{"id":5721,"date":"2019-10-05T21:53:06","date_gmt":"2019-10-06T04:53:06","guid":{"rendered":"https:\/\/zxi.mytechroad.com\/blog\/?p=5721"},"modified":"2019-10-06T22:32:34","modified_gmt":"2019-10-07T05:32:34","slug":"leetcode-1220-count-vowels-permutation","status":"publish","type":"post","link":"https:\/\/zxi.mytechroad.com\/blog\/dynamic-programming\/leetcode-1220-count-vowels-permutation\/","title":{"rendered":"\u82b1\u82b1\u9171 LeetCode 1220. Count Vowels Permutation"},"content":{"rendered":"\n<figure class=\"wp-block-embed-youtube wp-block-embed is-type-video is-provider-youtube wp-embed-aspect-4-3 wp-has-aspect-ratio\"><div class=\"wp-block-embed__wrapper\">\n<iframe loading=\"lazy\" title=\"\u82b1\u82b1\u9171 LeetCode 1220. Count Vowels Permutation - \u5237\u9898\u627e\u5de5\u4f5c EP272\" width=\"500\" height=\"375\" src=\"https:\/\/www.youtube.com\/embed\/6v7m6SgFEZU?feature=oembed\" frameborder=\"0\" allow=\"accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture; web-share\" referrerpolicy=\"strict-origin-when-cross-origin\" allowfullscreen><\/iframe>\n<\/div><\/figure>\n\n\n\n<p>Given an integer&nbsp;<code>n<\/code>, your task is to count how many strings of length&nbsp;<code>n<\/code>&nbsp;can be formed under the following rules:<\/p>\n\n\n\n<ul class=\"wp-block-list\"><li>Each character is a lower case vowel&nbsp;(<code>'a'<\/code>,&nbsp;<code>'e'<\/code>,&nbsp;<code>'i'<\/code>,&nbsp;<code>'o'<\/code>,&nbsp;<code>'u'<\/code>)<\/li><li>Each vowel&nbsp;<code>'a'<\/code>&nbsp;may only be followed by an&nbsp;<code>'e'<\/code>.<\/li><li>Each vowel&nbsp;<code>'e'<\/code>&nbsp;may only be followed by an&nbsp;<code>'a'<\/code>&nbsp;or an&nbsp;<code>'i'<\/code>.<\/li><li>Each vowel&nbsp;<code>'i'<\/code>&nbsp;<strong>may not<\/strong>&nbsp;be followed by another&nbsp;<code>'i'<\/code>.<\/li><li>Each vowel&nbsp;<code>'o'<\/code>&nbsp;may only be followed by an&nbsp;<code>'i'<\/code>&nbsp;or a&nbsp;<code>'u'<\/code>.<\/li><li>Each vowel&nbsp;<code>'u'<\/code>&nbsp;may only be followed by an&nbsp;<code>'a'.<\/code><\/li><\/ul>\n\n\n\n<p>Since the answer&nbsp;may be too large,&nbsp;return it modulo&nbsp;<code>10^9 + 7.<\/code><\/p>\n\n\n\n<p><strong>Example 1:<\/strong><\/p>\n\n\n\n<pre class=\"wp-block-preformatted;crayon:false\"><strong>Input:<\/strong> n = 1\n<strong>Output:<\/strong> 5\n<strong>Explanation:<\/strong> All possible strings are: \"a\", \"e\", \"i\" , \"o\" and \"u\".\n<\/pre>\n\n\n\n<p><strong>Example 2:<\/strong><\/p>\n\n\n\n<pre class=\"wp-block-preformatted;crayon:false\"><strong>Input:<\/strong> n = 2\n<strong>Output:<\/strong> 10\n<strong>Explanation:<\/strong> All possible strings are: \"ae\", \"ea\", \"ei\", \"ia\", \"ie\", \"io\", \"iu\", \"oi\", \"ou\" and \"ua\".