mirror of
https://gitee.com/coder-xiaomo/leetcode-problemset
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167 lines
31 KiB
JSON
167 lines
31 KiB
JSON
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"title": "Minimum Cost to Convert String II",
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"content": "<p>You are given two <strong>0-indexed</strong> strings <code>source</code> and <code>target</code>, both of length <code>n</code> and consisting of <strong>lowercase</strong> English characters. You are also given two <strong>0-indexed</strong> string arrays <code>original</code> and <code>changed</code>, and an integer array <code>cost</code>, where <code>cost[i]</code> represents the cost of converting the string <code>original[i]</code> to the string <code>changed[i]</code>.</p>\n\n<p>You start with the string <code>source</code>. In one operation, you can pick a <strong>substring</strong> <code>x</code> from the string, and change it to <code>y</code> at a cost of <code>z</code> <strong>if</strong> there exists <strong>any</strong> index <code>j</code> such that <code>cost[j] == z</code>, <code>original[j] == x</code>, and <code>changed[j] == y</code>. You are allowed to do <strong>any</strong> number of operations, but any pair of operations must satisfy <strong>either</strong> of these two conditions:</p>\n\n<ul>\n\t<li>The substrings picked in the operations are <code>source[a..b]</code> and <code>source[c..d]</code> with either <code>b < c</code> <strong>or</strong> <code>d < a</code>. In other words, the indices picked in both operations are <strong>disjoint</strong>.</li>\n\t<li>The substrings picked in the operations are <code>source[a..b]</code> and <code>source[c..d]</code> with <code>a == c</code> <strong>and</strong> <code>b == d</code>. In other words, the indices picked in both operations are <strong>identical</strong>.</li>\n</ul>\n\n<p>Return <em>the <strong>minimum</strong> cost to convert the string </em><code>source</code><em> to the string </em><code>target</code><em> using <strong>any</strong> number of operations</em>. <em>If it is impossible to convert</em> <code>source</code> <em>to</em> <code>target</code>,<em> return</em> <code>-1</code>.</p>\n\n<p><strong>Note</strong> that there may exist indices <code>i</code>, <code>j</code> such that <code>original[j] == original[i]</code> and <code>changed[j] == changed[i]</code>.</p>\n\n<p> </p>\n<p><strong class=\"example\">Example 1:</strong></p>\n\n<pre>\n<strong>Input:</strong> source = "abcd", target = "acbe", original = ["a","b","c","c","e","d"], changed = ["b","c","b","e","b","e"], cost = [2,5,5,1,2,20]\n<strong>Output:</strong> 28\n<strong>Explanation:</strong> To convert "abcd" to "acbe", do the following operations:\n- Change substring source[1..1] from "b" to "c" at a cost of 5.\n- Change substring source[2..2] from "c" to "e" at a cost of 1.\n- Change substring source[2..2] from "e" to "b" at a cost of 2.\n- Change substring source[3..3] from "d" to "e" at a cost of 20.\nThe total cost incurred is 5 + 1 + 2 + 20 = 28. \nIt can be shown that this is the minimum possible cost.\n</pre>\n\n<p><strong class=\"example\">Example 2:</strong></p>\n\n<pre>\n<strong>Input:</strong> source = "abcdefgh", target = "acdeeghh", original = ["bcd","fgh","thh"], changed = ["cde","thh","ghh"], cost = [1,3,5]\n<strong>Output:</strong> 9\n<strong>Explanation:</strong> To convert "abcdefgh" to "acdeeghh", do the following operations:\n- Change substring source[1..3] from "bcd" to "cde" at a cost of 1.