POJ - 3436 ACM Computer Factory （ISAP EK Dinic）
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题目大意：有N台机器，每台机器能处理相应型态的电脑，处理完后，电脑将变成另一种形态。
每台机器有相应的工作限度，每次至多处理K台
现在问，在一次流水线生产中，最多可以产生多少台完整的电脑（流水线指的是在每一台机器的工作限度下）
解题思路：题目比较难理解，理解题目的话，就比较好做了
首先，将每台机器的点拆成两个点，权值为工作限度
如果机器能处理的电脑的状态全是0的话，就将其和超级源点连接，表示该机器进行第一步加工
如果机器处理完后的形态与另一台机器能处理的最初形态相同，就将其连线，表示下一台机器可以将其处理完的电脑再进一步加工
如果机器处理完后形态都为1，表示完工，将其和超级汇点相连，接着跑最大流
ISAP
#include <cstdio>#include <cstring>#include <algorithm>#include <vector>#include <queue>using namespace std;#define N 1010#define INF 0x3f3f3f3fstruct Edge { int from, to, cap, flow; Edge() {} Edge(int from, int to, int cap, int flow): from(from), to(to), cap(cap), flow(flow) {}};int g[70][70];struct ISAP { int p[N], num[N], cur[N], d[N]; int t, s, n, m; bool vis[N]; vector<int> G[N]; vector<Edge> edges; void init(int n) { this->n = n; for (int i = 0; i <= n; i++) { G[i].clear(); d[i] = INF; } edges.clear(); } void AddEdge(int from, int to, int cap) { edges.push_back(Edge(from, to, cap, 0)); edges.push_back(Edge(to, from, 0, 0)); int 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; d[t] = 0; vis[t] = 1; Q.push(t); while (!Q.empty()) { int u = Q.front(); Q.pop(); for (int i = 0; i < G[u].size(); i++) { Edge &e = edges[G[u][i] ^ 1]; if (!vis[e.from] && e.cap > e.flow) { vis[e.from] = true; d[e.from] = d[u] + 1; Q.push(e.from); } } } return vis[s]; } int Augment() { int u = t, flow = INF; while (u != s) { Edge &e = edges[p[u]]; flow = min(flow, e.cap - e.flow); u = edges[p[u]].from; } u = t; while (u != s) { edges[p[u]].flow += flow; edges[p[u] ^ 1].flow -= flow; u = edges[p[u]].from; } return flow; } int Maxflow(int s, int t) { this->s = s; this->t = t; int flow = 0; BFS(); if (d[s] >= n) return 0; memset(num, 0, sizeof(num)); memset(cur, 0, sizeof(cur)); for (int i = 0; i < n; i++) if (d[i] < INF) num[d[i]]++; int u = s; while (d[s] < n) { if (u == t) { flow += Augment(); u = s; } bool ok = false; for (int i = cur[u]; i < G[u].size(); i++) { Edge &e = edges[G[u][i]]; if (e.cap > e.flow && d[u] == d[e.to] + 1) { ok = true; p[e.to] = G[u][i]; cur[u] = i; u = e.to; break; } } if (!ok) { int Min = n - 1 ; for (int i = 0; i < G[u].size(); i++) { Edge &e = edges[G[u][i]]; if (e.cap > e.flow) Min = min(Min, d[e.to]); } if (--num[d[u]] == 0) break; num[d[u] = Min + 1]++; cur[u] = 0; if (u != s) u = edges[p[u]].from; } } return flow; }};ISAP isap;#define M 70#define P 20int in[M][P], out[M][P], f[M];int n, m;bool NullJudge(int cur) { for (int i = 1; i <= n; i++) if (in[cur][i] == 1) return false; return true;}bool FullJudge(int cur) { for (int i = 1; i <= n; i++) if (!out[cur][i]) return false; return true;}bool connect(int x, int y) { for (int i = 1; i <= n; i++) if (out[x][i] + in[y][i] == 1) return false; return true;}void init() { for (int i = 1; i <= m; i++) { scanf("%d", &f[i]); for (int