swap u and v in dfs (#164)

Author: lrvideckis

library/graphs/bcc_callback.hpp

@@ -9,31 +9,31 @@
 //!       int count_edges = 0;
 //!       rep (i, 0, sz(nodes) - 1) {
 //!         seen[nodes[i]] = 1;
-//!         for (int v : adj[nodes[i]]) if (!seen[v]) {
-//!           // edge nodes[i] <=> v is in current BCC
+//!         for (int u : adj[nodes[i]]) if (!seen[u]) {
+//!           // edge nodes[i] <=> u is in current BCC
 //!           count_edges++;
 //!         }
 //!       }
 //!       if (count_edges == 1) {
 //!         // nodes[0] <=> nodes[1] is a bridge
 //!         return;
 //!       }
-//!       for (int v : nodes) uf.join(v, nodes[0]);
+//!       for (int u : nodes) uf.join(u, nodes[0]);
 //!     });
 //!     vector<basic_string<int>> bridge_tree(n);
 //!     rep (i, 0, n)
-//!       for (int v : adj[i])
-//!         if (!uf.sameSet(i, v))
-//!           bridge_tree[uf.find(i)] += uf.find(v);
+//!       for (int u : adj[i])
+//!         if (!uf.sameSet(i, u))
+//!           bridge_tree[uf.find(i)] += uf.find(u);
 //!   }
 //!
 //!   vector<basic_string<int>> adj(n);
 //!   vector<basic_string<int>> block_vertex_tree(2 * n);
 //!   int bcc_id = n;
 //!   bcc_callback(adj, [&](const vi& nodes) {
-//!     for (int v : nodes) {
-//!       block_vertex_tree[v] += bcc_id;
-//!       block_vertex_tree[bcc_id] += v;
+//!     for (int u : nodes) {
+//!       block_vertex_tree[u] += bcc_id;
+//!       block_vertex_tree[bcc_id] += u;
 //!     }
 //!     bcc_id++;
 //!   });
@@ -44,13 +44,13 @@
 void bcc_callback(const auto& adj, auto f) {
   int n = sz(adj), q = 0, s = 0;
   vi t(n), st(n);
-  auto dfs = [&](auto&& self, int v) -> int {
-    int l = t[v] = ++q;
-    for (int u : adj[v]) {
+  auto dfs = [&](auto&& self, int u) -> int {
+    int l = t[u] = ++q;
+    for (int v : adj[u]) {
       int siz = s, lu = 0;
-      l = min(l, t[u] ?: (lu = self(self, st[s++] = u)));
-      if (lu >= t[v]) {
-        st[s++] = v;
+      l = min(l, t[v] ?: (lu = self(self, st[s++] = v)));
+      if (lu >= t[u]) {
+        st[s++] = u;
         f({siz + all(st) - n + s});
         s = siz;
       }

library/graphs/hopcroft_karp.hpp

@@ -29,31 +29,31 @@ struct hopcroft_karp {
       mvc_l.assign(lsz, 1);
       mvc_r.assign(rsz, 0);
       while (!empty(q)) {
-        int v = q.front();
+        int u = q.front();
         q.pop();
-        mvc_l[v] = 0;
-        for (int u : adj[v]) {
-          mvc_r[u] = 1;
-          int w = to_l[u];
+        mvc_l[u] = 0;
+        for (int v : adj[u]) {
+          mvc_r[v] = 1;
+          int w = to_l[v];
           if (w == -1) found = 1;
           else if (level[w] == -1) {
-            level[w] = level[v] + 1;
+            level[w] = level[u] + 1;
             q.push(w);
           }
         }
       }
       if (!found) break;
-      auto dfs = [&](auto&& self, int v) -> bool {
-        for (int u : adj[v]) {
-          int w = to_l[u];
+      auto dfs = [&](auto&& self, int u) -> bool {
+        for (int v : adj[u]) {
+          int w = to_l[v];
           if (w == -1 ||
-            (level[v] + 1 == level[w] && self(self, w))) {
-            to_r[v] = u;
-            to_l[u] = v;
+            (level[u] + 1 == level[w] && self(self, w))) {
+            to_r[u] = v;
+            to_l[v] = u;
             return 1;
           }
         }
-        level[v] = INT_MAX;
+        level[u] = INT_MAX;
         return 0;
       };
       rep(i, 0, lsz) m_sz +=

