leetcode-problemset/leetcode/originData/count-the-number-of-winning-sequences.json

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            "title": "Count The Number of Winning Sequences",
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            "content": "<p>Alice and Bob are playing a fantasy battle game consisting of <code>n</code> rounds where they summon one of three magical creatures each round: a Fire Dragon, a Water Serpent, or an Earth Golem. In each round, players <strong>simultaneously</strong> summon their creature and are awarded points as follows:</p>\n\n<ul>\n\t<li>If one player summons a Fire Dragon and the other summons an Earth Golem, the player who summoned the <strong>Fire Dragon</strong> is awarded a point.</li>\n\t<li>If one player summons a Water Serpent and the other summons a Fire Dragon, the player who summoned the <strong>Water Serpent</strong> is awarded a point.</li>\n\t<li>If one player summons an Earth Golem and the other summons a Water Serpent, the player who summoned the <strong>Earth Golem</strong> is awarded a point.</li>\n\t<li>If both players summon the same creature, no player is awarded a point.</li>\n</ul>\n\n<p>You are given a string <code>s</code> consisting of <code>n</code> characters <code>&#39;F&#39;</code>, <code>&#39;W&#39;</code>, and <code>&#39;E&#39;</code>, representing the sequence of creatures Alice will summon in each round:</p>\n\n<ul>\n\t<li>If <code>s[i] == &#39;F&#39;</code>, Alice summons a Fire Dragon.</li>\n\t<li>If <code>s[i] == &#39;W&#39;</code>, Alice summons a Water Serpent.</li>\n\t<li>If <code>s[i] == &#39;E&#39;</code>, Alice summons an Earth Golem.</li>\n</ul>\n\n<p>Bob&rsquo;s sequence of moves is unknown, but it is guaranteed that Bob will never summon the same creature in two consecutive rounds. Bob <em>beats</em> Alice if the total number of points awarded to Bob after <code>n</code> rounds is <strong>strictly greater</strong> than the points awarded to Alice.</p>\n\n<p>Return the number of distinct sequences Bob can use to beat Alice.</p>\n\n<p>Since the answer may be very large, return it <strong>modulo</strong> <code>10<sup>9</sup> + 7</code>.</p>\n\n<p>&nbsp;</p>\n<p><strong class=\"example\">Example 1:</strong></p>\n\n<div class=\"example-block\">\n<p><strong>Input:</strong> <span class=\"example-io\">s = &quot;FFF&quot;</span></p>\n\n<p><strong>Output:</strong> <span class=\"example-io\">3</span></p>\n\n<p><strong>Explanation:</strong></p>\n\n<p>Bob can beat Alice by making one of the following sequences of moves: <code>&quot;WFW&quot;</code>, <code>&quot;FWF&quot;</code>, or <code>&quot;WEW&quot;</code>. Note that other winning sequences like <code>&quot;WWE&quot;</code> or <code>&quot;EWW&quot;</code> are invalid since Bob cannot make the same move twice in a row.</p>\n</div>\n\n<p><strong class=\"example\">Example 2:</strong></p>\n\n<div class=\"example-block\">\n<p><strong>Input:</strong> <span class=\"example-io\">s = &quot;FWEFW&quot;</span></p>\n\n<p><strong>Output:</strong> <span class=\"example-io\">18</span></p>\n\n<p><strong>Explanation:</strong></p>\n\n<p><w>Bob can beat Alice by making one of the following sequences of moves: <code>&quot;FWFWF&quot;</code>, <code>&quot;FWFWE&quot;</code>, <code>&quot;FWEFE&quot;</code>, <code>&quot;FWEWE&quot;</code>, <code>&quot;FEFWF&quot;</code>, <code>&quot;FEFWE&quot;</code>, <code>&quot;FEFEW&quot;</code>, <code>&quot;FEWFE&quot;</code>, <code>&quot;WFEFE&quot;</code>, <code>&quot;WFEWE&quot;</code>, <code>&quot;WEFWF&quot;</code>, <code>&quot;WEFWE&quot;</code>, <code>&quot;WEFEF&quot;</code>, <code>&quot;WEFEW&quot;</code>, <code>&quot;WEWFW&quot;</code>, <code>&quot;WEWFE&quot;</code>, <code>&quot;EWFWE&quot;</code>, or <code>&quot;EWEWE&quot;</code>.</w></p>\n</div>\n\n<p>&nbsp;</p>\n<p><strong>Constraints:</strong></p>\n\n<ul>\n\t<li><code>1 &lt;= s.length &lt;= 1000</code></li>\n\t<li><code>s[i]</code> is one of <code>&#39;F&#39;</code>, <code>&#39;W&#39;</code>, or <code>&#39;E&#39;</code>.</li>\n</ul>\n",
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                    "code": "defmodule Solution do\n  @spec count_winning_sequences(s :: String.t) :: integer\n  def count_winning_sequences(s) do\n    \n  end\nend",
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                "Use dynamic programming.",
                "For <code>0 < i < n - 1</code>, <code>-n < j < n</code>, and <code>k</code> in <code>{’F’, ‘W’, ‘E’}</code>, let <code>dp[i][j][k]</code>  be the number of sequences consisting of the first <code>i</code> moves such that the difference between bob’s points and alice’s point is equal to <code>j</code> and the <code>i<sup>th</sup></code> move that Bob played is <code>k</code>.",
                "The answer is the sum of <code>dp[n - 1][j][k]</code>over all <code>j > 0</code> and over all <code>k</code>."
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