• Edmonds-Karp
  BFS找增廣路，找到增廣路，更新殘余網絡。

// 臨接矩陣 // pre記錄前驅節點 int G[maxn][maxn], pre[maxn], vis[maxn], n, m; // BFS找增廣路 bool bfs(int s, int e) {memset(vis, 0, sizeof(vis));memset(pre, -1, sizeof(pre));pre[s] = s;vis[s] = 1;queue<int> que;que.push(s);while (!que.empty()) {int u = que.front();que.pop();// 訪問u所有的出邊， 判斷能否增廣for (int i = 0; i <= e; i++) {if (G[u][i] && !vis[i]) {pre[i] = u;que.push(i);vis[i] = 1;if (i == e) return 1; // 到匯點存在增廣路}}}return 0; } int EK(int s, int e) {int ans = 0;while (bfs(s, e)) { // 判斷是否存在增廣路int MIN = inf;// 遍歷增廣路上所有邊取流量最小的邊for (int i = e; i != s; i = pre[i]) {MIN = min(MIN, G[pre[i]][i]);}// 更新增廣路上的流量， 正向減，反向加for (int i = e; i != s; i = pre[i]) {G[pre[i]][i] -= MIN;G[i][pre[i]] += MIN;}ans += MIN;}return ans; } int cnt; struct ac{int v, c, nex; }edge[maxn << 8]; int vis[maxn], head[maxn], path[maxn]; void init() {cnt = 0;memset(head, -1, sizeof(head)); } void addedge(int u, int v, int c) {// 正向邊edge[cnt] = {v, c, head[u]};head[u] = cnt++;// 反向邊edge[cnt] = {u, 0, head[v]};head[v] = cnt++; } bool bfs(int s, int t) {memset(vis, 0, sizeof(vis));memset(path, -1, sizeof(path));queue<int> que;que.push(s);vis[s] = 1;while (!que.empty()) {int u = que.front();que.pop();// 遍歷u的所有出邊for (int i = head[u]; i != -1; i = edge[i].nex) {int v = edge[i].v;int c = edge[i].c;// 判斷能否增廣if (c == 0 || vis[v]) continue;path[v] = i;vis[v] = 1;que.push(v);if (v == t) return true;}}return false; } int EK(int s, int t) {int ans = 0;while (bfs(s, t)) {int flow = inf;for (int i = path[t]; i != -1; i = path[edge[i^1].v]) {flow = min(flow, edge[i].c);}for (int i = path[t]; i != -1; i = path[edge[i^1].v]) {edge[i].c -= flow;edge[i^1].c += flow;} ans += flow;}return ans; }

• Dinic

struct ac{int v, c, nex; }edge[maxn << ]; int s, e; int head[maxn], dis[maxn], curedge[maxn], cnt; void init() {cnt = 0;memset(head, -1, sizeof(head)); } void addedge(int u, int v, int c) {// 正向建邊edge[cnt] = {v, c, head[u]};head[u] = cnt++;// 反向建邊, 流量為0edge[cnt] = {u, 0, head[v]};head[v] = cnt++; } bool bfs() {queue<int> que;que.push(s);memset(dis, 0, sizeof(dis)); // 對圖進行分層dis[s] = 1;while (!que.empty()) {int u = que.front();que.pop();for (int i = head[u]; i != -1; i = edge[i].nex) {int v = edge[i].v;int c = edge[i].c;// 如果節點v已經分過層或者u->v流量為0, continueif (dis[v] || c == 0) continue;dis[v] = dis[u] + 1; // 對v進行標記并加入隊列que.push(v);}}return dis[e] > 0; // 判斷是否存在增廣路，s是否能到達e }int dfs(int u, int flow) { // 增廣路走到u點的最小流量為flowif (u == e || flow == 0) return flow;// 遍歷u的所有出邊for (int &i = curedge[u]; i != -1; i = edge[i].nex) { // 當前弧優化int v = edge[i].v;int c = edge[i].c;// 判斷能否u->v增廣if (dis[v] != dis[u] + 1 || c == 0) continue;int d = dfs(v, min(flow, c));if (d > 0) { // 找到一條增廣路，修改增廣路上的正反向邊edge[i].c -= d;edge[i^1].c += d;return d;} }dis[u] = -1; // // 炸點優化return 0; } int Dinic() {int sum = 0, d;while (bfs()) { // 判讀是否存在增廣路for (int i = 0; i <= e; ++i) curedge[i] = head[i]; // copy head數組，在dfs中可以直接得到下一條沒有被增廣過的邊while ((d = dfs(s, inf)) > 0) sum += d; // 多次dfs找增廣路}return sum; }

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