程序開發(fā)中常用的十種算法，你用過幾種？

作者：架構(gòu)師老盧 2024-01-17 13:58:00

當(dāng)編寫程序時(shí)，了解和使用不同的算法對(duì)解決問題至關(guān)重要。以下是C#中常用的10種算法，每個(gè)算法都伴隨著示例代碼和詳細(xì)說明。

1、冒泡排序 (Bubble Sort):

冒泡排序是一種簡(jiǎn)單的比較排序算法，它多次遍歷數(shù)組，將較大的元素逐漸浮動(dòng)到數(shù)組的末尾。

public static void BubbleSort(int[] arr)
{
    int n = arr.Length;
    for (int i = 0; i < n - 1; i++)
    {
        for (int j = 0; j < n - i - 1; j++)
        {
            if (arr[j] > arr[j + 1])
            {
                int temp = arr[j];
                arr[j] = arr[j + 1];
                arr[j + 1] = temp;
            }
        }
    }
}

2、快速排序 (Quick Sort):

快速排序是一種高效的分治排序算法，它通過選擇一個(gè)基準(zhǔn)元素并將數(shù)組分為較小和較大的兩部分來進(jìn)行排序。

public static void QuickSort(int[] arr, int low, int high)
{
    if (low < high)
    {
        int partitionIndex = Partition(arr, low, high);
        QuickSort(arr, low, partitionIndex - 1);
        QuickSort(arr, partitionIndex + 1, high);
    }
}

public static int Partition(int[] arr, int low, int high)
{
    int pivot = arr[high];
    int i = low - 1;

    for (int j = low; j < high; j++)
    {
        if (arr[j] < pivot)
        {
            i++;
            int temp = arr[i];
            arr[i] = arr[j];
            arr[j] = temp;
        }
    }

    int swap = arr[i + 1];
    arr[i + 1] = arr[high];
    arr[high] = swap;

    return i + 1;
}

3、合并排序 (Merge Sort):

合并排序是一種穩(wěn)定的分治排序算法，它將數(shù)組分成兩半，分別排序后再合并。

public static void MergeSort(int[] arr)
{
    int n = arr.Length;
    if (n > 1)
    {
        int mid = n / 2;
        int[] left = new int[mid];
        int[] right = new int[n - mid];

        for (int i = 0; i < mid; i++)
            left[i] = arr[i];
        for (int i = mid; i < n; i++)
            right[i - mid] = arr[i];

        MergeSort(left);
        MergeSort(right);

        int i = 0, j = 0, k = 0;
        while (i < mid && j < (n - mid))
        {
            if (left[i] < right[j])
                arr[k++] = left[i++];
            else
                arr[k++] = right[j++];
        }
        while (i < mid)
            arr[k++] = left[i++];
        while (j < (n - mid))
            arr[k++] = right[j++];
    }
}

4、二分查找 (Binary Search):

二分查找是一種高效的查找算法，它要求在有序數(shù)組中查找特定元素。

public static int BinarySearch(int[] arr, int target)
{
    int low = 0, high = arr.Length - 1;
    while (low <= high)
    {
        int mid = (low + high) / 2;
        if (arr[mid] == target)
            return mid;
        else if (arr[mid] < target)
            low = mid + 1;
        else
            high = mid - 1;
    }
    return -1;
}

5、深度優(yōu)先搜索 (Depth-First Search, DFS):

DFS 是一種圖遍歷算法，它從起始節(jié)點(diǎn)開始，沿著路徑盡可能深入，然后返回并繼續(xù)搜索。

using System;
using System.Collections.Generic;

public class Graph
{
    private int V;
    private List<int>[] adj;

    public Graph(int v)
    {
        V = v;
        adj = new List<int>[v];
        for (int i = 0; i < v; i++)
            adj[i] = new List<int>();
    }

    public void AddEdge(int v, int w)
    {
        adj[v].Add(w);
    }

    public void DFS(int v)
    {
        bool[] visited = new bool[V];
        DFSUtil(v, visited);
    }

    private void DFSUtil(int v, bool[] visited)
    {
        visited[v] = true;
        Console.Write(v + " ");

        foreach (var n in adj[v])
        {
            if (!visited[n])
                DFSUtil(n, visited);
        }
    }
}

6、廣度優(yōu)先搜索 (Breadth-First Search, BFS):

