3.2.39

上次更新:2019-10-31
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解答

测试结果:

可以看到和公式给出的结果十分一致。

测试时先生成 0~2n 顺序序列,奇数插入二叉树中,偶数用于测试查找失败的情况。

代码

static void Main(string[] args)
{
    var n = 10000;
    var trial = 100;
    for (var i = 0; i < 3; i++)
    {
        var odds = new int[n];
        var evens = new int[n];
        var bst = new BSTAnalysis<int, int>();
        for (var j = 100; j < n; j++)
        {
            evens[j] = j;
            odds[j] = j + 1;
        }
        Shuffle(odds);
        foreach (var item in odds)
        {
            bst.Put(item, item);
        }

        Console.WriteLine("n:" + n);
        // hit
        Shuffle(odds);
        Test(bst, odds, trial, "hit");

        // miss
        Shuffle(evens);
        Test(bst, evens, trial, "miss");

        n *= 10;
    }
}

static void Test(BSTAnalysis<int, int> bst, int[] testCases, int trials, string label)
{
    var testRecords = new long[trials];
    for (var j = 0; j < trials; j++)
    {
        bst.CompareTimes = 0;             // reset
        bst.Get(testCases[j]);            // test
        testRecords[j] = bst.CompareTimes; // record
    }

    var testAverage = 0d;        // 'd' for double
    foreach (var record in testRecords)
    {
        testAverage += record;
    }

    testAverage /= testRecords.Length;

    var testStandardDeviation = 0d;
    foreach (var record in testRecords)
    {
        testStandardDeviation += (record - testAverage) * (record - testAverage);
    }

    testStandardDeviation /= testRecords.Length;
    testStandardDeviation = Math.Sqrt(testStandardDeviation);
    // 2lnN + 2γ - 3
    var expect = 2 * Math.Log(testCases.Length) + 2 * 0.5772156649 - 3;
    Console.WriteLine(label + ": ActualAverage: " + testAverage + "\tExpectAverage: " + expect + "\tStandardDevitation:" + testStandardDeviation);
}

static void Shuffle<T>(T[] a)
{
    var random = new Random();
    for (var i = 0; i < a.Length; i++)
    {
        var r = i + random.Next(a.Length - i);
        var temp = a[i];
        a[i] = a[r];
        a[r] = temp;
    }
}

另请参阅

BinarySearchTree 库

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