library/graphs/scc.hpp

@@ -4,21 +4,21 @@
 //!   vector<basic_string<int>> adj(n);
 //!   auto [num_sccs, scc_id] = sccs(adj);
 //! @endcode
-//! scc_id[v] = id, 0<=id<num_sccs
+//! scc_id[u] = id, 0<=id<num_sccs
 //! for each edge u -> v: scc_id[u] >= scc_id[v]
 //! @time O(n + m)
 //! @space O(n)
 auto sccs(const auto& adj) {
   int n = sz(adj), num_sccs = 0, q = 0, s = 0;
   vi scc_id(n, -1), tin(n), st(n);
-  auto dfs = [&](auto&& self, int v) -> int {
-    int low = tin[v] = ++q;
-    st[s++] = v;
-    for (int u : adj[v])
-      if (scc_id[u] < 0)
-        low = min(low, tin[u] ?: self(self, u));
-    if (tin[v] == low) {
-      while (scc_id[v] < 0) scc_id[st[--s]] = num_sccs;
+  auto dfs = [&](auto&& self, int u) -> int {
+    int low = tin[u] = ++q;
+    st[s++] = u;
+    for (int v : adj[u])
+      if (scc_id[v] < 0)
+        low = min(low, tin[v] ?: self(self, v));
+    if (tin[u] == low) {
+      while (scc_id[u] < 0) scc_id[st[--s]] = num_sccs;
       num_sccs++;
     }
     return low;

library/graphs/strongly_connected_components/add_edges_strongly_connected.hpp

@@ -23,18 +23,18 @@ vector<pii> extra_edges(const auto& adj, int num_sccs,
   int n = sz(adj);
   vector<vi> scc_adj(num_sccs);
   vector<bool> zero_in(num_sccs, 1);
-  rep(i, 0, n) for (int u : adj[i]) {
-    if (scc_id[i] == scc_id[u]) continue;
-    scc_adj[scc_id[i]].push_back(scc_id[u]);
-    zero_in[scc_id[u]] = 0;
+  rep(i, 0, n) for (int v : adj[i]) {
+    if (scc_id[i] == scc_id[v]) continue;
+    scc_adj[scc_id[i]].push_back(scc_id[v]);
+    zero_in[scc_id[v]] = 0;
   }
   vector<bool> vis(num_sccs);
-  auto dfs = [&](auto&& self, int v) {
-    if (empty(scc_adj[v])) return v;
-    for (int u : scc_adj[v])
-      if (!vis[u]) {
-        vis[u] = 1;
-        int zero_out = self(self, u);
+  auto dfs = [&](auto&& self, int u) {
+    if (empty(scc_adj[u])) return u;
+    for (int v : scc_adj[u])
+      if (!vis[v]) {
+        vis[v] = 1;
+        int zero_out = self(self, v);
         if (zero_out != -1) return zero_out;
       }
     return -1;
@@ -55,7 +55,7 @@ vector<pii> extra_edges(const auto& adj, int num_sccs,
       in_unused.pop_back();
     } else edges.emplace_back(i, num_sccs - 1);
   }
-  for (int v : in_unused) edges.emplace_back(0, v);
+  for (int u : in_unused) edges.emplace_back(0, u);
   vi to_node(num_sccs);
   rep(i, 0, n) to_node[scc_id[i]] = i;
   for (auto& [u, v] : edges)

library/graphs/uncommon/bridges.hpp

@@ -18,15 +18,15 @@
 auto bridges(const auto& adj, int m) {
   int n = sz(adj), num_ccs = 0, q = 0, s = 0;
   vi br_id(n, -1), is_br(m), tin(n), st(n);
-  auto dfs = [&](auto&& self, int v, int p) -> int {
-    int low = tin[v] = ++q;
-    st[s++] = v;
-    for (auto [u, e] : adj[v])
-      if (e != p && br_id[u] < 0)
-        low = min(low, tin[u] ?: self(self, u, e));
-    if (tin[v] == low) {
+  auto dfs = [&](auto&& self, int u, int p) -> int {
+    int low = tin[u] = ++q;
+    st[s++] = u;
+    for (auto [v, e] : adj[u])
+      if (e != p && br_id[v] < 0)
+        low = min(low, tin[v] ?: self(self, v, e));
+    if (tin[u] == low) {
       if (p != -1) is_br[p] = 1;
-      while (br_id[v] < 0) br_id[st[--s]] = num_ccs;
+      while (br_id[u] < 0) br_id[st[--s]] = num_ccs;
       num_ccs++;
     }
     return low;

