class Graph {
  constructor(directed = true) {
    this.directed = directed;
    this.nodes = [];
    this.edges = new Map();
  }

  addNode(key, value = key) {
    this.nodes.push({ key, value });
  }

  addEdge(a, b, weight) {
    this.edges.set(JSON.stringify([a, b]), { a, b, weight });
    if (!this.directed)
      this.edges.set(JSON.stringify([b, a]), { a: b, b: a, weight });
  }

  removeNode(key) {
    this.nodes = this.nodes.filter(n => n.key !== key);
    [...this.edges.values()].forEach(({ a, b }) => {
      if (a === key || b === key) this.edges.delete(JSON.stringify([a, b]));
    });
  }

  removeEdge(a, b) {
    this.edges.delete(JSON.stringify([a, b]));
    if (!this.directed) this.edges.delete(JSON.stringify([b, a]));
  }

  findNode(key) {
    return this.nodes.find(x => x.key === key);
  }

  hasEdge(a, b) {
    return this.edges.has(JSON.stringify([a, b]));
  }

  setEdgeWeight(a, b, weight) {
    this.edges.set(JSON.stringify([a, b]), { a, b, weight });
    if (!this.directed)
      this.edges.set(JSON.stringify([b, a]), { a: b, b: a, weight });
  }

  getEdgeWeight(a, b) {
    return this.edges.get(JSON.stringify([a, b])).weight;
  }

  adjacent(key) {
    return [...this.edges.values()].reduce((acc, { a, b }) => {
      if (a === key) acc.push(b);
      return acc;
    }, []);
  }

  indegree(key) {
    return [...this.edges.values()].reduce((acc, { a, b }) => {
      if (b === key) acc++;
      return acc;
    }, 0);
  }

  outdegree(key) {
    return [...this.edges.values()].reduce((acc, { a, b }) => {
      if (a === key) acc++;
      return acc;
    }, 0);
  }
}


const g = new Graph();

g.addNode('a');
g.addNode('b');
g.addNode('c');
g.addNode('d');

g.addEdge('a', 'c');
g.addEdge('b', 'c');
g.addEdge('c', 'b');
g.addEdge('d', 'a');

g.nodes.map(x => x.value);  // ['a', 'b', 'c', 'd']
[...g.edges.values()].map(({ a, b }) => `${a} => ${b}`);
// ['a => c', 'b => c', 'c => b', 'd => a']

g.adjacent('c');            // ['b']

g.indegree('c');            // 2
g.outdegree('c');           // 1

g.hasEdge('d', 'a');        // true
g.hasEdge('a', 'd');        // false

g.removeEdge('c', 'b');

[...g.edges.values()].map(({ a, b }) => `${a} => ${b}`);
// ['a => c', 'b => c', 'd => a']

g.removeNode('c');

g.nodes.map(x => x.value);  // ['a', 'b', 'd']
[...g.edges.values()].map(({ a, b }) => `${a} => ${b}`);
// ['d => a']

g.setEdgeWeight('d', 'a', 5);
g.getEdgeWeight('d', 'a');  // 5

const binomialCoefficient = (n, k) => {
  if (Number.isNaN(n) || Number.isNaN(k)) return NaN;
  if (k < 0 || k > n) return 0;
  if (k === 0 || k === n) return 1;
  if (k === 1 || k === n - 1) return n;
  if (n - k < k) k = n - k;
  let res = n;
  for (let j = 2; j <= k; j++) res *= (n - j + 1) / j;
  return Math.round(res);
};

binomialCoefficient(8, 2); // 28

const heapsort = arr => {
  const a = [...arr];
  let l = a.length;

  const heapify = (a, i) => {
    const left = 2 * i + 1;
    const right = 2 * i + 2;
    let max = i;
    if (left < l && a[left] > a[max]) max = left;
    if (right < l && a[right] > a[max]) max = right;
    if (max !== i) {
      [a[max], a[i]] = [a[i], a[max]];
      heapify(a, max);
    }
  };

  for (let i = Math.floor(l / 2); i >= 0; i -= 1) heapify(a, i);
  for (i = a.length - 1; i > 0; i--) {
    [a[0], a[i]] = [a[i], a[0]];
    l--;
    heapify(a, 0);
  }
  return a;
};

heapsort([6, 3, 4, 1]); // [1, 3, 4, 6]

const bucketSort = (arr, size = 5) => {
  const min = Math.min(...arr);
  const max = Math.max(...arr);
  const buckets = Array.from(
    { length: Math.floor((max - min) / size) + 1 },
    () => []
  );
  arr.forEach(val => {
    buckets[Math.floor((val - min) / size)].push(val);
  });
  return buckets.reduce((acc, b) => [...acc, ...b.sort((a, b) => a - b)], []);
};

bucketSort([6, 3, 4, 1]); // [1, 3, 4, 6]

class TreeNode {
  constructor(key, value = key, parent = null) {
    this.key = key;
    this.value = value;
    this.parent = parent;
    this.children = [];
  }

  get isLeaf() {
    return this.children.length === 0;
  }

  get hasChildren() {
    return !this.isLeaf;
  }
}

class Tree {
  constructor(key, value = key) {
    this.root = new TreeNode(key, value);
  }

  *preOrderTraversal(node = this.root) {
    yield node;
    if (node.children.length) {
      for (let child of node.children) {
        yield* this.preOrderTraversal(child);
      }
    }
  }

  *postOrderTraversal(node = this.root) {
    if (node.children.length) {
      for (let child of node.children) {
        yield* this.postOrderTraversal(child);
      }
    }
    yield node;
  }

  insert(parentNodeKey, key, value = key) {
    for (let node of this.preOrderTraversal()) {
      if (node.key === parentNodeKey) {
        node.children.push(new TreeNode(key, value, node));
        return true;
      }
    }
    return false;
  }

  remove(key) {
    for (let node of this.preOrderTraversal()) {
      const filtered = node.children.filter(c => c.key !== key);
      if (filtered.length !== node.children.length) {
        node.children = filtered;
        return true;
      }
    }
    return false;
  }

  find(key) {
    for (let node of this.preOrderTraversal()) {
      if (node.key === key) return node;
    }
    return undefined;
  }
}

const tree = new Tree(1, 'AB');

tree.insert(1, 11, 'AC');
tree.insert(1, 12, 'BC');
tree.insert(12, 121, 'BG');

[...tree.preOrderTraversal()].map(x => x.value);
// ['AB', 'AC', 'BC', 'BCG']

tree.root.value;              // 'AB'
tree.root.hasChildren;        // true

tree.find(12).isLeaf;         // false
tree.find(121).isLeaf;        // true
tree.find(121).parent.value;  // 'BC'

tree.remove(12);

[...tree.postOrderTraversal()].map(x => x.value);
// ['AC', 'AB']

const permutations = arr => {
  if (arr.length <= 2) return arr.length === 2 ? [arr, [arr[1], arr[0]]] : arr;
  return arr.reduce(
    (acc, item, i) =>
      acc.concat(
        permutations([...arr.slice(0, i), ...arr.slice(i + 1)]).map(val => [
          item,
          ...val,
        ])
      ),
    []
  );
};
permutations([1, 33, 5]);
// [ [1, 33, 5], [1, 5, 33], [33, 1, 5], [33, 5, 1], [5, 1, 33], [5, 33, 1] ]