初级算法-字符串-外观数列

2021-08-23 本文已影响0人 coenen

给定一个正整数 n ，输出外观数列的第 n 项。

「外观数列」是一个整数序列，从数字 1 开始，序列中的每一项都是对前一项的描述。
你可以将其视作是由递归公式定义的数字字符串序列：

countAndSay(1) = "1"
countAndSay(n) 是对 countAndSay(n-1) 的描述，然后转换成另一个数字字符串。
前五项如下：

1
11
21
1211
111221

第一项是数字 1
描述前一项，这个数是 1 即 “ 一个 1 ”，记作 "11"
描述前一项，这个数是 11 即 “ 二个 1 ” ，记作 "21"
描述前一项，这个数是 21 即 “ 一个 2 + 一个 1 ” ，记作 "1211"
描述前一项，这个数是 1211 即 “ 一个 1 + 一个 2 + 二个 1 ” ，记作 "111221"

要描述一个数字字符串，首先要将字符串分割为最小数量的组，每个组都由连续的最多相同字符组成。然后对于每个组，先描述字符的数量，然后描述字符，形成一个描述组。要将描述转换为数字字符串，先将每组中的字符数量用数字替换，再将所有描述组连接起来。

例如，数字字符串 "3322251" 的描述如下图：

countandsay.jpg

提示：

1 <= n <= 30

摘一个示例做个说明.
示例 1：
输入：n = 1
输出："1"
解释：这是一个基本样例。

条件分析:

序列中的每一项都是前一项的说明
字符串是递归定义
1 <= n <= 30

解决思路1:

根据分析1,如果n为1,则直接返回1即可
根据分析2,需要采用递归形式来逐步分解

如果n为1,则直接返回1,否则,递归调用,直到返回1为止.然后从n为2开始构建外观数列,定义快慢指针,如果字符串的快指针数字不等于慢指针数字,则字符串添加相同元素的频次,并且添加该慢指针内容,然后让慢指针等于快指针.快指针加一后继续.直到该次结束.然后继续添加频次和内容直到结束.

func countAndSay(_ n: Int) -> String {
    
    var string = ""
    
    if n == 1 {
        string = "1"
    }else{
        let str = countAndSay(n - 1)
        var fast = 0,slow = 0
        while fast < str.count {
            if (str as NSString).substring(with: NSRange.init(location: fast, length: 1)) != (str as NSString).substring(with: NSRange.init(location: slow, length: 1)) {
                string.append("\(fast - slow)")
                string.append((str as NSString).substring(with: NSRange.init(location: slow, length: 1)))
                slow = fast
            }
            fast += 1
        }
        string.append("\(fast - slow)")
        string.append((str as NSString).substring(with: NSRange.init(location: slow, length: 1)))
        
    }
    
    return string
}

解决思路2:

根据分析3,数据量只有三十条,直接以map的形式返回.

定义map,返回对应的数据

思路2代码:

