如何在IList<T>上执行二进制搜索?

我怀疑在.NET中是否存在这样的通用二进制搜索方法,除了某些基类中存在的方法(但显然不存在于接口中),所以这里是我的通用方法。

public static Int32 BinarySearchIndexOf<T>(this IList<T> list, T value, IComparer<T> comparer = null)
{
    if (list == null)
        throw new ArgumentNullException(nameof(list));

    comparer = comparer ?? Comparer<T>.Default;

    Int32 lower = 0;
    Int32 upper = list.Count - 1;

    while (lower <= upper)
    {
        Int32 middle = lower + (upper - lower) / 2;
        Int32 comparisonResult = comparer.Compare(value, list[middle]);
        if (comparisonResult == 0)
            return middle;
        else if (comparisonResult < 0)
            upper = middle - 1;
        else
            lower = middle + 1;
    }

    return ~lower;
}

当然,这假设所讨论的列表已经按照比较器将使用的相同规则进行了排序。

这是我的Lasse代码版本。我发现能够使用lambda表达式来执行搜索非常有用。在对象列表中搜索时,它只允许传递用于排序的键。使用IComparer的实现基本上就是从这个实现派生出来的。

我也喜欢在找不到匹配项时返回~lower。Array.BinarySearch执行此操作,它允许您知道您搜索的项目应该插入到何处,以便保持顺序。

/// <summary>
/// Performs a binary search on the specified collection.
/// </summary>
/// <typeparam name="TItem">The type of the item.</typeparam>
/// <typeparam name="TSearch">The type of the searched item.</typeparam>
/// <param name="list">The list to be searched.</param>
/// <param name="value">The value to search for.</param>
/// <param name="comparer">The comparer that is used to compare the value
/// with the list items.</param>
/// <returns></returns>
public static int BinarySearch<TItem, TSearch>(this IList<TItem> list,
    TSearch value, Func<TSearch, TItem, int> comparer)
{
    if (list == null)
    {
        throw new ArgumentNullException("list");
    }
    if (comparer == null)
    {
        throw new ArgumentNullException("comparer");
    }

    int lower = 0;
    int upper = list.Count - 1;

    while (lower <= upper)
    {
        int middle = lower + (upper - lower) / 2;
        int comparisonResult = comparer(value, list[middle]);
        if (comparisonResult < 0)
        {
            upper = middle - 1;
        }
        else if (comparisonResult > 0)
        {
            lower = middle + 1;
        }
        else
        {
            return middle;
        }
    }

    return ~lower;
}

/// <summary>
/// Performs a binary search on the specified collection.
/// </summary>
/// <typeparam name="TItem">The type of the item.</typeparam>
/// <param name="list">The list to be searched.</param>
/// <param name="value">The value to search for.</param>
/// <returns></returns>
public static int BinarySearch<TItem>(this IList<TItem> list, TItem value)
{
    return BinarySearch(list, value, Comparer<TItem>.Default);
}

/// <summary>
/// Performs a binary search on the specified collection.
/// </summary>
/// <typeparam name="TItem">The type of the item.</typeparam>
/// <param name="list">The list to be searched.</param>
/// <param name="value">The value to search for.</param>
/// <param name="comparer">The comparer that is used to compare the value
/// with the list items.</param>
/// <returns></returns>
public static int BinarySearch<TItem>(this IList<TItem> list, TItem value,
    IComparer<TItem> comparer)
{
    return list.BinarySearch(value, comparer.Compare);
}

这实际上是Jon Bentley在其著作《编程珍珠》(Programming Pearls)中的实现,它受到了一个20年左右未被发现的数字溢出错误的影响。如果IList中有大量项,则(上+下)会溢出Int32。解决这个问题的一个办法是,用减法来做中间的计算,方法稍有不同;中间=下部+(上部-下部)/2;

Bentley在《Pearls编程》中还警告说,虽然二进制搜索算法于1946年发布,第一个正确的实现直到1962年才发布。

http://en.wikipedia.org/wiki/Binary_search#Numerical_difficulties

一段时间以来,我一直在努力把这件事做好。特别是MSDN中规定的边缘情况的返回值: http://msdn.microsoft.com/en-us/library/w4e7fxsh.aspx

我现在从.NET 4.0复制了ArraySortHelper.InternalBinarySearch(),并出于各种原因制作了自己的风格。

var numbers = new List<int>() { ... };
var items = new List<FooInt>() { ... };

int result1 = numbers.BinarySearchIndexOf(5);
int result2 = items.BinarySearchIndexOfBy(foo => foo.bar, 5);

