Initial import

libc/alg/tarjan.c

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+/*-*- mode:c;indent-tabs-mode:nil;c-basic-offset:2;tab-width:8;coding:utf-8 -*-│
+│vi: set net ft=c ts=2 sts=2 sw=2 fenc=utf-8                                :vi│
+╞══════════════════════════════════════════════════════════════════════════════╡
+│ Copyright 2020 Justine Alexandra Roberts Tunney                              │
+│                                                                              │
+│ This program is free software; you can redistribute it and/or modify         │
+│ it under the terms of the GNU General Public License as published by         │
+│ the Free Software Foundation; version 2 of the License.                      │
+│                                                                              │
+│ This program is distributed in the hope that it will be useful, but          │
+│ WITHOUT ANY WARRANTY; without even the implied warranty of                   │
+│ MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU             │
+│ General Public License for more details.                                     │
+│                                                                              │
+│ You should have received a copy of the GNU General Public License            │
+│ along with this program; if not, write to the Free Software                  │
+│ Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA                │
+│ 02110-1301 USA                                                               │
+╚─────────────────────────────────────────────────────────────────────────────*/
+#include "libc/alg/alg.h"
+#include "libc/assert.h"
+#include "libc/bits/safemacros.h"
+#include "libc/limits.h"
+#include "libc/mem/mem.h"
+
+/**
+ * @fileoverview Tarjan's Strongly Connected Components Algorithm.
+ *
+ *    “The data structures that [Tarjan] devised for this problem fit
+ *     together in an amazingly beautiful way, so that the quantities
+ *     you need to look at while exploring a directed graph are always
+ *     magically at your fingertips. And his algorithm also does
+ *     topological sorting as a byproduct.” ──D.E. Knuth
+ */
+
+struct Vertex {
+  uint32_t Vi;
+  uint32_t Ei;
+  uint32_t index;
+  uint32_t lowlink;
+  bool onstack;
+  bool selfreferential;
+};
+
+struct TarjanStack {
+  size_t i;
+  size_t n;
+  uint32_t *p;
+};
+
+struct Tarjan {
+  uint32_t Vn;
+  uint32_t En;
+  struct Vertex *V;
+  const uint32_t (*E)[2];
+  uint32_t *R;
+  uint32_t *C;
+  uint32_t Ci;
+  uint32_t Ri;
+  uint32_t index;
+  struct TarjanStack S;
+};
+
+static uint32_t TarjanPush(struct TarjanStack *st, uint32_t Vi) {
+  if (st->i < st->n || grow(&st->p, &st->n, sizeof(uint32_t), 0)) {
+    return (st->p[st->i++] = Vi);
+  } else {
+    return -1;
+  }
+}
+
+static uint32_t TarjanPop(struct TarjanStack *st) {
+  assert(st->i != 0);
+  return st->p[--st->i];
+}
+
+static int TarjanConnect(struct Tarjan **tj, uint32_t Vi) {
+  struct Vertex *v = &(*tj)->V[Vi];
+  v->index = (*tj)->index;
+  v->lowlink = (*tj)->index;
+  v->onstack = true;
+  (*tj)->index++;
+  if (TarjanPush(&(*tj)->S, Vi) == -1) return -1;
+  uint32_t fs = (*tj)->V[Vi].Ei;
+  if (fs != -1) {
+    for (uint32_t Ei = fs; Ei < (*tj)->En && Vi == (*tj)->E[Ei][0]; ++Ei) {
+      struct Vertex *w = &(*tj)->V[(*tj)->E[Ei][1]];
+      if (!w->index) {
+        if (TarjanConnect(tj, w->Vi) == -1) return -1;
+        v->lowlink = min(v->lowlink, w->lowlink);
+      } else if (w->onstack) {
+        v->lowlink = min(v->lowlink, w->index);
+      }
+      if (w == v) {
+        w->selfreferential = true;
+      }
+    }
+  }
+  if (v->lowlink == v->index) {
+    struct Vertex *w;
+    do {
+      w = &(*tj)->V[TarjanPop(&(*tj)->S)];
+      w->onstack = false;
+      (*tj)->R[(*tj)->Ri++] = w->Vi;
+    } while (w != v);
+    if ((*tj)->C) (*tj)->C[(*tj)->Ci++] = (*tj)->Ri;
+  }
+  return 0;
+}
+
+/**
+ * Determines order of things in network and finds tangled clusters too.
+ *
+ * @param vertices is an array of vertex values, which isn't passed to
+ *     this function, since the algorithm only needs to consider indices
+ * @param vertex_count is the number of items in the vertices array
+ * @param edges are grouped directed links between indices of vertices,
+ *     which can be thought of as "edge[i][0] depends on edge[i][1]" or
+ *     "edge[i][1] must come before edge[i][0]" in topological order
+ * @param edge_count is the number of items in edges, which may be 0 if
+ *     there aren't any connections between vertices in the graph
+ * @param out_sorted receives indices into the vertices array in
+ *     topologically sorted order, and must be able to store
+ *     vertex_count items, and that's always how many are stored
+ * @param out_opt_components receives indices into the out_sorted array,
+ *     indicating where each strongly-connected component ends; must be
+ *     able to store vertex_count items; and it may be NULL
+ * @param out_opt_componentcount receives the number of cycle indices
+ *     written to out_opt_components, which will be vertex_count if
+ *     there aren't any cycles in the graph; and may be NULL if
+ *     out_opt_components is NULL
+ * @return 0 on success or -1 w/ errno
+ * @error ENOMEM
+ * @note Tarjan's Algorithm is O(|V|+|E|)
+ */
+int tarjan(uint32_t vertex_count, const uint32_t (*edges)[2],
+           uint32_t edge_count, uint32_t out_sorted[],
+           uint32_t out_opt_components[], uint32_t *out_opt_componentcount) {
+  assert(edge_count <= INT_MAX);
+  assert(vertex_count <= INT_MAX);
+  for (unsigned i = 0; i < edge_count; ++i) {
+    if (i) assert(edges[i - 1][0] <= edges[i][0]);
+    assert(edges[i][0] < vertex_count);
+    assert(edges[i][1] < vertex_count);
+  }
+  int rc;
+  struct Tarjan *tj;
+  if ((tj = calloc(1, (sizeof(struct Tarjan) +
+                       sizeof(struct Vertex) * vertex_count)))) {
+    tj->V = (struct Vertex *)((char *)tj + sizeof(struct Tarjan));
+    tj->Vn = vertex_count;
+    tj->E = edges;
+    tj->En = edge_count;
+    tj->R = out_sorted;
+    tj->C = out_opt_components;
+    tj->index = 1;
+    uint32_t Vi, Ei;
+    for (Vi = 0; Vi < tj->Vn; ++Vi) {
+      tj->V[Vi].Vi = Vi;
+      tj->V[Vi].Ei = -1u;
+    }
+    for (Ei = 0, Vi = -1u; Ei < tj->En; ++Ei) {
+      if (tj->E[Ei][0] == Vi) continue;
+      Vi = tj->E[Ei][0];
+      tj->V[Vi].Ei = Ei;
+    }
+    rc = 0;
+    for (Vi = 0; Vi < tj->Vn; ++Vi) {
+      if (!tj->V[Vi].index) {
+        if ((rc = TarjanConnect(&tj, Vi)) == -1) {
+          break;
+        }
+      }
+    }
+    free(tj->S.p);
+    assert(tj->Ri == vertex_count);
+    if (out_opt_components) *out_opt_componentcount = tj->Ci;
+  } else {
+    rc = -1;
+  }
+  free(tj);
+  return rc;
+}