UVA11248【最大流最小割入门】

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http://uva.onlinejudge.org/index.php?option=com_onlinejudge&Itemid=8&page=show_problem&problem=2205

给定一个有向网络，每条边均有一个容量。问是否存在一个从点1->n，流量为C的流。如果不存在，是否可以恰好修改一条弧的容量，使得这样的流存在？

第一行输入 N ,E, C (n个点, e条边）

下面e行u v cap 表示边

求最大流，如果流量>=c，则输出possible

否则修改边，边一定是最小割中的边。

依次把边增加到C中，然后求最大流，看最大流是否达到C

优化：求完最大流之后保存，每次在此基础上增广

ISAP

#include <cstdio>#include <cstring>#include <queue>#include <vector>#include <algorithm>using namespace std;const int maxn=100+10;const int INF = 1000000000;struct Edge{int from, to, cap, flow; };bool operator < (const Edge& a, const Edge& b) {  return a.from < b.from || (a.from == b.from && a.to < b.to);}struct ISAP{  int n, m, s, t;  vector<Edge> edges;  vector<int> G[maxn];   // 邻接表，G[i][j]表示结点i的第j条边在e数组中的序号  bool vis[maxn];        // BFS使用  int d[maxn];           // 从起点到i的距离  int cur[maxn];        // 当前弧指针  int p[maxn];          // 可增广路上的上一条弧  int num[maxn];        // 距离标号计数    void AddEdge(int from, int to, int cap) {    edges.push_back((Edge){from, to, cap, 0});    edges.push_back((Edge){to, from, 0, 0});    m = edges.size();    G[from].push_back(m-2);    G[to].push_back(m-1);  }    bool BFS() {    memset(vis, 0, sizeof(vis));    queue<int> Q;    Q.push(t);    vis[t] = 1;    d[t] = 0;    while(!Q.empty()) {      int x = Q.front(); Q.pop();      for(int i = 0; i < G[x].size(); i++) {        Edge& e = edges[G[x][i]^1];        if(!vis[e.from] && e.cap > e.flow) {          vis[e.from] = 1;          d[e.from] = d[x] + 1;          Q.push(e.from);        }      }    }    return vis[s];  }    void ClearAll(int n) {    this->n = n;    for(int i = 0; i < n; i++) G[i].clear();    edges.clear();  }    void ClearFlow() {    for(int i = 0; i < edges.size(); i++) edges[i].flow = 0;      }    int  Augment(){  int x=t,a=INF;  while(x!=s){  Edge &e=edges[p[x]];  a=min(a,e.cap-e.flow);  x=edges[p[x]].from;  }  x=t;  while(x != s) {      edges[p[x]].flow += a;      edges[p[x]^1].flow -= a;      x = edges[p[x]].from;    }    return a;  }    int Maxflow(int s, int t, int need) {    this->s = s; this->t = t;    int flow = 0;    BFS();    memset(num, 0, sizeof(num));    for(int i = 0; i < n; i++) num[d[i]]++;    int x = s;    memset(cur, 0, sizeof(cur));    while(d[s] < n) {      if(x == t) {        flow += Augment();        if(flow >= need) return flow;        x = s;      }      int ok = 0;      for(int i = cur[x]; i < G[x].size(); i++) {        Edge& e = edges[G[x][i]];        if(e.cap > e.flow && d[x] == d[e.to] + 1) { // Advance          ok = 1;          p[e.to] = G[x][i];          cur[x] = i; // 注意          x = e.to;          break;        }      }      if(!ok) { // Retreat        int m = n-1; // 初值注意        for(int i = 0; i < G[x].size(); i++) {          Edge& e = edges[G[x][i]];          if(e.cap > e.flow) m = min(m, d[e.to]);        }        if(--num[d[x]] == 0) break;        num[d[x] = m+1]++;        cur[x] = 0; // 注意        if(x != s) x = edges[p[x]].from;      }    }    return flow;  }    vector<int> Mincut() { // call this after maxflow    BFS();    vector<int> ans;    for(int i = 0; i < edges.size(); i++) {      Edge& e = edges[i];      if(!vis[e.from] && vis[e.to] && e.cap > 0) ans.push_back(i);    }    return ans;  }  void Reduce() {    for(int i = 0; i < edges.size(); i++) edges[i].cap -= edges[i].flow;  }  void print() {    printf("Graph:\n");    for(int i = 0; i < edges.size(); i++)      printf("%d->%d, %d, %d\n", edges[i].from, edges[i].to , edges[i].cap, edges[i].flow);  }};ISAP g;int main(){int n,e,c,kase=0;while(scanf("%d%d%d",&n,&e,&c)==3&&n){g.ClearAll(n);while(e--) {//读入边      int b1, b2, fp;      scanf("%d%d%d", &b1, &b2, &fp);      g.AddEdge(b1-1, b2-1, fp);    }int flow = g.Maxflow(0, n-1, INF);    printf("Case %d: ", ++kase);    if(flow >= c) printf("possible\n");    else {      vector<int> cut = g.Mincut();      g.Reduce();      vector<Edge> ans;      for(int i = 0; i < cut.size(); i++) {        Edge& e = g.edges[cut[i]];        e.cap = c;        g.ClearFlow();        if(flow + g.Maxflow(0, n-1, c-flow) >= c) ans.push_back(e);        e.cap = 0;      }      if(ans.empty()) printf("not possible\n");      else {        sort(ans.begin(), ans.end());        printf("possible option:(%d,%d)", ans[0].from+1, ans[0].to+1);        for(int i = 1; i < ans.size(); i++)          printf(",(%d,%d)", ans[i].from+1, ans[i].to+1);        printf("\n");      }    }  }  return 0;}

