toplogical sorting in javascript

Author: luckyb13

javascript/toposort.js

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+// topoSort.js
+// Topological sort with cycle detection for dependency graphs.
+// Accepts either: adjacency-list object or edge list. Throws on cycles.
+
+/**
+ * @typedef {Record<string,string[]>} Graph
+ * @typedef {[string,string]} Edge  // [from, to]
+ */
+
+/**
+ * Build adjacency list from edges or return copy of given graph.
+ * @param {Graph|Edge[]} input
+ * @returns {Graph}
+ */
+function toGraph(input) {
+  /** @type {Graph} */
+  const g = {};
+  if (Array.isArray(input)) {
+    for (const [u, v] of input) {
+      if (!g[u]) g[u] = [];
+      if (!g[v]) g[v] = [];
+      g[u].push(v);
+    }
+  } else {
+    for (const k of Object.keys(input)) g[k] = [...(input[k] || [])];
+  }
+  // Ensure all nodes appear
+  for (const k of Object.keys(g)) for (const v of g[k]) if (!g[v]) g[v] = [];
+  return g;
+}
+
+/**
+ * Topologically sort nodes. Throws Error with cycle nodes if cyclic.
+ * @param {Graph|Edge[]} input
+ * @returns {string[]} order
+ */
+export function topoSort(input) {
+  const g = toGraph(input);
+  /** @type {Record<string,0|1|2>} */ // 0=unvisited,1=visiting,2=done
+  const state = {};
+  const order = [];
+  const stack = [];
+
+  const visit = (node) => {
+    const st = state[node] || 0;
+    if (st === 1) {
+      // Found a back-edge → cycle is the suffix of the stack up to node
+      const idx = stack.lastIndexOf(node);
+      const cycle = stack.slice(idx).concat(node);
+      const msg = `Cycle detected: ${cycle.join(" -> ")}`;
+      const err = new Error(msg);
+      // @ts-ignore attach for debugging
+      err.cycle = cycle;
+      throw err;
+    }
+    if (st === 2) return;
+
+    state[node] = 1;
+    stack.push(node);
+    for (const nei of g[node]) visit(nei);
+    stack.pop();
+    state[node] = 2;
+    order.push(node);
+  };
+
+  for (const node of Object.keys(g)) if (!state[node]) visit(node);
+  return order.reverse();
+}
+
+/**
+ * Group nodes by "level" (distance from sources) using Kahn's algorithm.
+ * If graph has a cycle, throws like topoSort.
+ * @param {Graph|Edge[]} input
+ * @returns {string[][]} levels, where levels[0] are sources
+ */
+export function topoLevels(input) {
+  const g = toGraph(input);
+  const indeg = Object.fromEntries(Object.keys(g).map(k => [k,0]));
+  for (const u of Object.keys(g)) for (const v of g[u]) indeg[v]++;
+
+  /** @type {string[][]} */
+  const levels = [];
+  let layer = Object.keys(indeg).filter(k => indeg[k] === 0);
+
+  let visited = 0;
+  while (layer.length) {
+    levels.push(layer);
+    const next = [];
+    for (const u of layer) {
+      visited++;
+      for (const v of g[u]) {
+        if (--indeg[v] === 0) next.push(v);
+      }
+    }
+    layer = next;
+  }
+
+  if (visited !== Object.keys(g).length) {
+    // cycle present; derive one cycle path using DFS utility
+    topoSort(g); // will throw with details
+  }
+  return levels;
+}
+
+// // Example usage:
+// // const order = topoSort([["a","b"],["a","c"],["b","d"],["c","d"]]);
+// // const levels = topoLevels({ a:["b","c"], b:["d"], c:["d"], d:[] });