\n<\/pre>\n\n\n\n<p><strong>Example 3:&nbsp;<\/strong><\/p>\n\n\n\n<pre class=\"wp-block-preformatted;crayon:false\"><strong>Input:<\/strong> n = 5\n<strong>Output:<\/strong> 68<\/pre>\n\n\n\n<p><strong>Constraints:<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\"><li><code>1 &lt;= n &lt;= 2 * 10^4<\/code><\/li><\/ul>\n\n\n\n<h2 class=\"wp-block-heading\"><strong>Solution: DP<\/strong><\/h2>\n\n\n\n<figure class=\"wp-block-image\"><img loading=\"lazy\" decoding=\"async\" width=\"960\" height=\"540\" src=\"https:\/\/zxi.mytechroad.com\/blog\/wp-content\/uploads\/2019\/10\/1220-ep272-1.png\" alt=\"\" class=\"wp-image-5725\" srcset=\"https:\/\/zxi.mytechroad.com\/blog\/wp-content\/uploads\/2019\/10\/1220-ep272-1.png 960w, https:\/\/zxi.mytechroad.com\/blog\/wp-content\/uploads\/2019\/10\/1220-ep272-1-300x169.png 300w, https:\/\/zxi.mytechroad.com\/blog\/wp-content\/uploads\/2019\/10\/1220-ep272-1-768x432.png 768w\" sizes=\"auto, (max-width: 960px) 100vw, 960px\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image\"><img loading=\"lazy\" decoding=\"async\" width=\"960\" height=\"540\" src=\"https:\/\/zxi.mytechroad.com\/blog\/wp-content\/uploads\/2019\/10\/1220-ep272-2.png\" alt=\"\" class=\"wp-image-5726\" srcset=\"https:\/\/zxi.mytechroad.com\/blog\/wp-content\/uploads\/2019\/10\/1220-ep272-2.png 960w, https:\/\/zxi.mytechroad.com\/blog\/wp-content\/uploads\/2019\/10\/1220-ep272-2-300x169.png 300w, https:\/\/zxi.mytechroad.com\/blog\/wp-content\/uploads\/2019\/10\/1220-ep272-2-768x432.png 768w\" sizes=\"auto, (max-width: 960px) 100vw, 960px\" \/><\/figure>\n\n\n\n<p>dp[i][c] := number of strings of length i ends with letter c<br>transition: follow the definition<br>ans = sum(dp[n])<\/p>\n\n\n\n<p>Time complexity: O(n)<br>Space complexity: O(n) -&gt; O(1)<\/p>\n\n\n\n<div class=\"responsive-tabs\">\n<h2 class=\"tabtitle\">C++<\/h2>\n<div class=\"tabcontent\">\n\n<pre lang=\"C++\">\n\/\/ Author: Huahua\nclass Solution {\npublic:\n  int countVowelPermutation(int n) {\n    constexpr int kMod = 1e9 + 7;\n    vector<vector<long>> dp(n + 1, vector<long>(5));\n    fill(begin(dp[1]), end(dp[1]), 1);\n    \/\/ 0: a, 1: e, 2: i, 3: o, 4: u\n    for (int i = 2; i <= n; ++i) {\n      dp[i][1] += dp[i - 1][0]; \/\/ a -> e\n      \n      dp[i][0] += dp[i - 1][1]; \/\/ e -> a\n      dp[i][2] += dp[i - 1][1]; \/\/ e -> i\n      \n      for (int j = 0; j < 5; ++j) {\n        if (j == 2) continue;\n        dp[i][j] += dp[i - 1][2]; \/\/ i -> *\n      }\n      \n      dp[i][2] += dp[i - 1][3]; \/\/ o -> i\n      dp[i][4] += dp[i - 1][3]; \/\/ o -> u\n      \n      dp[i][0] += dp[i - 1][4]; \/\/ u -> a\n      \n      for (int j = 0; j < 5; ++j)\n        dp[i][j] %= kMod;\n    }\n    return accumulate(begin(dp[n]), end(dp[n]), 0L) % kMod;\n  }\n};\n<\/pre>\n\n<\/div><h2 class=\"tabtitle\">C++\/O(1)<\/h2>\n<div class=\"tabcontent\">\n\n<pre lang=\"C++\">\n\/\/ Author: Huahua\nclass Solution {\npublic:\n  int countVowelPermutation(int n) {\n    constexpr int kMod = 1e9 + 7;\n    long a = 1, e = 1, i = 1, o = 1, u = 1;\n    \n    for (int