Project Euler 054~056
關(guān)于啥是Project Euler 詳見 https://projecteuler.net/about?
觀前聲明：? ?
這是個人興趣使然的對自己入坑pe的記錄，僅提供思路和部分代碼；各個方面肯定都是有著優(yōu)化與提升空間的，甚至在許多大佬看來這應(yīng)該是初學者的淺薄而未經(jīng)剪枝的丑碼，如果能幫到有興趣的人自是最好，也歡迎能醍醐灌頂?shù)纳疃扔懻摗??
大佬看到了笑笑就行，還請輕噴。
帶著惡意，抬杠者...俺也噴不過您，也不能拿您咋樣...畢竟這只是我個人興趣使然的行為或者說是學習記錄分享。?（說是記錄，但因為是早先寫的所以其實是在各種意義上公開處刑和吐槽自己 并嘗試補救優(yōu)化）
語言是c++，用的VS平臺
（都忘記上次更新是啥時了...）
Poker hands
Problem 54
In the card game poker, a hand consists of five cards and are ranked, from lowest to highest, in the following way:
High Card: Highest value card.
One Pair: Two cards of the same value.
Two Pairs: Two different pairs.
Three of a Kind: Three cards of the same value.
Straight: All cards are consecutive values.
Flush: All cards of the same suit.
Full House: Three of a kind and a pair.
Four of a Kind: Four cards of the same value.
Straight Flush: All cards are consecutive values of same suit.
Royal Flush: Ten, Jack, Queen, King, Ace, in same suit.
The cards are valued in the order:
2, 3, 4, 5, 6, 7, 8, 9, 10, Jack, Queen, King, Ace.
If two players have the same ranked hands then the rank made up of the highest value wins; for example, a pair of eights beats a pair of fives (see example 1 below). But if two ranks tie, for example, both players have a pair of queens, then highest cards in each hand are compared (see example 4 below); if the highest cards tie then the next highest cards are compared, and so on.
Consider the following five hands dealt to two players:
The file,?poker.txt, contains one-thousand random hands dealt to two players. Each line of the file contains ten cards (separated by a single space): the first five are Player 1's cards and the last five are Player 2's cards. You can assume that all hands are valid (no invalid characters or repeated cards), each player's hand is in no specific order, and in each hand there is a clear winner.
How many hands does Player 1 win?
題目大意：
在撲克游戲中，一局牌由五張牌組成，組成的牌的大小由低到高如下：
High Card: 最高值的牌.
One Pair: 兩張面值一樣的牌.
Two Pairs: 兩個值不同的One Pair.
Three of a Kind: 三張面值一樣的牌.
Straight: 所有的牌面值為連續(xù)數(shù)值.
Flush: 所有的牌花色相同.
Full House: Three of a Kind 加一個One Pair.
Four of a Kind: 四張牌面值相同.
Straight Flush: 所有的牌花色相同并且為連續(xù)數(shù)值.
Royal Flush: 10，J，Q，K和A，并且為相同花色。
牌的面值大小排序如下：
2, 3, 4, 5, 6, 7, 8, 9, 10, Jack, Queen, King, Ace.
如果兩個玩家的牌具有同樣的排序（上面介紹的幾種），那么他們牌的大小由手中最大的牌決定。
例如，一對8比一對5大（見下面例一）；
但是如果兩個玩家都用一對Q，那么他們手中最大的牌就用來比較大小（見下面例四）；
如果他們最高面值的牌也相等，那么就用次高面值的牌比較，以此類推。
（例子見英文）
文件 poker.txt （https://projecteuler.net/project/resources/p054_poker.txt）包含一千局隨機牌。
每一行包含十張牌（用空格分隔）；前五張是玩家1的牌，后五張是玩家2的牌。
所有的牌都是合理的（沒有非法字符或者重復的牌）。每個玩家的牌沒有順序，并且每一局都有明確的輸贏。
其中玩家1能贏多少局？
這是當時我做到的最惡心的題 沒有之一
題本身不難 僅僅只用考慮清楚判斷條件而已
但是，但是..要考慮完所有情況，就很難受了 我記得我寫這題的時候非常酸爽，直到現(xiàn)在都不愿再面對.純屬惡心人，我寫的這些個判斷沒有任何技巧 至今也不想優(yōu)化.
分為2個函數(shù).checklevel函數(shù)判斷手牌等級，judge函數(shù)仲裁2者輸贏，需要細寫的基本就是手牌同級后的其他判斷。
可以在全局先用string數(shù)組存儲好1000對手牌 然后慢慢寫
實在不想細說這個我直接貼代碼了 畢竟真的沒啥技巧.