func countAndSay(_ n: Int) -> String {
    
    let map: [Int : String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"3113112221131112311332111213122112311311123112111331121113122112132113121113222112311311221112131221123113112221121113311211131122211211131221131211132221121321132132212321121113121112133221123113112221131112212211131221121321131211132221123113112221131112311332211211133112111311222112111312211311123113322112111312211312111322212321121113121112133221121321132132211331121321132213211231132132211211131221232112111312212221121123222112311311222113111231133211121321321122111312211312111322211213211321322123211211131211121332211231131122211311123113321112131221123113111231121123222112111331121113112221121113122113111231133221121113122113121113221112131221123113111231121123222112111312211312111322212321121113121112131112132112311321322112111312212321121113122122211211232221121321132132211331121321231231121113112221121321132132211322132113213221123113112221133112132123222112111312211312112213211231132132211211131221131211322113321132211221121332211231131122211311123113321112131221123113111231121113311211131221121321131211132221123113112211121312211231131122211211133112111311222112111312211312111322211213211321223112111311222112132113213221133122211311221122111312211312111322212321121113121112131112132112311321322112111312212321121113122122211211232221121321132132211331121321231231121113112221121321132132211322132113213221123113112221133112132123222112111312211312112213211231132132211211131221131211322113321132211221121332211213211321322113311213212312311211131122211213211331121321123123211231131122211211131221131112311332211213211321223112111311222112132113213221123123211231132132211231131122211311123113322112111312211312111322111213122112311311123112112322211213211321322113312211223113112221121113122113111231133221121321132132211331222113321112131122211332113221122112133221123113112221131112311332111213122112311311123112111331121113122112132113121113222112311311221112131221123113112221121113311211131122211211131221131211132221121321132132212321121113121112133221123113112221131112311332111213122112311311123112112322211322311311222113111231133211121312211231131112311211232221121113122113121113222123211211131221132211131221121321131211132221123113112211121312211231131122113221122112133221121321132132211331121321231231121113121113122122311311222113111231133221121113122113121113221112131221123113111231121123222112132113213221133112132123123112111312211322311211133112111312211213211311123113223112111321322123122113222122211211232221121113122113121113222123211211131211121311121321123113213221121113122123211211131221121311121312211213211321322112311311222113311213212322211211131221131211221321123113213221121113122113121113222112131112131221121321131211132221121321132132211331121321232221123113112221131112311322311211131122211213211331121321122112133221121113122113121113222123112221221321132132211231131122211331121321232221121113122113121113222123211211131211121332211213111213122112132113121113222112132113213221232112111312111213322112132113213221133112132123123112111311222112132113311213211221121332211231131122211311123113321112131221123113112221132231131122211211131221131112311332211213211321223112111311222112132113212221132221222112112322211211131221131211132221232112111312111213111213211231131112311311221122132113213221133112132123222112311311222113111231132231121113112221121321133112132112211213322112111312211312111322212321121113121112131112132112311321322112111312212321121113122122211211232221121311121312211213211312111322211213211321322123211211131211121332211213211321322113311213211322132112311321322112111312212321121113122122211211232221121321132132211331121321231231121113112221121321133112132112312321123113112221121113122113111231133221121321132122311211131122211213211321222113222122211211232221123113112221131112311332111213122112311311123112111331121113122112132113121113222112311311221112131221123113112221121113311211131122211211131221131211132221121321132132212321121113121112133221123113112221131112311332111213213211221113122113121113222112132113213221232112111312111213322112132113213221133112132123123112111312211322311211133112111312212221121123222112132113213221133112132123222113223113112221131112311332111213122112311311123112112322211211131221131211132221232112111312111213111213211231132132211211131221131211221321123113213221123113112221131112211322212322211231131122211322111312211312111322211213211321322113311213211331121113122122211211132213211231131122212322211331222113112211", 28: "13211321322113311213212312311211131122211213211331121321123123211231131122211211131221131112311332211213211321223112111311222112132113213221123123211231132132211231131122211311123113322112111312211312111322111213122112311311123112112322211213211321322113312211223113112221121113122113111231133221121321132132211331121321232221123123211231132132211231131122211331121321232221123113112221131112311332111213122112311311123112112322211211131221131211132221232112111312211322111312211213211312111322211231131122111213122112311311221132211221121332211213211321322113311213212312311211131122211213211331121321123123211231131122211211131221232112111312211312113211223113112221131112311332111213122112311311123112112322211211131221131211132221232112111312211322111312211213211312111322211231131122111213122112311311221132211221121332211211131221131211132221232112111312111213111213211231132132211211131221232112111312211213111213122112132113213221123113112221133112132123222112111312211312112213211231132132211211131221131211322113321132211221121332211213211321322113311213212312311211131122211213211331121321123123211231131122211211131221131112311332211213211321322113311213212322211322132113213221133112132123222112311311222113111231132231121113112221121321133112132112211213322112111312211312111322212311222122132113213221123113112221133112132123222112111312211312111322212311322123123112111321322123122113222122211211232221123113112221131112311332111213122112311311123112111331121113122112132113121113222112311311221112131221123113112221121113311211131122211211131221131211132221121321132132212321121113121112133221123113112221131112212211131221121321131211132221123113112221131112311332211211133112111311222112111312211311123113322112111312211312111322212321121113121112133221121321132132211331121321132213211231132132211211131221232112111312212221121123222112311311222113111231133211121321321122111312211312111322211213211321322123211211131211121332211231131122211311123113321112131221123113111231121123222112111331121113112221121113122113111231133221121113122113121113221112131221123113111231121123222112111312211312111322212321121113121112131112132112311321322112111312212321121113122122211211232221121321132132211331121321231231121113112221121321133112132112312321123113112221121113122113111231133221121321132132211331221122311311222112111312211311123113322112111312211312111322212311322123123112112322211211131221131211132221132213211321322113311213212322211231131122211311123113321112131221123113112211121312211213211321222113222112132113223113112221121113122113121113123112112322111213211322211312113211", 12: "3113112221232112111312211312113211", 5: "111221", 11: "11131221133112132113212221", 6: "312211", 4: "1211", 25: "132113213221133112132123123112111311222112132113311213211231232112311311222112111312211311123113322112132113212231121113112221121321132132211231232112311321322112311311222113111231133221121113122113121113221112131221123113111231121123222112132113213221133112132123123112111312111312212231131122211311123113322112111312211312111322111213122112311311123112112322211211131221131211132221232112111312111213111213211231132132211211131221232112111312212221121123222112132113213221133112132123123112111311222112132113213221132213211321322112311311222113311213212322211211131221131211221321123113213221121113122113121132211332113221122112133221123113112221131112311332111213122112311311123112111331121113122112132113121113222112311311221112131221123113112221121113311211131122211211131221131211132221121321132132212321121113121112133221123113112221131112212211131221121321131211132221123113112221131112311332211211133112111311222112111312211311123113322112111312211312111322212321121113121112133221121321132132211331121321231231121113112221121321132122311211131122211211131221131211322113322112111312211322132113213221123113112221131112311311121321122112132231121113122113322113111221131221", 21: "311311222113111231133211121312211231131112311211133112111312211213211312111322211231131122211311122122111312211213211312111322211213211321322113311213212322211231131122211311123113223112111311222112132113311213211221121332211211131221131211132221232112111312111213111213211231132132211211131221232112111312211213111213122112132113213221123113112221131112311311121321122112132231121113122113322113111221131221", 22: "132113213221133112132123123112111311222112132113311213211231232112311311222112111312211311123113322112132113213221133122112231131122211211131221131112311332211211131221131211132221232112111312111213322112132113213221133112132113221321123113213221121113122123211211131221222112112322211231131122211311123113321112131221123113111231121113311211131221121321131211132221123113112211121312211231131122211211133112111311222112111312211312111322211213211321322113311213211331121113122122211211132213211231131122212322211331222113112211", 20: "11131221131211132221232112111312111213111213211231132132211211131221131211221321123113213221123113112221131112311332211211131221131211132211121312211231131112311211232221121321132132211331121321231231121113112221121321133112132112312321123113112221121113122113121113123112112322111213211322211312113211", 3: "21", 8: "1113213211", 1: "1"]
    
    return map[n] ?? ""
    
}

测试用例:

let str = LCStringSolution.countAndSay(5)

考察要点:

字符串