Dinic

#include<cstdio>#include<cstring>#include<queue>#include<vector>#include<algorithm>using namespace std;const int maxn = 100 + 10;const int INF = 1000000000;struct Edge {  int from, to, cap, flow;};bool operator < (const Edge& a, const Edge& b) {  return a.from < b.from || (a.from == b.from && a.to < b.to);}struct Dinic {  int n, m, s, t;  vector<Edge> edges;    // 边数的两倍  vector<int> G[maxn];   // 邻接表，G[i][j]表示结点i的第j条边在e数组中的序号  bool vis[maxn];         // BFS使用  int d[maxn];           // 从起点到i的距离  int cur[maxn];        // 当前弧指针  void ClearAll(int n) {    for(int i = 0; i < n; i++) G[i].clear();    edges.clear();  }  void ClearFlow() {    for(int i = 0; i < edges.size(); i++) edges[i].flow = 0;      }  void AddEdge(int from, int to, int cap) {    edges.push_back((Edge){from, to, cap, 0});    edges.push_back((Edge){to, from, 0, 0});    m = edges.size();    G[from].push_back(m-2);    G[to].push_back(m-1);  }  bool BFS() {    memset(vis, 0, sizeof(vis));    queue<int> Q;    Q.push(s);    vis[s] = 1;    d[s] = 0;    while(!Q.empty()) {      int x = Q.front(); Q.pop();      for(int i = 0; i < G[x].size(); i++) {        Edge& e = edges[G[x][i]];        if(!vis[e.to] && e.cap > e.flow) {          vis[e.to] = 1;          d[e.to] = d[x] + 1;          Q.push(e.to);        }      }    }    return vis[t];  }  int DFS(int x, int a) {    if(x == t || a == 0) return a;    int flow = 0, f;    for(int& i = cur[x]; i < G[x].size(); i++) {      Edge& e = edges[G[x][i]];      if(d[x] + 1 == d[e.to] && (f = DFS(e.to, min(a, e.cap-e.flow))) > 0) {        e.flow += f;        edges[G[x][i]^1].flow -= f;        flow += f;        a -= f;        if(a == 0) break;      }    }    return flow;  }  int Maxflow(int s, int t) {    this->s = s; this->t = t;    int flow = 0;    while(BFS()) {      memset(cur, 0, sizeof(cur));      flow += DFS(s, INF);    }    return flow;  }  vector<int> Mincut() { // call this after maxflow    vector<int> ans;    for(int i = 0; i < edges.size(); i++) {      Edge& e = edges[i];      if(vis[e.from] && !vis[e.to] && e.cap > 0) ans.push_back(i);    }    return ans;  }  void Reduce() {    for(int i = 0; i < edges.size(); i++) edges[i].cap -= edges[i].flow;  }};Dinic g;int main() {  int n, e, c, kase = 0;  while(scanf("%d%d%d", &n, &e, &c) == 3 && n) {    g.ClearAll(n);    while(e--) {      int b1, b2, fp;      scanf("%d%d%d", &b1, &b2, &fp);      g.AddEdge(b1-1, b2-1, fp);    }    int flow = g.Maxflow(0, n-1);    printf("Case %d: ", ++kase);    if(flow >= c) printf("possible\n");    else {      vector<int> cut = g.Mincut();      g.Reduce();      vector<Edge> ans;      for(int i = 0; i < cut.size(); i++) {        Edge& e = g.edges[cut[i]];        e.cap = c;        g.ClearFlow();        if(flow + g.Maxflow(0, n-1) >= c) ans.push_back(e);        e.cap = 0;      }      if(ans.empty()) printf("not possible\n");      else {        sort(ans.begin(), ans.end());        printf("possible option:(%d,%d)", ans[0].from+1, ans[0].to+1);        for(int i = 1; i < ans.size(); i++)          printf(",(%d,%d)", ans[i].from+1, ans[i].to+1);        printf("\n");      }    }  }  return 0;}

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