是否可以使用 LINQ 检查列表中的所有数字是否单调增加？

Question

我很想知道在 LINQ 中是否有一种方法可以检查列表中的所有数字是否都单调递增？

示例

List<double> list1 = new List<double>() { 1, 2, 3, 4 };
Debug.Assert(list1.IsIncreasingMonotonically() == true);

List<double> list2 = new List<double>() { 1, 2, 100, -5 };
Debug.Assert(list2.IsIncreasingMonotonically() == false);

我问的原因是我想知道将列表中的元素与其前一个元素进行比较的技术，这是我在使用 LINQ 时从未理解过的。

完成的 C# 示例类

根据下面@Servy 的官方回答，这是我现在正在使用的完整课程。它向您的项目添加扩展方法，以检查列表是单调增加/减少，还是严格单调减少。我正在努力适应函数式编程风格，这是一种很好的学习方式。

using System;
using System.Collections.Generic;
using System.Diagnostics;
using System.Linq;
using System.Text;
using System.Threading.Tasks;

namespace MyHelper
{
    /// <summary>
    /// Classes to check if a list is increasing or decreasing monotonically. See:
    /// http://stackoverflow.com/questions/14815356/is-it-possible-to-use-linq-to-check-if-all-numbers-in-a-list-are-increasing-mono#14815511
    /// Note the difference between strictly monotonic and monotonic, see:
    /// http://en.wikipedia.org/wiki/Monotonic_function
    /// </summary>
    public static class IsMonotonic
    {
        /// <summary>
        /// Returns true if the elements in the are increasing monotonically.
        /// </summary>
        /// <typeparam name="T">Type of elements in the list.</typeparam>
        /// <param name="list">List we are interested in.</param>
        /// <returns>True if all of the the elements in the list are increasing monotonically.</returns>
        public static bool IsIncreasingMonotonically<T>(this List<T> list) where T : IComparable
        {
            return list.Zip(list.Skip(1), (a, b) => a.CompareTo(b) <= 0).All(b => b);
        }

        /// <summary>
        /// Returns true if the elements in the are increasing strictly monotonically.
        /// </summary>
        /// <typeparam name="T">Type of elements in the list.</typeparam>
        /// <param name="list">List we are interested in.</param>
        /// <returns>True if all of the the elements in the list are increasing monotonically.</returns>
        public static bool IsIncreasingStrictlyMonotonically<T>(this List<T> list) where T : IComparable
        {
            return list.Zip(list.Skip(1), (a, b) => a.CompareTo(b) < 0).All(b => b);
        }

        /// <summary>
        /// Returns true if the elements in the are decreasing monotonically.
        /// </summary>
        /// <typeparam name="T">Type of elements in the list.</typeparam>
        /// <param name="list">List we are interested in.</param>
        /// <returns>True if all of the the elements in the list are decreasing monotonically.</returns>
        public static bool IsDecreasingMonotonically<T>(this List<T> list) where T : IComparable
        {
            return list.Zip(list.Skip(1), (a, b) => a.CompareTo(b) >= 0).All(b => b);
        }

        /// <summary>
        /// Returns true if the elements in the are decreasing strictly monotonically.
        /// </summary>
        /// <typeparam name="T">Type of elements in the list.</typeparam>
        /// <param name="list">List we are interested in.</param>
        /// <returns>True if all of the the elements in the list are decreasing strictly monotonically.</returns>
        public static bool IsDecreasingStrictlyMonotonically<T>(this List<T> list) where T : IComparable
        {
            return list.Zip(list.Skip(1), (a, b) => a.CompareTo(b) > 0).All(b => b);
        }

        /// <summary>
        /// Returns true if the elements in the are increasing monotonically.
        /// </summary>
        /// <typeparam name="T">Type of elements in the list.</typeparam>
        /// <param name="list">List we are interested in.</param>
        /// <returns>True if all of the the elements in the list are increasing monotonically.</returns>
        public static bool IsIncreasingMonotonicallyBy<T>(this List<T> list, Func<T> x) where T : IComparable
        {
            return list.Zip(list.Skip(1), (a, b) => a.CompareTo(b) <= 0).All(b => b);
        }

        public static void UnitTest()
        {
            {
                List<double> list = new List<double>() { 1, 2, 3, 4 };
                Debug.Assert(list.IsIncreasingMonotonically<double>() == true);
                Debug.Assert(list.IsIncreasingStrictlyMonotonically<double>() == true);
                Debug.Assert(list.IsDecreasingMonotonically<double>() == false);
                Debug.Assert(list.IsDecreasingStrictlyMonotonically<double>() == false);
            }

            {
                List<double> list = new List<double>() { 1, 2, 100, -5 };
                Debug.Assert(list.IsIncreasingMonotonically() == false);
                Debug.Assert(list.IsIncreasingStrictlyMonotonically() == false);
                Debug.Assert(list.IsDecreasingMonotonically() == false);
                Debug.Assert(list.IsDecreasingStrictlyMonotonically() == false);
            }

            {
                List<double> list = new List<double>() {1, 1, 2, 2, 3, 3, 4, 4};
                Debug.Assert(list.IsIncreasingMonotonically() == true);
                Debug.Assert(list.IsIncreasingStrictlyMonotonically<double>() == false);
                Debug.Assert(list.IsDecreasingMonotonically() == false);
                Debug.Assert(list.IsDecreasingStrictlyMonotonically() == false);
            }

