopen("ditch.in" ,"r",stdin ); //freopen("ditch.out","w",stdout); int i,j,f,t,flow,tans; while (scanf("%d%d",&M,&N)!=EOF){ memset(tab,0,sizeof(tab)); for (i=1;i<=M;i++) { scanf("%d%d%d",&f,&t,&flow); tab[f][t]+=flow; } // ANS=0; while (BFS())//要不停地建立分层图,如果BFS不到汇点才结束 { while(tans=find(1,0x7fffffff))ANS+=tans;//一次BFS要不停地找增广路,直到找不到为止 } printf("%d ",ANS); } }
sap算法：（出现断链时直接退出；对当前弧优化）
#include<iostream> #include<cstdio> #include<memory.h> #include<cmath> using namespace std; #define MAXN 500 #define MAXE 40000 #define INF 0x7fffffff long ne,nv,tmp,s,t,index; struct Edge{ long next,pair; long v,cap,flow; }edge[MAXE]; long net[MAXN]; long ISAP() { long numb[MAXN],dist[MAXN],curedge[MAXN],pre[MAXN]; long cur_flow,max_flow,u,tmp,neck,i; memset(dist,0,sizeof(dist)); memset(numb,0,sizeof(numb)); memset(pre,-1,sizeof(pre)); for(i = 1 ; i <= nv ; ++i) curedge[i] = net[i]; numb[nv] = nv; max_flow = 0; u = s; while(dist[s] < nv) { /* first , check if has augmemt flow */ if(u == t) { cur_flow = INF; for(i = s; i != t;i = edge[curedge[i]].v) { if(cur_flow > edge[curedge[i]].cap) { neck = i; cur_flow = edge[curedge[i]].cap; } } for(i = s; i != t; i = edge[curedge[i]].v) { tmp = curedge[i]; edge[tmp].cap -= cur_flow; edge[tmp].flow += cur_flow; tmp = edge[tmp].pair; edge[tmp].cap += cur_flow; edge[tmp].flow -= cur_flow; } max_flow += cur_flow; u = neck; } /* if .... else ... */ for(i = curedge[u]; i != -1; i = edge[i].next) if(edge[i].cap > 0 && dist[u] == dist[edge[i].v]+1) break; if(i != -1) { curedge[u] = i; pre[edge[i].v] = u; u = edge[i].v; }else{ if(0 == --numb[dist[u]]) break; curedge[u] = net[u]; for(tmp = nv,i = net[u]; i != -1; i = edge[i].next) if(edge[i].cap > 0) tmp = tmp<dist[edge[i].v]?tmp:dist[edge[i].v]; dist[u] = tmp + 1; ++numb[dist[u]]; if(u != s) u = pre[u]; } } return max_flow; } int main() { long i,j,np,nc,m,n; long a,b,val; long g[MAXN][MAXN]; while(scanf("%d%d",&ne,&nv)!=EOF) { s = 1; t = nv; memset(g,0,sizeof(g)); memset(net,-1,sizeof(net)); for(i=0;i<ne;++i) { scanf("%ld%ld%ld",&a,&b,&val); g[a][b] += val; } for(i=1;i<=nv;++i) for(j = i; j <= nv;++j) if(g[i][j]||g[j][i]) { edge[index].next = net[i]; edge[index].v = j; edge[index].cap = g[i][j]; edge[index].flow = 0; edge[index].pair = index+1; net[i] = index++; edge[index].next = net[j]; edge[index].v = i; edge[index].cap = g[j][i]; edge[index].flow = 0; edge[index].pair = index-1; net[j] = index++; } printf("%ld ",ISAP()); } return 0; }