j = 1; j <= n; j++) scanf("%d", &in[i][j]); for (int j = 1; j <= n; j++) scanf("%d", &out[i][j]); } int s = 2 * m + 1; int t = 2 * m + 2; isap.init(t); for (int i = 1; i <= m; i++) { isap.AddEdge(i, i + m, f[i]); if (NullJudge(i)) isap.AddEdge(s, i, f[i]); if (FullJudge(i)) isap.AddEdge(i + m, t, f[i]); for (int j = 1; j <= m; j++) if (i != j && connect(i, j)) isap.AddEdge(i + m, j, f[i]); } int ans[M][P]; int flow = isap.Maxflow(s, t); int cnt = 0; for (int i = m + 1; i <= m + m; i++) for (int j = 0; j < isap.G[i].size(); j++) { int v = isap.G[i][j]; Edge &e = isap.edges[v]; if (e.flow > 0 && e.to <= m) { ans[cnt][0] = i - m; ans[cnt][1] = e.to; ans[cnt][2] = e.flow; cnt++; } } printf("%d %d\n", flow, cnt); for (int i = 0; i < cnt; i++) printf("%d %d %d\n", ans[i][0], ans[i][1], ans[i][2]);}int main() { while (scanf("%d%d", &n, &m) == 2) { init(); } return 0;}EK
#include <cstdio>#include <cstring>#include <queue>#include <algorithm>#include <vector>using namespace std;#define N 1010#define INF 0x3f3f3f3fstruct Edge{ int from, to, cap, flow; Edge() {} Edge(int from, int to, int cap, int flow): from(from), to(to), cap(cap), flow(flow){}};struct EK{ vector<int> G[N]; vector<Edge> edges; int s, t, n, m, p[N]; bool vis[N]; void init(int n) { this->n = n; for (int i = 0; i <= n; i++) G[i].clear(); edges.clear(); } 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() { queue<int> q; memset(vis, 0, sizeof(vis)); vis[s] = 1; q.push(s); while (!q.empty()) { int u = q.front(); q.pop(); for (int i = 0; i < G[u].size(); i++) { Edge &e = edges[G[u][i]]; if (!vis[e.to] && e.cap > e.flow) { vis[e.to] = true; p[e.to] = G[u][i]; if (e.to == t) return true; q.push(e.to); } } } return false; } int Augment() { int flow = INF, u = t; while (u != s) { Edge &e = edges[p[u]]; flow = min(flow, e.cap - e.flow); u = e.from; } u = t; while (u != s) { edges[p[u]].flow += flow; edges[p[u] ^ 1].flow -= flow; u = edges[p[u]].from; } return flow; } int Maxflow(int s, int t) { this->s = s; this->t = t; int flow = 0; while (BFS()) { flow += Augment(); } return flow; }};EK ek;#define M 70#define P 20int in[M][P], out[M][P], f[M];int n, m;bool NullJudge(int cur) { for (int i = 1; i <= n; i++) if (in[cur][i] == 1) return false; return true;}bool FullJudge(int cur) { for (int i = 1; i <= n; i++) if (!out[cur][i]) return false; return true;}bool connect(int x, int y) { for (int i = 1; i <= n; i++) if (out[x][i] + in[y][i] == 1) return false; return true;}void init() { for (int i = 1; i <= m; i++) { scanf("%d", &f[i]); for (int j = 1; j <= n; j++) scanf("%d", &in[i][j]); for (int j = 1; j <= n; j++) scanf("%d", &out[i][j]); } int s = 2 * m + 1; int t = 2 * m + 2; ek.init(t); for (int i = 1; i <= m; i++) { ek.AddEdge(i, i + m, f[i]); if (NullJudge(i)) ek.AddEdge(s, i, f[i]); if (FullJudge(i)) ek.AddEdge(i + m, t, f[i]); for (int