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[Graph] 2. Graph 的基本運算

Graph 的基本運算​

我們會以 Adjacency List + Undirected Graph 的前提來實作，後續要轉成 Directed Graph 也很容易。 總的來說，Graph 的基本運算有 4 個：

  • Add Vertex
  • Add Edge
  • Remove Edge
  • Remove Vertex

我們先以 Class 的方式建立 Graph，並先寫出其基本 data structure：

class Graph {
    constructor() {
        this.adjacencyList = [];
    }
}


接著我們來一步步實現這 4 個 methods：


加入 Vertex​

加入 vertex 很簡單，只要在 adjacency list 中新增一個 index / key 並給他一個空陣列即可

class Graph {
    ...
    addVertex(vertex) {
        if (!this.adjacencyList[vertex]) {
            this.adjacencyList[vertex] = [];
        }
    }
}


加入 Edge​

加入 edge，我們需要先確認對應的 vertex 是否存在，如果不存在的話，我們需要先加入 vertex

class Graph {
    ...
    addEdge(vertex1, vertex2) {
        if (!this.adjacencyList[vertex1]) {
            this.addVertex(vertex1);
        }
        if (!this.adjacencyList[vertex2]) {
            this.addVertex(vertex2);
        }

        this.adjacencyList[vertex1].push(vertex2);
        this.adjacencyList[vertex2].push(vertex1);
    }
}


移除 Edge​

移除 edge 需要傳入兩個 vertex，並分別在兩個 vertex 的 adjacency list 中將對方的 vertex 移除

class Graph {
    ...
    removeEdge(vertex1, vertex2) {
        this.adjacencyList[vertex1] = this.adjacencyList[vertex1]
            .filter(v => v !== vertex2);

        this.adjacencyList[vertex2] = this.adjacencyList[vertex2]
            .filter(v => v !== vertex1);
    }
}


移除 Vertex​

移除 vertex V1，我們需要 V1 的 adjacency list 中所有 vertex 移除，並移除 vertex 跟 V1 的 Edge，並且最後再把 V1 adjacency list 移除

class Graph {
    ...
    removeVertex(vertex) {
        while (this.adjacencyList[vertex].length) {
            const adjacentVertex = this.adjacencyList[vertex].pop();
            this.removeEdge(vertex, adjacentVertex);
        }

        delete this.adjacencyList[vertex];
    }
}


完整程式碼​

class Graph {
    constructor() {
        this.adjacencyList = [];
    }

    addVertex(vertex) {
        if (!this.adjacencyList[vertex]) {
            this.adjacencyList[vertex] = [];
        }
    }

    addEdge(vertex1, vertex2) {
        if (!this.adjacencyList[vertex1]) {
            this.addVertex(vertex1);
        }
        if (!this.adjacencyList[vertex2]) {
            this.addVertex(vertex2);
        }

        this.adjacencyList[vertex1].push(vertex2);
        this.adjacencyList[vertex2].push(vertex1);
    }

    removeEdge(vertex1, vertex2) {
        this.adjacencyList[vertex1] = this.adjacencyList[vertex1]
            .filter(v => v !== vertex2);

        this.adjacencyList[vertex2] = this.adjacencyList[vertex2]
            .filter(v => v !== vertex1);
    }

    removeVertex(vertex) {
        while (this.adjacencyList[vertex].length) {
            const adjacentVertex = this.adjacencyList[vertex].pop();
            this.removeEdge(vertex, adjacentVertex);
        }

        delete this.adjacencyList[vertex];
    }
}


JS Graph 的快速實現​

除了用 Class 實作，我們也可以用 Js 的 array / object literal 來快速實作，這樣的好處是比較直觀，幫助我們在面試時快速實作

  • Array
const graph = [];

function addVertex(vertex) {
    if (!graph[vertex]) {
        graph[vertex] = [];
    }
}

function addEdge(vertex1, vertex2) {
    if (!(vertex1 in graph)) addVertex(vertex1);
    if (!(vertex2 in graph)) addVertex(vertex2);

    graph[vertex1].push(vertex2);
    graph[vertex2].push(vertex1);
}

function removeEdge(vertex1, vertex2) {
    if (graph[vertex1]) graph[vertex1] = graph[vertex1].filter(v => v !== vertex2);
    if (graph[vertex2]) graph[vertex2] = graph[vertex2].filter(v => v !== vertex1);
}

function removeVertex(vertex) {
    while (graph[vertex].length) {
        const adjacentVertex = graph[vertex].pop();
        removeEdge(vertex, adjacentVertex);
    }

    delete graph[vertex];
}


  • Object Literal
const graph = {};

function addVertex(vertex) {
    if (!graph[vertex]) {
        graph[vertex] = [];
    }
}

function addEdge(vertex1, vertex2) {
    if (!(vertex1 in graph)) addVertex(vertex1);
    if (!(vertex2 in graph)) addVertex(vertex2);

    graph[vertex1].push(vertex2);
    graph[vertex2].push(vertex1);
}

function removeEdge(vertex1, vertex2) {
    if (vertex1 in graph) graph[vertex1] = graph[vertex1].filter(v => v !== vertex2);
    if (vertex2 in graph) graph[vertex2] = graph[vertex2].filter(v => v !== vertex1);
}

function removeVertex(vertex) {
    while (graph[vertex].length) {
        const adjacentVertex = graph[vertex].pop();
        removeEdge(vertex, adjacentVertex);
    }

    delete graph[vertex];
}


結論​

  1. Graph 的基本運算有 4 個：Add Vertex, Add Edge, Remove Edge, Remove Vertex
  2. 在做基本運算時，vertex 的運算需要考慮 Edge，Edge 的運算需要考慮 vertex
  3. Graph 可以用 Class 實現，在 JS 也可以用 Array / Object Literal 快速實現



參考資料​