POJ 3801 有上下界最小流
时间：2014-05-08 23:31:26
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1: /**
2: POJ 3801 有上下界的最小流
3: 4: 1、对supersrc到supersink 求一次最大流，记为f1。（在有源汇的情况下，先使整个网络趋向必须边尽量满足的情况）
5: 2、添加一条边sink -> src，流量上限为INF，这条边记为p。（构造无源汇网络）
6: 3、对supersrc到supersink再次求最大流，记为f2,这里判断是否为可行流。（要判断可行，必须先构造无源汇网络流，因此要再次求最大流）
7: 8: 此网络流的最小流即为 sink -> src 的流量
9: */
10: 11: #include<iostream> 12: #include<cmath> 13: #include<memory>14: #include <string.h>
15: #include <cstdio> 16: #include <vector>17: using namespace std;
18: 19: #define V 150 // vertex
20: #define E (V*V) // edge
21: #define INF 0x3F3F3F3F // 1061109567
22: 23: int i,j,k;
24: #define REP(i,n) for((i)=0;(i)<(int)(n);(i)++)
25: #define snuke(c,itr) for(__typeof((c).begin()) itr=(c).begin();itr!=(c).end();itr++)
26: 27: struct MaxFlow
28: {29: struct Edge
30: {31: int v, w, next; //w for capicity
32: int lb,up;
33: } edge[E]; 34: 35: int head[V]; // head[u]表示顶点u第一条邻接边的序号, 若head[u] = -1, u没有邻接边
36: int e; // the index of the edge
37: int src, sink;
38: int net[V]; // 流入此节点的流的下界和 - 流出此节点的流的下界和,对于带上下界的来进行使用
39: 40: 41: void addedge(int u, int v, int w, int lb = 0, int up = INF, int rw = 0)
42: { 43: edge[e].v = v; 44: edge[e].w= w; 45: edge[e].next = head[u]; 46: edge[e].lb = lb, edge[e].up = up; 47: head[u] = e++;48: // reverse edge v -> u
49: edge[e].v = u; 50: edge[e].w = rw; 51: edge[e].lb = lb, edge[e].up = up; 52: edge[e].next = head[v]; 53: head[v] = e++; 54: } 55: 56: int ISAP(int VertexNum )
57: {58: int u, v, max_flow, aug, min_lev;
59: int curedge[V], parent[V], level[V];
60: int count[V], augment[V];
61: 62: memset(level, 0, sizeof(level));
63: memset(count, 0, sizeof(count));
64: REP(i,VertexNum+1) curedge[i] = head[i]; 65: max_flow = 0; 66: augment[src] = INF; 67: parent[src] = -1; 68: u = src; 69: 70: while (level[src] < VertexNum)
71: {72: if (u == sink)
73: { 74: max_flow += augment[sink]; 75: aug = augment[sink];76: for (v = parent[sink]; v != -1; v = parent[v])
77: { 78: i = curedge[v]; 79: edge[i].w -= aug; 80: edge[i^1].w += aug; 81: augment[edge[i].v] -= aug;82: if (edge[i].w == 0) u = v;
83: } 84: }85: for (i = curedge[u]; i != -1; i = edge[i].next)
86: { 87: v = edge[i].v;88: if (edge[i].w > 0 && level[u] == (level[v]+1))
89: { 90: augment[v] = min(augment[u], edge[i].w); 91: curedge[u] = i; 92: parent[v] = u; 93: u = v;94: break;
95: } 96: }97: if (i == -1)
98: {99: if (--count[level[u]] == 0) break;
100: curedge[u] = head[u]; 101: min_lev = VertexNum;102: for (i = head[u]; i != -1; i = edge[i].next)
103: if (edge[i].w > 0)
104: min_lev = min(level[edge[i].v], min_lev); 105: level[u] = min_lev + 1; 106: count[level[u]]++;107: if (u != src ) u = parent[u];
108: } 109: }110: return max_flow;
111: }112: void solve()
113: {114: int n, m;
115: while (scanf("%d %d", &n, &m) != EOF)
116: {117: if (n+m == 0) break;
118: e = 0;119: memset(head, -1, sizeof(head));
120: memset(net, 0, sizeof(net));
121: 122: int s = n+1, t = n+2;
123: src = n+3, sink = n+4;124: char a[5], b[5];
125: int c;
126: while (m--)
127: {128: scanf("%s %s %d", a, b, &c);
129: int u, v;
130: if (a[0] == ‘+‘) u = s;
131: else sscanf(a, "%d", &u); // 注意这里读取信息
132: if (b[0] == ‘-‘) v = t;
133: else sscanf(b, "%d", &v);
134: net[v] += c, net[u] -= c; 135: addedge(u,v,INF,c, INF); 136: }137: vector<int> CE;
138: for(int i=1; i<=n+2; i++)
139: {140: if(net[i] >=0)
141: { 142: CE.push_back(e); 143: addedge(src, i, net[i]); 144: }145: else
146: { 147: CE.push_back(e); 148: addedge(i, sink, -net[i]); 149: } 150: }151: int flow = 0;
152: flow = ISAP(n+4);153: int p = e;
154: addedge(t, s, INF, 0, INF); 155: flow += ISAP(n+4);156: bool flag = true;
157: for(int i= 0; i< CE.size(); i++)
158: {159: if(edge[CE[i]].w !=0)
160: {161: flag = false;
162: break;
163: } 164: }165: if (!flag)
166: printf("impossible\n");
167: else
168: printf("%d\n", edge[p^1].w);
169: } 170: } 171: } sap; 172: 173: int main()
174: {175: // freopen("1.txt","r",stdin);
176: sap.solve();177: return 0;
178: }
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