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typescript实现快排

东东么么哒 人气:0

前言

本文执行环境typescript,版本4.7.4

不使用typescript的计算能力,通过类型来实现快排

元组快排

能否将元组 [3, 1, 2, 4] 通过泛型转换成 [1, 2, 3, 4]

如何实现快排?

实现逻辑

实现数字的大小比较

在typescript类型中没有比较符,那如何判断 5 和 6 谁更大?

typescript类型不知道,所以需要找到在typescript中已经存在的递增数列,通过这个数列来实现

怎么理解呢?

类似有 张三 和 李四 两个人,要比较他们谁的位置靠前,需要有一个他们排队的数列,然后依次查看,先看到 张三,那么 张三 的位置明显靠前

typescript中有这样的递增数列吗?

有的:元组下标,只需要递归元组,就可以实现依次点名

实现 A 是否 小于或等于 B

type SmallerThan<
    A extends number,
    B extends number,
    T extends number[] = []
> = T['length'] extends A ? true :
    T['length'] extends B ? false :
    SmallerThan<A, B, [...T, 0]>;

实现 A 是否 大于或等于 B

逻辑同理:

无限递归,直到匹配到 A 或者 B

type LargerThan<
    A extends number,
    B extends number,
    T extends number[] = []
> = T['length'] extends A ? false :
    T['length'] extends B ? true :
    LargerThan<A, B, [...T, 0]>;

当然也可以依赖 SmallerThan 泛型来实现

type LargerThan<
    A extends number,
    B extends number,
    T extends number[] = []
> = SmallerThan<A, B, T> extends true ? false : true;

实现Filter

type FilterLargerThan<
    T extends number[],
    A extends number,
    Z extends number[] = [],
    R extends number[] = []
> = T['length'] extends R['length'] ?
    Z : FilterLargerThan<
        T,
        A,
        LargerThan<T[R['length']], A> extends true ? [...Z, T[R['length']]] : Z,
        [...R, 0]
    >;

type FilterSmallerThan<
    T extends number[],
    A extends number,
    Z extends number[] = [],
    R extends number[] = []
> = T['length'] extends R['length'] ?
    Z : FilterSmallerThan<
        T,
        A,
        SmallerThan<T[R['length']], A> extends true ? [...Z, T[R['length']]] : Z,
        [...R, 0]
    >;

优化Filter

Filter写的很重复了,将泛型作为参数传进去

重构数字的大小值比较

如何把泛型作为参数传入,然后在参数中限定...好问题

// 目标是实现这种
type Test<A extends number, T extends ?> = T<A>;

貌似不太行,那变个思路:

实现一个对象,每个键值对实现一个泛型,最后只需要传入这个对象的key来获取泛型,在参数的限定可以变成对key的限定,通过keyof 对象即可实现

type F<A extends number> = A;
type Demo<A extends number> = {
    a: F<A>;
}
type Test<A extends number, T extends keyof Demo<number>> = Demo<A>[T];
type t1 = Test<1, 'a'>;

复用逻辑,将对应的泛型改成键值对

type Compare<A extends number, B extends number, T extends number[] = []> = {
    ['SmallerThan']:
        T['length'] extends A ? true :
            T['length'] extends B ? false :
                Compare<A, B, [...T, 0]>['SmallerThan'];

    ['LargerThan']:
        T['length'] extends A ? false :
            T['length'] extends B ? true :
            Compare<A, B, [...T, 0]>['LargerThan'];
}

重构Filter

复用逻辑,将对应的泛型改成键值对,key需要手动传入

type Filter<
    T extends number[],
    A extends number,
    key extends keyof Compare<number, number>,
    Z extends number[] = [],
    R extends number[] = [],
> = T['length'] extends R['length'] ?
    Z : Filter<
        T,
        A,
        key,
        Compare<T[R['length']], A>[key] extends true ? [...Z, T[R['length']]] : Z,
        [...R, 0]
    >;

实现快排

type UNSHIFT<T extends number[]> = T extends [number, ...infer U] ? U: [];

// 快排
type QuickSort<T extends any[]> = T['length'] extends 0 | 1 ?
    T : [
        ...QuickSort<Filter<UNSHIFT<T>, T[0], 'SmallerThan'>>,
        T[0],
        ...QuickSort<Filter<UNSHIFT<T>, T[0], 'LargerThan'>>
    ];

测试快排

type ARR1 = [5, 2, 4, 1, 0, 6];
type test1 = QuickSort<ARR1>;
// [0, 1, 2, 4, 5, 6]

type ARR2 = [3, 2, 7, 1, 0, 6, 9, 5, 8, 4];
type test2 = QuickSort<ARR2>;
// [0, 1, 2, 3, 4, 5, 6, 7, 8, 9]

type ARR3 = [1, 1, 0, 1, 1, 0, 0];
type test3 = QuickSort<ARR3>;
// [0, 0, 0, 1, 1, 1, 1]

看起来一切正常,可以发现遗漏了负数

测试负数的时候问题出现了

因为最开始的大小值对比,是从0开始无限递归的

结束条件是命中其中一个数,然而负数是永远不会命中,这就是致命bug!