j = 1; j <= m; j++) if (i != j && connect(i, j)) ek.AddEdge(i + m, j, f[i]); } int ans[M][P]; int flow = ek.Maxflow(s, t); int cnt = 0; for (int i = m + 1; i <= m + m; i++) for (int j = 0; j < ek.G[i].size(); j++) { int v = ek.G[i][j]; Edge &e = ek.edges[v]; if (e.flow > 0 && e.to <= m) { ans[cnt][0] = i - m; ans[cnt][1] = e.to; ans[cnt][2] = e.flow; cnt++; } } printf("%d %d\n", flow, cnt); for (int i = 0; i < cnt; i++) printf("%d %d %d\n", ans[i][0], ans[i][1], ans[i][2]);}int main() { while (scanf("%d%d", &n, &m) == 2) { init(); } return 0;}Dinic
#include <cstdio>#include <cstring>#include <algorithm>#include <vector>#include <queue>using namespace std;#define N 1010#define INF 0x3f3f3f3fstruct Edge{ int from, to, cap, flow; Edge() {} Edge(int from, int to, int cap, int flow) : from(from), to(to), cap(cap), flow(flow) {}};struct Dinic{ int n, m, s, t; vector<Edge> edges; vector<int> G[N]; bool vis[N]; int d[N], cur[N]; void init(int n) { this->n = n; for (int i = 0; i <= n; i++) { G[i].clear(); } edges.clear(); } void AddEdge(int from, int to, int cap) { edges.push_back(Edge(from, to, cap, 0)); edges.push_back(Edge(to, from, 0, 0)); int 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 u = Q.front(); Q.pop(); for (int i = 0; i < G[u].size(); i++) { Edge &e = edges[G[u][i]]; if (!vis[e.to] && e.cap > e.flow) { vis[e.to] = true; d[e.to] = d[u] + 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; }};Dinic dinic;#define M 70#define P 20int in[M][P], out[M][P], f[M];int n, m;bool NullJudge(int cur) { for (int i = 1; i <= n; i++) if (in[cur][i] == 1) return false; return true;}bool FullJudge(int cur) { for (int i = 1; i <= n; i++) if (!out[cur][i]) return false; return true;}bool connect(int x, int y) { for (int i = 1; i <= n; i++) if (out[x][i] + in[y][i] == 1) return false; return true;}void init() { for (int i = 1; i <= m; i++) { scanf("%d", &f[i]); for (int j = 1; j <= n; j++) scanf("%d", &in[i][j]); for (int j = 1; j <= n; j++) scanf("%d", &out[i][j]); } int s = 2 * m + 1; int t = 2 * m + 2; dinic.init(t); for (int i = 1; i <= m; i++) { dinic.AddEdge(i, i + m, f[i]); if (NullJudge(i)) dinic.AddEdge(s, i, f[i]); if (FullJudge(i)) dinic.AddEdge(i + m, t, f[i]); for (int j = 1; j <= m; j++) if (i != j && connect(i, j)) dinic.AddEdge(i + m, j, f[i]); } int ans[M][P]; int flow = dinic.Maxflow(s, t); int cnt = 0; for (int i = m + 1; i <= m + m; i++) for (int j = 0; j < dinic.G[i].size(); j++) { int v = dinic.G[i][j]; Edge &e = dinic.edges[v]; if (e.flow > 0 && e.to <= m) { ans[cnt][0] = i - m; ans[cnt][1] = e.to; ans[cnt][2] = e.flow; cnt++; } } printf("%d %d\n", flow, cnt); for (int i = 0; i < cnt; i++) printf("%d %d %d\n", ans[i][0], ans[i][1], ans[i][2]);}int main() { while (scanf("%d%d", &n, &m) == 2) { init(); } return 0;} 0 0
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