            {
                List<double> list = new List<double>() { 4, 3, 2, 1 };
                Debug.Assert(list.IsIncreasingMonotonically() == false);
                Debug.Assert(list.IsIncreasingStrictlyMonotonically<double>() == false);
                Debug.Assert(list.IsDecreasingMonotonically() == true);
                Debug.Assert(list.IsDecreasingStrictlyMonotonically() == true);
            }

            {
                List<double> list = new List<double>() { 4, 4, 3, 3, 2, 2, 1, 1 };
                Debug.Assert(list.IsIncreasingMonotonically() == false);
                Debug.Assert(list.IsIncreasingStrictlyMonotonically<double>() == false);
                Debug.Assert(list.IsDecreasingMonotonically() == true);
                Debug.Assert(list.IsDecreasingStrictlyMonotonically() == false);
            }
        }
    }
}

Answer 1

public static bool IsIncreasingMontonically<T>(List<T> list) 
    where T : IComparable
{
    return list.Zip(list.Skip(1), (a, b) => a.CompareTo(b) <= 0)
        .All(b => b);
}

请注意，这会重复序列两次。对于List，这根本不是问题，对于IEnumerable 或IQueryable，这可能很糟糕，所以在将List<T> 更改为IEnumerable<T> 之前要小心。

Answer 2

您不会使用OrderBy() 对列表进行排序并将它们与原始列表进行比较吗？如果它们相同，那么它会给你的答案是伪口语：

var increasing = orignalList.OrderBy(m=>m.value1).ToList();
var decreasing = orignalList.OrderByDescending(m=>m.value1).ToList();

var mono = (originalList == increasing || originalList == decreasing)

Answer 3

这是一个可以工作的单行：

var isIncreasing = list.OrderBy(x => x).SequenceEqual(list);

或者，如果您要提高性能，这里有一个单行代码，它只会遍历列表一次，并在到达乱序元素时立即退出：

var isIncreasing = !list.SkipWhile((x, i) => i == 0 || list[i - 1] <= x).Any();

Answer 4

通过使用Enumerable.Aggregate 方法：

list1.Aggregate((a, i) => a > i ? double.MaxValue : i) != double.MaxValue;

Answer 5

使用循环！它简短、快速且易读。除了 Servy 的回答之外，这个线程中的大多数解决方案都非常慢（排序需要 'n log n' 时间）。

// Test whether a sequence is strictly increasing.
public bool IsIncreasing(IEnumerable<double> list)
{
    bool initial = true;
    double last = Double.MinValue;
    foreach(var x in list)
    {
        if (!initial && x <= last)
            return false;

        initial = false;
        last = x;
    }

    return true;
}

示例

1. IsIncreasing(new List<double>{1,2,3}) 返回真
2. IsIncreasing(new List<double>{1,3,2}) 返回 False

Answer 6

如果你想检查一个列表是否总是从一个索引增加到另一个索引：

IEnumerable<int> list = new List<int>() { 1, 2, 3, 4, 5, 6, 7, 10 };
bool allIncreasing = !list
    .Where((i, index) => index > 0 && list.ElementAt(index - 1) >= i)
    .Any();

Demo

但在我看来，在这种情况下，一个简单的循环会更具可读性。

Answer 7

考虑如下的实现，它只枚举给定的 IEnumerable 一次。枚举可能会产生副作用，如果可能的话，调用者通常会期望一次传递。

public static bool IsIncreasingMonotonically<T>(
    this IEnumerable<T> _this)
    where T : IComparable<T>
{
    using (var e = _this.GetEnumerator())
    {
        if (!e.MoveNext())
            return true;
        T prev = e.Current;
        while (e.MoveNext())
        {
            if (prev.CompareTo(e.Current) > 0)
                return false;
            prev = e.Current;
        }
        return true;
    }
}

Answer 8

public static class EnumerableExtensions
{
    private static bool CompareAdjacentElements<TSource>(this IEnumerable<TSource> source,
        Func<TSource, TSource, bool> comparison)
    {
        using (var iterator = source.GetEnumerator())
        {
            if (!iterator.MoveNext())
                throw new ArgumentException("The input sequence is empty", "source");
            var previous = iterator.Current;
            while (iterator.MoveNext())
            {
                var next = iterator.Current;
                if (comparison(previous, next)) return false;
                previous = next;
            }
            return true;
        }
    }

    public static bool IsSorted<TSource>(this IEnumerable<TSource> source)
        where TSource : IComparable<TSource>
    {
        return CompareAdjacentElements(source, (previous, next) => previous.CompareTo(next) > 0);
    }

    public static bool IsSorted<TSource>(this IEnumerable<TSource> source, Comparison<TSource> comparison)
    {
        return CompareAdjacentElements(source, (previous, next) => comparison(previous, next) > 0);
    }

    public static bool IsStrictSorted<TSource>(this IEnumerable<TSource> source)
        where TSource : IComparable<TSource>
    {
        return CompareAdjacentElements(source, (previous, next) => previous.CompareTo(next) >= 0);
    }

    public static bool IsStrictSorted<TSource>(this IEnumerable<TSource> source, Comparison<TSource> comparison)
    {
        return CompareAdjacentElements(source, (previous, next) => comparison(previous, next) >= 0);
    }
}