这应该适用于所有.NET类型。到目前为止,我已经尝试了int、long和double。

实施:

public static class BinarySearchUtils
{
    public static int BinarySearchIndexOf<TItem>(this IList<TItem> list,
        TItem targetValue, IComparer<TItem> comparer = null)
    {
        Func<TItem, TItem, int> compareFunc =
            comparer != null ? comparer.Compare :
            (Func<TItem, TItem, int>) Comparer<TItem>.Default.Compare;
        int index = BinarySearchIndexOfBy(list, compareFunc, targetValue);
        return index;
    }

    public static int BinarySearchIndexOfBy<TItem, TValue>(this IList<TItem> list,
        Func<TItem, TValue, int> comparer, TValue value)
    {
        if (list == null)
            throw new ArgumentNullException("list");

        if (comparer == null)
            throw new ArgumentNullException("comparer");

        if (list.Count == 0)
            return -1;

        // Implementation below copied largely from .NET4
        // ArraySortHelper.InternalBinarySearch()
        int lo = 0;
        int hi = list.Count - 1;
        while (lo <= hi)
        {
            int i = lo + ((hi - lo) >> 1);
            int order = comparer(list[i], value);

            if (order == 0)
                return i;
            if (order < 0)
            {
                lo = i + 1;
            }
            else
            {
                hi = i - 1;
            }
        }

        return ~lo;
    }
}

单元测试:

[TestFixture]
public class BinarySearchUtilsTest
{
    [Test]
    public void BinarySearchReturnValueByMsdnSpecification()
    {
        var numbers = new List<int>() { 1, 3 };

        // Following the MSDN documentation for List<T>.BinarySearch:
        // http://msdn.microsoft.com/en-us/library/w4e7fxsh.aspx

        // The zero-based index of item in the sorted List(Of T), if item is found;
        int index = numbers.BinarySearchIndexOf(1);
        Assert.AreEqual(0, index);

        index = numbers.BinarySearchIndexOf(3);
        Assert.AreEqual(1, index);


        // otherwise, a negative number that is the bitwise complement of the
        // index of the next element that is larger than item
        index = numbers.BinarySearchIndexOf(0);
        Assert.AreEqual(~0, index);

        index = numbers.BinarySearchIndexOf(2);
        Assert.AreEqual(~1, index);


        // or, if there is no larger element, the bitwise complement of Count.
        index = numbers.BinarySearchIndexOf(4);
        Assert.AreEqual(~numbers.Count, index);
    }
}

希望通过一个工作实现一次性解决问题,至少根据MSDN规范。

在搜索二进制文件时会遇到一些问题 IList<T> ,首先,正如你提到的 BinarySearch 关于 List<T> 界面其次,您无法在搜索之前对列表进行排序(这是二进制搜索必须执行的操作)。

我认为你最好的选择是创造一个新的 列表<T> ,对其进行排序,然后进行搜索。它并不完美,但如果你有一个 IList<T> .

请注意,下面Antoine提供的实现中有一个bug:搜索大于列表中任何项的项时。返回值应为~lower而不是~middle。反编译方法ArraySortHelper.InternalBinarySearch(mscorlib)以查看框架实现。

如果您需要一个现成的二进制搜索实现 IList<T> s Wintellect's Power Collections has one Algorithms.cs ):

/// <summary>
/// Searches a sorted list for an item via binary search. The list must be sorted
/// by the natural ordering of the type (it's implementation of IComparable&lt;T&gt;).
/// </summary>
/// <param name="list">The sorted list to search.</param>
/// <param name="item">The item to search for.</param>
/// <param name="index">Returns the first index at which the item can be found. If the return
/// value is zero, indicating that <paramref name="item"/> was not present in the list, then this
/// returns the index at which <paramref name="item"/> could be inserted to maintain the sorted
/// order of the list.</param>
/// <returns>The number of items equal to <paramref name="item"/> that appear in the list.</returns>
public static int BinarySearch<T>(IList<T> list, T item, out int index)
        where T: IComparable<T>
{
    // ...
}

你可以用 List<T>.BinarySearch(T item) . 如果要使用自定义比较器,请使用 List<T>.BinarySearch(T item, IComparer<T> comparer) . 看看这个MSDN link 更多细节。

如果可以使用.NET 3.5,则可以使用内置Linq扩展方法:

using System.Linq;

IList<string> ls = ...;
var orderedList = ls.OrderBy(x => x).ToList();
orderedList.BinarySearch(...);

然而,对于Andrew Hare的解决方案,这实际上只是一种稍微不同的方式,并且只有在您从同一个有序列表中多次搜索时才真正有用。