\n- Change substring source[5..7] from "fgh" to "thh" at a cost of 3. We can do this operation because indices [5,7] are disjoint with indices picked in the first operation.\n- Change substring source[5..7] from "thh" to "ghh" at a cost of 5. We can do this operation because indices [5,7] are disjoint with indices picked in the first operation, and identical with indices picked in the second operation.\nThe total cost incurred is 1 + 3 + 5 = 9.\nIt can be shown that this is the minimum possible cost.\n</pre>\n\n<p><strong class=\"example\">Example 3:</strong></p>\n\n<pre>\n<strong>Input:</strong> source = "abcdefgh", target = "addddddd", original = ["bcd","defgh"], changed = ["ddd","ddddd"], cost = [100,1578]\n<strong>Output:</strong> -1\n<strong>Explanation:</strong> It is impossible to convert "abcdefgh" to "addddddd".\nIf you select substring source[1..3] as the first operation to change "abcdefgh" to "adddefgh", you cannot select substring source[3..7] as the second operation because it has a common index, 3, with the first operation.\nIf you select substring source[3..7] as the first operation to change "abcdefgh" to "abcddddd", you cannot select substring source[1..3] as the second operation because it has a common index, 3, with the first operation.\n</pre>\n\n<p> </p>\n<p><strong>Constraints:</strong></p>\n\n<ul>\n\t<li><code>1 <= source.length == target.length <= 1000</code></li>\n\t<li><code>source</code>, <code>target</code> consist only of lowercase English characters.</li>\n\t<li><code>1 <= cost.length == original.length == changed.length <= 100</code></li>\n\t<li><code>1 <= original[i].length == changed[i].length <= source.length</code></li>\n\t<li><code>original[i]</code>, <code>changed[i]</code> consist only of lowercase English characters.</li>\n\t<li><code>original[i] != changed[i]</code></li>\n\t<li><code>1 <= cost[i] <= 10<sup>6</sup></code></li>\n</ul>\n",
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"translatedTitle": "转换字符串的最小成本 II",
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"translatedContent": "<p>给你两个下标从 <strong>0</strong> 开始的字符串 <code>source</code> 和 <code>target</code> ，它们的长度均为 <code>n</code> 并且由 <strong>小写 </strong>英文字母组成。</p>\n\n<p>另给你两个下标从 <strong>0</strong> 开始的字符串数组 <code>original</code> 和 <code>changed</code> ，以及一个整数数组 <code>cost</code> ，其中 <code>cost[i]</code> 代表将字符串 <code>original[i]</code> 更改为字符串 <code>changed[i]</code> 的成本。</p>\n\n<p>你从字符串 <code>source</code> 开始。在一次操作中，<strong>如果 </strong>存在 <strong>任意</strong> 下标 <code>j</code> 满足 <code>cost[j] == z</code> 、<code>original[j] == x</code> 以及 <code>changed[j] == y</code> ，你就可以选择字符串中的 <strong>子串</strong> <code>x</code> 并以 <code>z</code> 的成本将其更改为 <code>y</code> 。 你可以执行 <strong>任意数量 </strong>的操作，但是任两次操作必须满足<strong> 以下两个 </strong>条件 <strong>之一</strong> ：</p>\n\n<ul>\n\t<li>在两次操作中选择的子串分别是 <code>source[a..b]</code> 和 <code>source[c..d]</code> ，满足 <code>b < c</code> <strong>或</strong> <code>d < a</code> 。换句话说，两次操作中选择的下标<strong> 不相交 </strong>。</li>\n\t<li>在两次操作中选择的子串分别是 <code>source[a..b]</code> 和 <code>source[c..d]</code> ，满足 <code>a == c</code> <strong>且</strong> <code>b == d</code> 。换句话说，两次操作中选择的下标<strong> 相同 </strong>。</li>\n</ul>\n\n<p>返回将字符串 <code>source</code> 转换为字符串 <code>target</code> 所需的<strong> 最小 </strong>成本。如果不可能完成转换，则返回 <code>-1</code> 。