k = 2; k <= n; ++k) {\n      long aa = (i + e + u) % kMod;\n      long ee = (i + a) % kMod;\n      long ii = (e + o) % kMod;\n      long oo = i % kMod;\n      long uu = (i + o) % kMod;\n      a = aa;\n      e = ee;\n      i = ii;\n      o = oo;\n      u = uu;\n    }\n    return (a + e + i + o + u) % kMod;\n  }\n};\n<\/pre>\n<\/div><\/div>\n\n\n\n<h2 class=\"wp-block-heading\"><strong>Solution 2: Matrix multiplication<\/strong><\/h2>\n\n\n\n<p>Time complexity: O(logn)<br>Space complexity: O(1)<\/p>\n\n\n\n<div class=\"responsive-tabs\">\n<h2 class=\"tabtitle\">C++<\/h2>\n<div class=\"tabcontent\">\n\n<pre lang=\"C++\">\n\/\/ Author: Huahua\nconstexpr int kMod = 1e9 + 7;\nvector<vector<long>> operator*(const vector<vector<long>>& A, const vector<vector<long>>& B) {\n  int m = A.size();\n  int x = A[0].size();\n  int n = B[0].size();\n  vector<vector<long>> C(m, vector<long>(n));\n  for (int i = 0; i < m; ++i)\n    for (int j = 0; j < n; ++j) {\n      for (int k = 0; k < x; ++k)\n        C[i][j] += A[i][k] * B[k][j];\n      C[i][j] %= kMod;\n    }\n  return C;\n}\n\nclass Solution {\npublic:\n  int countVowelPermutation(int n) {  \n    vector<vector<long>> m{\n      {0, 1, 0, 0, 0}, \/\/ a\n      {1, 0, 1, 0, 0}, \/\/ e\n      {1, 1, 0, 1, 1}, \/\/ i\n      {0, 0, 1, 0, 1}, \/\/ o\n      {1, 0, 0, 0, 0}  \/\/ u\n    };    \n    vector<vector<long>> ans{{1}, {1}, {1}, {1}, {1}};\n    \n    n -= 1;\n    while (n > 0) {\n      if (n % 2) ans = m * ans;      \n      m = m * m;      \n      n \/= 2;\n    }    \n    \n    long sum = 0;\n    for (int i = 0; i < 5; ++i)\n      sum += ans[i][0];\n    return sum % kMod;\n  }\n};\n<\/pre>\n<\/div><\/div>\n","protected":false},"excerpt":{"rendered":"<p>Given an integer&nbsp;n, your task is to count how many strings of length&nbsp;n&nbsp;can be formed under the following rules: Each character is a lower case&#8230;<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[46],"tags":[18,217,4],"class_list":["post-5721","post","type-post","status-publish","format-standard","hentry","category-dynamic-programming","tag-dp","tag-hard","tag-string","entry","simple"],"_links":{"self":[{"href":"https:\/\/zxi.mytechroad.com\/blog\/wp-json\/wp\/v2\/posts\/5721","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=5721"}],"version-history":[{"count":4,"href":"https:\/\/zxi.mytechroad.com\/blog\/wp-json\/wp\/v2\/posts\/5721\/revisions"}],"predecessor-version":[{"id":5727,"href":"https:\/\/zxi.mytechroad.com\/blog\/wp-json\/wp\/v2\/posts\/5721\/revisions\/5727"}],"wp:attachment":[{"href":"https:\/\/zxi.mytechroad.com\/blog\/wp-json\/wp\/v2\/media?parent=5721"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/zxi.mytechroad.com\/blog\/wp-json\/wp\/v2\/categories?post=5721"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/zxi.mytechroad.com\/blog\/wp-json\/wp\/v2\/tags?post=5721"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}