library/graphs/uncommon/cuts.hpp

@@ -19,16 +19,16 @@
 auto cuts(const auto& adj, int m) {
   int n = sz(adj), num_bccs = 0, q = 0, s = 0;
   vi bcc_id(m, -1), is_cut(n), tin(n), st(m);
-  auto dfs = [&](auto&& self, int v, int p) -> int {
-    int low = tin[v] = ++q;
-    for (auto [u, e] : adj[v]) {
-      assert(v != u);
+  auto dfs = [&](auto&& self, int u, int p) -> int {
+    int low = tin[u] = ++q;
+    for (auto [v, e] : adj[u]) {
+      assert(u != v);
       if (e == p) continue;
-      if (tin[u] < tin[v]) st[s++] = e;
+      if (tin[v] < tin[u]) st[s++] = e;
       int lu = -1;
-      low = min(low, tin[u] ?: (lu = self(self, u, e)));
-      if (lu >= tin[v]) {
-        is_cut[v] = p >= 0 || tin[v] + 1 < tin[u];
+      low = min(low, tin[v] ?: (lu = self(self, v, e)));
+      if (lu >= tin[u]) {
+        is_cut[u] = p >= 0 || tin[u] + 1 < tin[v];
         while (bcc_id[e] < 0) bcc_id[st[--s]] = num_bccs;
         num_bccs++;
       }

library/trees/hld.hpp

@@ -5,7 +5,7 @@
 //!   HLD<0> hld(adj);
 //!   hld.path(u, v, [&](int l, int r) { // [l, r)
 //!   });
-//!   auto [l, r] = hld.subtree(v); // [l, r)
+//!   auto [l, r] = hld.subtree(u); // [l, r)
 //! @endcode
 //! @time O(n + q log^2 n)
 //! @space O(n)
@@ -15,23 +15,23 @@ template<bool VALS_EDGES> struct HLD {
   vi p, siz, rt, tin;
   HLD(auto& adj):
     n(sz(adj)), p(n), siz(n, 1), rt(n), tin(n) {
-    auto dfs1 = [&](auto&& self, int v) -> void {
-      for (int& u : adj[v]) {
-        iter_swap(ranges::find(adj[u], v), rbegin(adj[u]));
-        adj[u].pop_back();
-        p[u] = v;
-        self(self, u);
-        siz[v] += siz[u];
-        if (siz[u] > siz[adj[v][0]]) swap(u, adj[v][0]);
+    auto dfs1 = [&](auto&& self, int u) -> void {
+      for (int& v : adj[u]) {
+        iter_swap(ranges::find(adj[v], u), rbegin(adj[v]));
+        adj[v].pop_back();
+        p[v] = u;
+        self(self, v);
+        siz[u] += siz[v];
+        if (siz[v] > siz[adj[u][0]]) swap(v, adj[u][0]);
       }
     };
     dfs1(dfs1, 0);
     int tim = 0;
-    auto dfs2 = [&](auto&& self, int v) -> void {
-      tin[v] = tim++;
-      for (int u : adj[v]) {
-        rt[u] = (u == adj[v][0] ? rt[v] : u);
-        self(self, u);
+    auto dfs2 = [&](auto&& self, int u) -> void {
+      tin[u] = tim++;
+      for (int v : adj[u]) {
+        rt[v] = (v == adj[u][0] ? rt[u] : v);
+        self(self, v);
       }
     };
     dfs2(dfs2, 0);
@@ -44,7 +44,7 @@ template<bool VALS_EDGES> struct HLD {
     }
     f(tin[u] + VALS_EDGES, tin[v] + 1);
   }
-  pii subtree(int v) {
-    return {tin[v] + VALS_EDGES, tin[v] + siz[v]};
+  pii subtree(int u) {
+    return {tin[u] + VALS_EDGES, tin[u] + siz[u]};
   }
 };