</p>\n\n<p><strong>注意</strong>，可能存在下标 <code>i</code> 、<code>j</code> 使得 <code>original[j] == original[i]</code> 且 <code>changed[j] == changed[i]</code> 。</p>\n\n<p> </p>\n\n<p><strong>示例 1：</strong></p>\n\n<pre>\n<strong>输入：</strong>source = \"abcd\", target = \"acbe\", original = [\"a\",\"b\",\"c\",\"c\",\"e\",\"d\"], changed = [\"b\",\"c\",\"b\",\"e\",\"b\",\"e\"], cost = [2,5,5,1,2,20]\n<strong>输出：</strong>28\n<strong>解释：</strong>将 \"abcd\" 转换为 \"acbe\"，执行以下操作：\n- 将子串 source[1..1] 从 \"b\" 改为 \"c\" ，成本为 5 。\n- 将子串 source[2..2] 从 \"c\" 改为 \"e\" ，成本为 1 。\n- 将子串 source[2..2] 从 \"e\" 改为 \"b\" ，成本为 2 。\n- 将子串 source[3..3] 从 \"d\" 改为 \"e\" ，成本为 20 。\n产生的总成本是 5 + 1 + 2 + 20 = 28 。 \n可以证明这是可能的最小成本。\n</pre>\n\n<p><strong>示例 2：</strong></p>\n\n<pre>\n<strong>输入：</strong>source = \"abcdefgh\", target = \"acdeeghh\", original = [\"bcd\",\"fgh\",\"thh\"], changed = [\"cde\",\"thh\",\"ghh\"], cost = [1,3,5]\n<strong>输出：</strong>9\n<strong>解释：</strong>将 \"abcdefgh\" 转换为 \"acdeeghh\"，执行以下操作：\n- 将子串 source[1..3] 从 \"bcd\" 改为 \"cde\" ，成本为 1 。\n- 将子串 source[5..7] 从 \"fgh\" 改为 \"thh\" ，成本为 3 。可以执行此操作，因为下标 [5,7] 与第一次操作选中的下标不相交。\n- 将子串 source[5..7] 从 \"thh\" 改为 \"ghh\" ，成本为 5 。可以执行此操作，因为下标 [5,7] 与第一次操作选中的下标不相交，且与第二次操作选中的下标相同。\n产生的总成本是 1 + 3 + 5 = 9 。\n可以证明这是可能的最小成本。\n</pre>\n\n<p><strong>示例 3：</strong></p>\n\n<pre>\n<strong>输入：</strong>source = \"abcdefgh\", target = \"addddddd\", original = [\"bcd\",\"defgh\"], changed = [\"ddd\",\"ddddd\"], cost = [100,1578]\n<strong>输出：</strong>-1\n<strong>解释：</strong>无法将 \"abcdefgh\" 转换为 \"addddddd\" 。\n如果选择子串 source[1..3] 执行第一次操作，以将 \"abcdefgh\" 改为 \"adddefgh\" ，你无法选择子串 source[3..7] 执行第二次操作，因为两次操作有一个共用下标 3 。\n如果选择子串 source[3..7] 执行第一次操作，以将 \"abcdefgh\" 改为 \"abcddddd\" ，你无法选择子串 source[1..3] 执行第二次操作，因为两次操作有一个共用下标 3 。\n</pre>\n\n<p> </p>\n\n<p><strong>提示：</strong></p>\n\n<ul>\n\t<li><code>1 <= source.length == target.length <= 1000</code></li>\n\t<li><code>source</code>、<code>target</code> 均由小写英文字母组成</li>\n\t<li><code>1 <= cost.length == original.length == changed.length <= 100</code></li>\n\t<li><code>1 <= original[i].length == changed[i].length <= source.length</code></li>\n\t<li><code>original[i]</code>、<code>changed[i]</code> 均由小写英文字母组成</li>\n\t<li><code>original[i] != changed[i]</code></li>\n\t<li><code>1 <= cost[i] <= 10<sup>6</sup></code></li>\n</ul>\n",
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"Give each unique string in <code>original</code> and <code>changed</code> arrays a unique id. There are at most <code>2 * m</code> unique strings in total where <code>m</code> is the length of the arrays. We can put them into a hash map to assign ids.",
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"We can pre-compute the smallest costs between all pairs of unique strings using Floyd Warshall algorithm in <code>O(m ^ 3)</code> time complexity.",
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"Let <code>dp[i]</code> be the smallest cost to change the first <code>i</code> characters (prefix) of <code>source</code> into <code>target</code>, leaving the suffix untouched.\r\nWe have <code>dp[0] = 0</code>.\r\n<code>dp[i] = min(\r\ndp[i - 1] if (source[i - 1] == target[i - 1]),\r\ndp[j-1] + cost[x][y] where x is the id of source[j..(i - 1)] and y is the id of target e[j..(i - 1)])\r\n)</code>.\r\nIf neither of the two conditions is satisfied, <code>dp[i] = infinity</code>.",
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