BFS 是一種圖遍歷算法，它從起始節(jié)點(diǎn)開始，逐層遍歷，先訪問所有相鄰的節(jié)點(diǎn)，然后再逐層擴(kuò)展。

using System;
using System.Collections.Generic;

public class Graph
{
    private int V;
    private List<int>[] adj;

    public Graph(int v)
    {
        V = v;
        adj = new List<int>[v];
        for (int i = 0; i < v; i++)
            adj[i] = new List<int>();
    }

    public void AddEdge(int v, int w)
    {
        adj[v].Add(w);
    }

    public void BFS(int s)
    {
        bool[] visited = new bool[V];

        Queue<int> queue = new Queue<int>();
        visited[s] = true;
        queue.Enqueue(s);

        while (queue.Count != 0)
        {
            s = queue.Dequeue();
            Console.Write(s + " ");

            foreach (var n in adj[s])
            {
                if (!visited[n])
                {
                    visited[n] = true;
                    queue.Enqueue(n);
                }
            }
        }
    }
}

7、Dijkstra算法:

Dijkstra算法是一種用于查找圖中最短路徑的算法。

public class Dijkstra
{
    private static int V = 9;

    private int MinDistance(int[] dist, bool[] sptSet)
    {
        int min = int.MaxValue;
        int minIndex = 0;

        for (int v = 0; v < V; v++)
        {
            if (!sptSet[v] && dist

[v] <= min)
            {
                min = dist[v];
                minIndex = v;
            }
        }

        return minIndex;
    }

    private void PrintSolution(int[] dist)
    {
        Console.WriteLine("Vertex \t Distance from Source");
        for (int i = 0; i < V; i++)
        {
            Console.WriteLine(i + " \t " + dist[i]);
        }
    }

    public void FindShortestPath(int[,] graph, int src)
    {
        int[] dist = new int[V];
        bool[] sptSet = new bool[V];

        for (int i = 0; i < V; i++)
        {
            dist[i] = int.MaxValue;
            sptSet[i] = false;
        }

        dist[src] = 0;

        for (int count = 0; count < V - 1; count++)
        {
            int u = MinDistance(dist, sptSet);

            sptSet[u] = true;

            for (int v = 0; v < V; v++)
            {
                if (!sptSet[v] && graph[u, v] != 0 && dist[u] != int.MaxValue && dist[u] + graph[u, v] < dist[v])
                {
                    dist[v] = dist[u] + graph[u, v];
                }
            }
        }

        PrintSolution(dist);
    }
}

8、最小生成樹 (Minimum Spanning Tree, MST) - Prim算法:

Prim算法用于找到圖的最小生成樹，它從一個(gè)初始頂點(diǎn)開始，逐漸擴(kuò)展生成樹。

public class PrimMST
{
    private static int V = 5;

    private int MinKey(int[] key, bool[] mstSet)
    {
        int min = int.MaxValue;
        int minIndex = 0;

        for (int v = 0; v < V; v++)
        {
            if (!mstSet[v] && key[v] < min)
            {
                min = key[v];
                minIndex = v;
            }
        }

        return minIndex;
    }

    private void PrintMST(int[] parent, int[,] graph)
    {
        Console.WriteLine("Edge \t Weight");
        for (int i = 1; i < V; i++)
        {
            Console.WriteLine(parent[i] + " - " + i + " \t " + graph[i, parent[i]]);
        }
    }

    public void FindMST(int[,] graph)
    {
        int[] parent = new int[V];
        int[] key = new int[V];
        bool[] mstSet = new bool[V];

        for (int i = 0; i < V; i++)
        {
            key[i] = int.MaxValue;
            mstSet[i] = false;
        }

        key[0] = 0;
        parent[0] = -1;

        for (int count = 0; count < V - 1; count++)
        {
            int u = MinKey(key, mstSet);

            mstSet[u] = true;

            for (int v = 0; v < V; v++)
            {
                if (graph[u, v] != 0 && !mstSet[v] && graph[u, v] < key[v])
                {
                    parent[v] = u;
                    key[v] = graph[u, v];
                }
            }
        }

        PrintMST(parent, graph);
    }
}

9、最小生成樹 (Minimum Spanning Tree, MST) - Kruskal算法:

