Create 1617-count-subtrees-with-max-distance-between-cities.js

Author: everthis

1617-count-subtrees-with-max-distance-between-cities.js

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+/**
+ * @param {number} n
+ * @param {number[][]} edges
+ * @return {number[]}
+ */
+const countSubgraphsForEachDiameter = function (n, edges) {
+  const graph = {};
+  for (let [u, v] of edges) {
+    if (!graph[u - 1]) graph[u - 1] = [];
+    if (!graph[v - 1]) graph[v - 1] = [];
+    graph[u - 1].push(v - 1);
+    graph[v - 1].push(u - 1);
+  }
+  let ans = Array(n - 1).fill(0);
+  for (let i = 1, len = 2 ** n; i < len; i++) {
+    const d = maxDistance(i);
+    if (d > 0) ans[d - 1] += 1;
+  }
+  return ans;
+  function bfs(src, cities) {
+    const visited = new Set();
+    visited.add(src);
+    const q = [[src, 0]]; // Pair of (vertex, distance)
+    let farthestDist = 0; // Farthest distance from src to other nodes
+    while (q.length > 0) {
+      const [u, d] = q.shift();
+      farthestDist = d;
+      for (let v of graph[u]) {
+        if (!visited.has(v) && cities.has(v)) {
+          visited.add(v);
+          q.push([v, d + 1]);
+        }
+      }
+    }
+    return [farthestDist, visited];
+  }
+  function maxDistance(state) {
+    // return: maximum distance between any two cities in our subset. O(n^2)
+    const cities = new Set();
+    for (let i = 0; i < n; i++) {
+      if ((state >> i) & (1 === 1)) cities.add(i);
+    }
+    let ans = 0;
+    for (let i of cities) {
+      const [farthestDist, visited] = bfs(i, cities);
+      if (visited.size < cities.size) return 0; // Can't visit all nodes of the tree -> Invalid tree
+      ans = Math.max(ans, farthestDist);
+    }
+    return ans;
+  }
+};