{"id":4087,"date":"2018-09-30T01:02:20","date_gmt":"2018-09-30T08:02:20","guid":{"rendered":"https:\/\/zxi.mytechroad.com\/blog\/?p=4087"},"modified":"2018-09-30T01:32:31","modified_gmt":"2018-09-30T08:32:31","slug":"leetcode-914-x-of-a-kind-in-a-deck-of-cards","status":"publish","type":"post","link":"https:\/\/zxi.mytechroad.com\/blog\/math\/leetcode-914-x-of-a-kind-in-a-deck-of-cards\/","title":{"rendered":"\u82b1\u82b1\u9171 LeetCode 914. X of a Kind in a Deck of Cards"},"content":{"rendered":"<h1><strong>Problem<\/strong><\/h1>\n<p>n a deck of cards, each card has an integer written on it.<\/p>\n<p>Return\u00a0<code>true<\/code>\u00a0if and only if you can choose\u00a0<code>X &gt;= 2<\/code>\u00a0such that\u00a0it is possible to split the entire deck\u00a0into 1 or more groups of cards, where:<\/p>\n<ul>\n<li>Each group has exactly\u00a0<code>X<\/code>\u00a0cards.<\/li>\n<li>All the cards in each group have the same integer.<\/li>\n<\/ul>\n<p><strong>Example 1:<\/strong><\/p>\n<pre class=\"crayon:false\"><strong>Input: <\/strong><span id=\"example-input-1-1\">[1,2,3,4,4,3,2,1]<\/span>\r\n<strong>Output: <\/strong><span id=\"example-output-1\">true\r\n<strong>Explanation<\/strong>: Possible partition [1,1],[2,2],[3,3],[4,4]<\/span>\r\n<\/pre>\n<div>\n<p><strong>Example 2:<\/strong><\/p>\n<pre class=\"crayon:false\"><strong>Input: <\/strong><span id=\"example-input-2-1\">[1,1,1,2,2,2,3,3]<\/span>\r\n<strong>Output: <\/strong><span id=\"example-output-2\">false\r\n<\/span><span id=\"example-output-1\"><strong>Explanation<\/strong>: No possible partition.<\/span>\r\n<\/pre>\n<div>\n<p><strong>Example 3:<\/strong><\/p>\n<pre class=\"crayon:false\"><strong>Input: <\/strong><span id=\"example-input-3-1\">[1]<\/span>\r\n<strong>Output: <\/strong><span id=\"example-output-3\">false\r\n<\/span><span id=\"example-output-1\"><strong>Explanation<\/strong>: No possible partition.<\/span>\r\n<\/pre>\n<div>\n<p><strong>Example 4:<\/strong><\/p>\n<pre class=\"crayon:false\"><strong>Input: <\/strong><span id=\"example-input-4-1\">[1,1]<\/span>\r\n<strong>Output: <\/strong><span id=\"example-output-4\">true\r\n<\/span><span id=\"example-output-1\"><strong>Explanation<\/strong>: Possible partition [1,1]<\/span>\r\n<\/pre>\n<div>\n<p><strong>Example 5:<\/strong><\/p>\n<pre class=\"crayon:false\"><strong>Input: <\/strong><span id=\"example-input-5-1\">[1,1,2,2,2,2]<\/span>\r\n<strong>Output: <\/strong><span id=\"example-output-5\">true\r\n<\/span><span id=\"example-output-1\"><strong>Explanation<\/strong>: Possible partition [1,1],[2,2],[2,2]<\/span>\r\n<\/pre>\n<p><strong>Note:<\/strong><\/p>\n<ol>\n<li><code>1 &lt;= deck.length &lt;= 10000<\/code><\/li>\n<li><code>0 &lt;= deck[i] &lt;\u00a010000<\/code><\/li>\n<\/ol>\n<h1><strong>Solution 1: HashTable + Brute Force<\/strong><\/h1>\n<p>Try all possible Xs. 2 ~ deck.size()<\/p>\n<p>Time complexity: ~O(n)<\/p>\n<p>Space complexity: O(1)<\/p>\n<div class=\"responsive-tabs\">\n<h2 class=\"tabtitle\">C++<\/h2>\n<div class=\"tabcontent\">\n\n<pre class=\"lang:c++ decode:true \">\/\/ Author: Huahua, 16 ms\r\nclass Solution {\r\npublic:\r\n  bool hasGroupsSizeX(vector&lt;int&gt;&amp; deck) {\r\n    unordered_map&lt;int, int&gt; counts;\r\n    for (int card : deck) ++counts[card];\r\n    for (int i = 2; i &lt;= deck.size(); ++i) {\r\n      if (deck.size() % i) continue;\r\n      bool ok = true;\r\n      for (const auto&amp; pair : counts)\r\n        if (pair.second % i) {\r\n          ok = false;\r\n          break;\r\n        }\r\n      if (ok) return true;\r\n    }\r\n    return false;\r\n  }\r\n};<\/pre>\n<\/div><\/div>\n<h1><strong>Solution 2: HashTable + GCD<\/strong><\/h1>\n<p>Time complexity: O(nlogn)<\/p>\n<p>Space complexity: O(1)<\/p>\n<div class=\"responsive-tabs\">\n<h2 class=\"tabtitle\">C++<\/h2>\n<div class=\"tabcontent\">\n\n<pre class=\"lang:default decode:true\">\/\/ Author: Huahua, 16 ms\r\nclass Solution {\r\npublic:\r\n  bool hasGroupsSizeX(vector&lt;int&gt;&amp; deck) {\r\n    unordered_map&lt;int, int&gt; counts;\r\n    for (int card : deck) ++counts[card];\r\n    int X = deck.size();\r\n    for (const auto&amp; p : counts) \r\n      X = __gcd(X, p.second);\r\n    return X &gt;= 2;\r\n  }\r\n};<\/pre>\n\n<\/div><h2 class=\"tabtitle\">Java<\/h2>\n<div class=\"tabcontent\">\n\n<pre class=\"lang:java decode:true \">\/\/ Author: Somebody\r\nclass Solution {\r\n    public boolean hasGroupsSizeX(int[] deck) {\r\n        HashMap&lt;Integer, Integer&gt; map = new HashMap&lt;Integer, Integer&gt;();\r\n        for (int i=0; i&lt;deck.length; i++) {\r\n            int curr = deck[i];\r\n            if (map.containsKey(curr)) {\r\n                map.put(curr, map.get(curr) + 1);\r\n            } else {\r\n                map.put(curr, 1);\r\n            }\r\n        }\r\n        \r\n        \/\/ O(nLogn)\r\n        int gcd = 0;\r\n        for(Integer key: map.keySet()) {\r\n            gcd = findGCDOfTwoNumbers(map.get(key), gcd);\r\n        }\r\n        \r\n        return gcd &gt;= 2;      \r\n    }\r\n    \r\n    \/\/ O(Log n)\r\n    public static int findGCDOfTwoNumbers (int a, int b) {\r\n        if (b == 0) {\r\n            return a;\r\n        }\r\n        return findGCDOfTwoNumbers(b, a%b);\r\n    }\r\n}<\/pre>\n<p>&nbsp;<\/p>\n<\/div><\/div>\n<p><strong>\u00a0<\/strong><\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n","protected":false},"excerpt":{"rendered":"<p>Problem n a deck of cards, each card has an integer written on it. Return\u00a0true\u00a0if and only if you can choose\u00a0X &gt;= 2\u00a0such that\u00a0it is&#8230;<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[49],"tags":[222,359,418,348],"class_list":["post-4087","post","type-post","status-publish","format-standard","hentry","category-math","tag-easy","tag-gcd","tag-hashatable","tag-parition","entry","simple"],"_links":{"self":[{"href":"https:\/\/zxi.mytechroad.com\/blog\/wp-json\/wp\/v2\/posts\/4087","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/zxi.mytechroad.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/zxi.mytechroad.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/zxi.mytechroad.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/zxi.mytechroad.com\/blog\/wp-json\/wp\/v2\/comments?post=4087"}],"version-history":[{"count":6,"href":"https:\/\/zxi.mytechroad.com\/blog\/wp-json\/wp\/v2\/posts\/4087\/revisions"}],"predecessor-version":[{"id":4093,"href":"https:\/\/zxi.mytechroad.com\/blog\/wp-json\/wp\/v2\/posts\/4087\/revisions\/4093"}],"wp:attachment":[{"href":"https:\/\/zxi.mytechroad.com\/blog\/wp-json\/wp\/v2\/media?parent=4087"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/zxi.mytechroad.com\/blog\/wp-json\/wp\/v2\/categories?post=4087"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/zxi.mytechroad.com\/blog\/wp-json\/wp\/v2\/tags?post=4087"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}