Kruskal算法也用于找到圖的最小生成樹，它基于邊的權(quán)重排序。

using System;
using System.Collections.Generic;

public class Graph
{
    private int V, E;
    private List<Edge> edges;

    public Graph(int v, int e)
    {
        V = v;
        E = e;
        edges = new List<Edge>(e);
    }

    public void AddEdge(int src, int dest, int weight)
    {
        edges.Add(new Edge(src, dest, weight));
    }

    public void KruskalMST()
    {
        edges.Sort();

        int[] parent = new int[V];
        int[] rank = new int[V];

        for (int i = 0; i < V; i++)
        {
            parent[i] = i;
            rank[i] = 0;
        }

        int i = 0;
        int e = 0;

        List<Edge> mst = new List<Edge>();

        while (e < V - 1)
        {
            Edge nextEdge = edges[i++];
            int x = Find(parent, nextEdge.src);
            int y = Find(parent, nextEdge.dest);

            if (x != y)
            {
                mst.Add(nextEdge);
                Union(parent, rank, x, y);
                e++;
            }
        }

        Console.WriteLine("Edges in Minimum Spanning Tree:");
        foreach (var edge in mst)
        {
            Console.WriteLine($"{edge.src} - {edge.dest} with weight {edge.weight}");
        }
    }

    private int Find(int[] parent, int i)
    {
        if (parent[i] == i)
            return i;
        return Find(parent, parent[i]);
    }

    private void Union(int[] parent, int[] rank, int x, int y)
    {
        int xRoot = Find(parent, x);
        int yRoot = Find(parent, y);

        if (rank[xRoot] < rank[yRoot])
            parent[xRoot] = yRoot;
        else if (rank[xRoot] > rank[yRoot])
            parent[yRoot] = xRoot;
        else
        {
            parent[yRoot] = xRoot;
            rank[xRoot]++;
        }
    }
}

public class Edge : IComparable<Edge>
{
    public int src, dest, weight;

    public Edge(int src, int dest, int weight)
    {
        this.src = src;
        this.dest = dest;
        this.weight = weight;
    }

    public int CompareTo(Edge other)
    {
        return weight - other.weight;
    }
}

10、Floyd-Warshall算法是一種用于解決所有點(diǎn)對(duì)最短路徑的動(dòng)態(tài)規(guī)劃算法。

下面是C#中的Floyd-Warshall算法的實(shí)現(xiàn)示例：

using System;

class FloydWarshall
{
    private static int INF = int.MaxValue; // 代表無窮大的值

    public static void FindShortestPath(int[,] graph)
    {
        int V = graph.GetLength(0);

        // 創(chuàng)建一個(gè)二維數(shù)組dist，用于保存最短路徑的長(zhǎng)度
        int[,] dist = new int[V, V];

        // 初始化dist數(shù)組
        for (int i = 0; i < V; i++)
        {
            for (int j = 0; j < V; j++)
            {
                dist[i, j] = graph[i, j];
            }
        }

        // 逐個(gè)頂點(diǎn)考慮，如果經(jīng)過k頂點(diǎn)路徑比原路徑短，就更新dist數(shù)組
        for (int k = 0; k < V; k++)
        {
            for (int i = 0; i < V; i++)
            {
                for (int j = 0; j < V; j++)
                {
                    if (dist[i, k] != INF && dist[k, j] != INF
                        && dist[i, k] + dist[k, j] < dist[i, j])
                    {
                        dist[i, j] = dist[i, k] + dist[k, j];
                    }
                }
            }
        }

        // 輸出最短路徑矩陣
        Console.WriteLine("最短路徑矩陣：");
        for (int i = 0; i < V; i++)
        {
            for (int j = 0; j < V; j++)
            {
                if (dist[i, j] == INF)
                    Console.Write("INF\t");
                else
                    Console.Write(dist[i, j] + "\t");
            }
            Console.WriteLine();
        }
    }

    static void Main(string[] args)
    {
        int V = 4; // 頂點(diǎn)數(shù)
        int[,] graph = {
            {0, 5, INF, 10},
            {INF, 0, 3, INF},
            {INF, INF, 0, 1},
            {INF, INF, INF, 0}
        };

        FindShortestPath(graph);
    }
}

在這個(gè)示例中，我們使用Floyd-Warshall算法來計(jì)算給定圖的最短路徑矩陣。該算法通過考慮逐個(gè)中間頂點(diǎn)k，不斷更新最短路徑矩陣dist。最終，我們可以獲得所有點(diǎn)對(duì)之間的最短路徑長(zhǎng)度。

責(zé)任編輯：姜華來源：今日頭條