[자료구조] 다익스트라 알고리즘 (길찾기)

1. 다익스트라 알고리즘

다익스트라의 이름을 딴 알고리즘으로 그래프의 두 정점사이에 존재하는 최단경로를 찾는 알고리즘이다.

그래프를 가로지르면서 순회하고 우선순위큐를 사용한다.

gps, 네트워크 라우팅, 전염병 등등 많은 부분에서 씅니다.

2. 우선순위큐

class PriorityQueue {
  constructor() {
    this.values = [];
  }
  enqueue(val, priority) {
    this.values.push({ val, priority });
    this.sort();
  }
  dequeue() {
    return this.values.shift();
  }
  sort() {
    this.values.sort((a, b) => a.priority - b.priority);
  }
}

3. 다익스트라 알고리즘

class PriorityQueue {
  constructor() {
    this.values = [];
  }
  enqueue(val, priority) {
    this.values.push({ val, priority });
    this.sort();
  }
  dequeue() {
    return this.values.shift();
  }
  sort() {
    this.values.sort((a, b) => a.priority - b.priority);
  }
}

class WeightedGraph {
  constructor() {
    this.adjacencyList = {};
  }
  addVertex(vertex) {
    if (!this.adjacencyList[vertex]) this.adjacencyList[vertex] = [];
  }
  addEdge(vertex1, vertex2, weight) {
    this.adjacencyList[vertex1].push({ node: vertex2, weight });
    this.adjacencyList[vertex2].push({ node: vertex1, weight });
  }
  Dijkstra(start, finish) {
    const nodes = new PriorityQueue();
    const distances = {};
    const previous = {};
    let path = []; //to return at end
    let smallest;
    for (let vertex in this.adjacencyList) {
      if (vertex === start) {
        distances[vertex] = 0;
        nodes.enqueue(vertex, 0);
      } else {
        distances[vertex] = Infinity;
        nodes.enqueue(vertex, Infinity);
      }
      previous[vertex] = null;
    }
    while (nodes.values.length) {
      smallest = nodes.dequeue().val;

      if (smallest === finish) {
        while (previous[smallest]) {
          path.push(smallest);
          smallest = previous[smallest];
        }
        break;
      }
      if (smallest || distances[smallest] !== Infinity) {
        for (let neighbor in this.adjacencyList[smallest]) {
          // 근처 노드 찾기
          let nextNode = this.adjacencyList[smallest][neighbor];
          // 거리 계산하기
          let candidate = distances[smallest] + nextNode.weight;
          let nextNeighbor = nextNode.node;
          if (candidate < distances[nextNeighbor]) {
            // 거리 설정
            distances[nextNeighbor] = candidate;
            // 전에 방문했던 정점 설정
            previous[nextNeighbor] = smallest;
            // 우선순위큐에 집어넣기
            nodes.enqueue(nextNeighbor, candidate);
          }
        }
      }
    }
    return path.concat(smallest).reverse();
  }
}

4. 우선순위큐 리팩터링

우선순위큐를 이진힙으로 바꾼다면 더 빠르게 작동시킬 수 있다.

class PriorityQueue {
  constructor() {
    this.values = [];
  }
  enqueue(val, priority) {
    let newNode = new Node(val, priority);
    this.values.push(newNode);
    this.bubbleUp();
  }
  bubbleUp() {
    let idx = this.values.length - 1;
    const element = this.values[idx];
    while (idx > 0) {
      let parentIdx = Math.floor((idx - 1) / 2);
      let parent = this.values[parentIdx];
      if (element.priority >= parent.priority) break;
      this.values[parentIdx] = element;
      this.values[idx] = parent;
      idx = parentIdx;
    }
  }
  dequeue() {
    const min = this.values[0];
    const end = this.values.pop();
    if (this.values.length > 0) {
      this.values[0] = end;
      this.sinkDown();
    }
    return min;
  }
  sinkDown() {
    let idx = 0;
    const length = this.values.length;
    const element = this.values[0];
    while (true) {
      let leftChildIdx = 2 * idx + 1;
      let rightChildIdx = 2 * idx + 2;
      let leftChild, rightChild;
      let swap = null;

      if (leftChildIdx < length) {
        leftChild = this.values[leftChildIdx];
        if (leftChild.priority < element.priority) {
          swap = leftChildIdx;
        }
      }
      if (rightChildIdx < length) {
        rightChild = this.values[rightChildIdx];
        if (
          (swap === null && rightChild.priority < element.priority) ||
          (swap !== null && rightChild.priority < leftChild.priority)
        ) {
          swap = rightChildIdx;
        }
      }
      if (swap === null) break;
      this.values[idx] = this.values[swap];
      this.values[swap] = element;
      idx = swap;
    }
  }
}

class Node {
  constructor(val, priority) {
    this.val = val;
    this.priority = priority;
  }
}