library/trees/lca_rmq.hpp

@@ -16,12 +16,12 @@ struct LCA {
   LCA(const auto& adj):
     n(sz(adj)), tin(n), siz(n, 1), d(n), p(n) {
     vi order;
-    auto dfs = [&](auto&& self, int v) -> void {
-      tin[v] = sz(order), order.push_back(v);
-      for (int u : adj[v])
-        if (u != p[v])
-          d[u] = d[p[u] = v] + 1, self(self, u),
-          siz[v] += siz[u];
+    auto dfs = [&](auto&& self, int u) -> void {
+      tin[u] = sz(order), order.push_back(u);
+      for (int v : adj[u])
+        if (v != p[u])
+          d[v] = d[p[v] = u] + 1, self(self, v),
+          siz[u] += siz[v];
     };
     dfs(dfs, 0);
     rmq = {order,

library/trees/linear_kth_par.hpp

@@ -21,28 +21,28 @@ template<int KAPPA = 2> struct linear_kth_par {
       jmp[t] = st[max(0, s - KAPPA * (t & -t))];
       t++;
     };
-    auto dfs = [&](auto&& self, int v, int p) -> void {
-      int& l = leaf[v] = st[d[v]] = v;
-      pos[v] = t;
-      calc(d[v]);
-      for (int u : adj[v])
-        if (u != p) {
-          d[u] = 1 + d[v];
-          self(self, u, v);
-          if (d[l] < d[leaf[u]]) l = leaf[u];
-          calc(d[v]);
+    auto dfs = [&](auto&& self, int u, int p) -> void {
+      int& l = leaf[u] = st[d[u]] = u;
+      pos[u] = t;
+      calc(d[u]);
+      for (int v : adj[u])
+        if (v != p) {
+          d[v] = 1 + d[u];
+          self(self, v, u);
+          if (d[l] < d[leaf[v]]) l = leaf[v];
+          calc(d[u]);
         }
-      int s = (d[l] - d[v]) * (2 * KAPPA + 3) / KAPPA;
+      int s = (d[l] - d[u]) * (2 * KAPPA + 3) / KAPPA;
       s = min(max(s, 2 * KAPPA), d[l] + 1);
       rep(i, sz(lad[l]), s) lad[l].push_back(st[d[l] - i]);
     };
     dfs(dfs, 0, 0);
   }
-  int kth_par(int v, int k) {
-    assert(0 <= k && k <= d[v]);
-    int anc_d = d[v] - k;
+  int kth_par(int u, int k) {
+    assert(0 <= k && k <= d[u]);
+    int anc_d = d[u] - k;
     if (unsigned j = k / (KAPPA + 1); j)
-      j = bit_floor(j), v = jmp[(pos[v] & -j) | j];
-    return v = leaf[v], lad[v][d[v] - anc_d];
+      j = bit_floor(j), u = jmp[(pos[u] & -j) | j];
+    return u = leaf[u], lad[u][d[u] - anc_d];
   }
 };

library/trees/linear_lca.hpp

@@ -13,19 +13,19 @@ struct linear_lca {
   linear_lca(const auto& adj):
     n(sz(adj)), d(n), in(n), asc(n), head(n + 1) {
     vector<pii> order;
-    auto dfs = [&](auto&& self, int v, int p) -> void {
-      order.emplace_back(v, p);
-      in[v] = sz(order);
-      for (int u : adj[v])
-        if (u != p) {
-          d[u] = 1 + d[v];
-          self(self, u, v);
-          head[in[u]] = v;
-          if (lsb(in[v]) < lsb(in[u])) in[v] = in[u];
+    auto dfs = [&](auto&& self, int u, int p) -> void {
+      order.emplace_back(u, p);
+      in[u] = sz(order);
+      for (int v : adj[u])
+        if (v != p) {
+          d[v] = 1 + d[u];
+          self(self, v, u);
+          head[in[v]] = u;
+          if (lsb(in[u]) < lsb(in[v])) in[u] = in[v];
         }
     };
     dfs(dfs, 0, 0);
-    for (auto [v, p] : order) asc[v] = asc[p] | lsb(in[v]);
+    for (auto [u, p] : order) asc[u] = asc[p] | lsb(in[u]);
   }
   int lca(int u, int v) {
     if (unsigned j = in[u] ^ in[v]; j) {