簡單說明下：
這里先用sx sy數(shù)組分別存儲手牌的數(shù)字和字母部分，便于之后的判斷；
scv工具字符串為判斷面值和數(shù)相同面值的牌的個數(shù)提供方便；
其他部分我代碼上//后都解釋了是啥等級我就懶得說了（節(jié)能）；
基本上也沒啥好解釋的? 這個函數(shù)前面幾行與checklevel函數(shù)是一樣的，后面都在考慮不同等級的2對手牌等級相等的情況下進行別的比較（寫了300+行 wsl）
這道題不論是題還是我（主要是我）都顯得很笨拙.建議入土
ans：376
Lychrel numbers
Problem 55
If we take 47, reverse and add, 47 + 74 = 121, which is palindromic.
Not all numbers produce palindromes so quickly. For example,
349 + 943 = 1292,
1292 + 2921 = 4213
4213 + 3124 = 7337
That is, 349 took three iterations to arrive at a palindrome.
Although no one has proved it yet, it is thought that some numbers, like 196, never produce a palindrome. A number that never forms a palindrome through the reverse and add process is called a Lychrel number. Due to the theoretical nature of these numbers, and for the purpose of this problem, we shall assume that a number is Lychrel until proven otherwise. In addition you are given that for every number below ten-thousand, it will either (i) become a palindrome in less than fifty iterations, or, (ii) no one, with all the computing power that exists, has managed so far to map it to a palindrome. In fact, 10677 is the first number to be shown to require over fifty iterations before producing a palindrome: 4668731596684224866951378664 (53 iterations, 28-digits).
Surprisingly, there are palindromic numbers that are themselves Lychrel numbers; the first example is 4994.
How many Lychrel numbers are there below ten-thousand?
NOTE: Wording was modified slightly on 24 April 2007 to emphasise the theoretical nature of Lychrel numbers.
本題新知識：利克瑞爾數(shù)..
47與自己的倒置74相加得到121是個回文數(shù)；
349需要經(jīng)過3次這樣的迭代才能得到回文數(shù)：
349 + 943 = 1292,
1292 + 2921 = 4213
4213 + 3124 = 7337
不能形成回文數(shù)的數(shù)被稱為利克瑞爾數(shù)（Lychrel numbers）
此外我們還知道：
對于每個一萬以下的數(shù)字，這個數(shù)如果不能在50次迭代以內(nèi)得到一個回文，那么就算用盡現(xiàn)有的所有運算能力也永遠不會得到。10677是第一個需要50次以上迭代得到回文的數(shù)，它可以通過53次迭代得到一個28位的回文：4668731596684224866951378664。
令人驚奇的是，有一些回文數(shù)本身也是Lychrel數(shù)，第一個例子是4994。
問10000以下有多少Lychrel數(shù)
當時剛寫完54，所以55就自暴自棄的暴搜了 （經(jīng)典“規(guī)模不大，BF也很快”）
基本就是利用大整數(shù)的加法，寫幾個函數(shù)：判斷數(shù)是否是回文數(shù)；得到數(shù)的逆序；將數(shù)本身與逆序相加得到新的數(shù)并存進數(shù)組；循環(huán)上述判斷50次迭代內(nèi)這個數(shù)能不能形成回文數(shù)
對10000以下每個數(shù)進行檢驗（可以通過一些數(shù)論知識進行剪枝優(yōu)化. 但 我懶）
直接上代碼了：
沒啥技巧可言的暴搜.
ans：249
Powerful digit sum
Problem 56
A googol (10^100) is a massive number: one followed by one-hundred zeros; 100^100?is almost unimaginably large: one followed by two-hundred zeros. Despite their size, the sum of the digits in each number is only 1.
Considering natural numbers of the form,?a,b, where?a, b?< 100, what is the maximum digital sum?
10^100，1后帶100個0，100^100，1后帶200個0，它們的每個位上的數(shù)相加后只有1
問當a,b<100時，所有a^b中，每個位上的數(shù)相加后，最大值是多少。
大整數(shù)乘法回憶復健題.搬搬以前的磚即可。
（因為寫過大整數(shù)乘法，所以就懶得用更為優(yōu)化的快速冪一類.
while循環(huán)內(nèi)即為大整數(shù)乘法；（這個函數(shù)的時間復雜度毫無優(yōu)化，因為每次指數(shù)運算中每次都要進行o^(n)的大整數(shù)乘法運算）但無所謂 a b<100時還是很快。
ans：972
隨緣更新后續(xù)
暑假余額一月不到.哭.