优化:负数

负数的判断

负数的特点:多了一个符号,也就是 '-',转换成字符串后拿第一个字符判断

type isFuShu<T extends number> = `${T}` extends `${infer P}${string}` ?
    P extends '-' : true : false;

type i1 = isFuShu<6>;  // false
type i2 = isFuShu<-6>;  // true

字符串转数字

但是这样拿到的是字符串,还要把字符串转成数字

和大小比较的逻辑一样

type ToNumber<S extends string, R extends number[] = []> =
    S extends `${R['length']}` ?
        R['length'] : ToNumber<S, [...R, 0]>;

获取负数的值

判断是负数后要拿到负数的值

type GetFushu<T extends number> = `${T}` extends `${string}${infer U}` ?
    ToNumber<U> : 0;

完善获取绝对值

type GetAbs<T extends number> = isFuShu<T> extends true ? GetFushu<T> : T;

重构数字的大小比较

负数的对比和正数相反,且正数一定比负数大

type CompareV2<A extends number, B extends number, T extends number[] = []> = {
    ['SmallerThan']:
        T['length'] extends A ? true :
            T['length'] extends B ? false :
                CompareV2<GetAbs<A>, GetAbs<B>, [...T, 0]>['SmallerThan'];

    ['SmallerThanV2']:
        isFuShu<A> extends true ?
            (isFuShu<B> extends true ?
                CompareV2<A, B>['LargerThan'] :
                true) :
            (isFuShu<B> extends true ?
                false :
                CompareV2<A, B>['SmallerThan']);

    ['LargerThan']:
        T['length'] extends A ? false :
            T['length'] extends B ? true :
                CompareV2<GetAbs<A>, GetAbs<B>, [...T, 0]>['LargerThan'];
    
    ['LargerThanV2']:
        isFuShu<A> extends true ?
            (isFuShu<B> extends true ?
                CompareV2<A, B>['SmallerThan'] :
                false) :
            (isFuShu<B> extends true ?
                true :
                CompareV2<A, B>['LargerThan']);
}

测试用例:

type h1 = CompareV2<-8, -6>['SmallerThanV2']; // true
type h2 = CompareV2<8, -6>['SmallerThanV2']; // false
type h3 = CompareV2<6, 8>['SmallerThanV2']; // true
type h4 = CompareV2<-8, 6>['SmallerThanV2']; // true

type i1 = CompareV2<-8, -6>['LargerThanV2']; // false
type i2 = CompareV2<8, -6>['LargerThanV2']; // true
type i3 = CompareV2<6, 8>['LargerThanV2']; // false
type i4 = CompareV2<-8, 6>['LargerThanV2']; // false

重构快排

type FilterV2<
    T extends number[],
    A extends number,
    key extends keyof CompareV2<number, number>,
    Z extends number[] = [],
    R extends number[] = [],
> = T['length'] extends R['length'] ?
    Z : FilterV2<
        T,
        A,
        key,
        CompareV2<T[R['length']], A>[key] extends true ? [...Z, T[R['length']]] : Z,
        [...R, 0]
    >;

// 快排
type QuickSortV2<T extends any[]> = T['length'] extends 0 | 1 ?
    T : [
        ...QuickSortV2<FilterV2<UNSHIFT<T>, T[0], 'SmallerThanV2'>>,
        T[0],
        ...QuickSortV2<FilterV2<UNSHIFT<T>, T[0], 'LargerThanV2'>>
    ];

测试快排V2

type ARR4 = [-5, -2, -4, -1, 0, -6];
type test4 = QuickSortV2<ARR4>;
// [-6, -5, -4, -2, -1, 0]

type ARR5 = [-5, -2, 4, -1, 0, -6, 2, -3, 7];
type test5 = QuickSortV2<ARR5>;
// [-6, -5, -3, -2, -1, 0, 2, 4, 7]

type ARR6 = [3, -2, 7, -1, 0, -6, 9, -5, 8, -4];
type test6 = QuickSortV2<ARR6>;
// [-6, -5, -4, -2, -1, 0, 3, 7, 8, 9]

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