{ "data": { "question": { "questionId": "3238", "questionFrontendId": "2977", "categoryTitle": "Algorithms", "boundTopicId": 2575710, "title": "Minimum Cost to Convert String II", "titleSlug": "minimum-cost-to-convert-string-ii", "content": "

You are given two 0-indexed strings source and target, both of length n and consisting of lowercase English characters. You are also given two 0-indexed string arrays original and changed, and an integer array cost, where cost[i] represents the cost of converting the string original[i] to the string changed[i].

\n\n

You start with the string source. In one operation, you can pick a substring x from the string, and change it to y at a cost of z if there exists any index j such that cost[j] == z, original[j] == x, and changed[j] == y. You are allowed to do any number of operations, but any pair of operations must satisfy either of these two conditions:

\n\n\n\n

Return the minimum cost to convert the string source to the string target using any number of operations. If it is impossible to convert source to target, return -1.

\n\n

Note that there may exist indices i, j such that original[j] == original[i] and changed[j] == changed[i].

\n\n

 

\n

Example 1:

\n\n
\nInput: 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]\nOutput: 28\nExplanation: 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
\n\n

Example 2:

\n\n
\nInput: source = "abcdefgh", target = "acdeeghh", original = ["bcd","fgh","thh"], changed = ["cde","thh","ghh"], cost = [1,3,5]\nOutput: 9\nExplanation: 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
\n\n

Example 3:

\n\n
\nInput: source = "abcdefgh", target = "addddddd", original = ["bcd","defgh"], changed = ["ddd","ddddd"], cost = [100,1578]\nOutput: -1\nExplanation: 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
\n\n

 

\n

Constraints:

\n\n\n", "translatedTitle": "转换字符串的最小成本 II", "translatedContent": "

给你两个下标从 0 开始的字符串 source 和 target ，它们的长度均为 n 并且由 小写 英文字母组成。

\n\n

另给你两个下标从 0 开始的字符串数组 original 和 changed ，以及一个整数数组 cost ，其中 cost[i] 代表将字符串 original[i] 更改为字符串 changed[i] 的成本。

\n\n

你从字符串 source 开始。在一次操作中，如果 存在 任意 下标 j 满足 cost[j] == z  、original[j] == x 以及 changed[j] == y ，你就可以选择字符串中的 子串 x 并以 z 的成本将其更改为 y 。 你可以执行 任意数量 的操作，但是任两次操作必须满足 以下两个 条件 之一 ：

\n\n\n\n

返回将字符串 source 转换为字符串 target 所需的 最小 成本。如果不可能完成转换，则返回 -1 。

\n\n

注意，可能存在下标 i 、j 使得 original[j] == original[i] 且 changed[j] == changed[i] 。

\n\n

 

\n\n

示例 1：

\n\n
\n输入：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输出：28\n解释：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
\n\n

示例 2：

\n\n
\n输入：source = \"abcdefgh\", target = \"acdeeghh\", original = [\"bcd\",\"fgh\",\"thh\"], changed = [\"cde\",\"thh\",\"ghh\"], cost = [1,3,5]\n输出：9\n解释：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
\n\n

示例 3：

\n\n
\n输入：source = \"abcdefgh\", target = \"addddddd\", original = [\"bcd\",\"defgh\"], changed = [\"ddd\",\"ddddd\"], cost = [100,1578]\n输出：-1\n解释：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
\n\n

 

\n\n

提示：

\n\n\n", "isPaidOnly": false, "difficulty": "Hard", "likes": 6, "dislikes": 0, "isLiked": null, "similarQuestions": "[]", "contributors": [], "langToValidPlayground": "{\"cpp\": false, \"java\": false, \"python\": false, \"python3\": false, \"mysql\": false, \"mssql\": false, \"oraclesql\": false, \"c\": false, \"csharp\": false, \"javascript\": false, \"typescript\": false, \"bash\": false, \"php\": false, \"swift\": false, \"kotlin\": false, \"dart\": false, \"golang\": false, \"ruby\": false, \"scala\": false, \"html\": false, \"pythonml\": false, \"rust\": false, \"racket\": false, \"erlang\": false, \"elixir\": false, \"pythondata\": false, \"react\": false, \"vanillajs\": false, \"postgresql\": false}", "topicTags": [], "companyTagStats": null, "codeSnippets": [ { "lang": "C++", "langSlug": "cpp", "code": "class Solution {\npublic:\n long long minimumCost(string source, string target, vector& original, vector& changed, vector& cost) {\n \n }\n};", "__typename": "CodeSnippetNode" }, { "lang": "Java", "langSlug": "java", "code": "class Solution {\n public long minimumCost(String source, String target, String[] original, String[] changed, int[] cost) {\n\n }\n}", "__typename": "CodeSnippetNode" }, { "lang": "Python", "langSlug": "python", "code": "class Solution(object):\n def minimumCost(self, source, target, original, changed, cost):\n \"\"\"\n :type source: str\n :type target: str\n :type original: List[str]\n :type changed: List[str]\n :type cost: List[int]\n :rtype: int\n \"\"\"", "__typename": "CodeSnippetNode" }, { "lang": "Python3", "langSlug": "python3", "code": "class Solution:\n def minimumCost(self, source: str, target: str, original: List[str], changed: List[str], cost: List[int]) -> int:", "__typename": "CodeSnippetNode" }, { "lang": "C", "langSlug": "c", "code": "long long minimumCost(char* source, char* target, char** original, int originalSize, char** changed, int changedSize, int* cost, int costSize) {\n \n}", "__typename": "CodeSnippetNode" }, { "lang": "C#", "langSlug": "csharp", "code": "public class Solution {\n public long MinimumCost(string source, string target, string[] original, string[] changed, int[] cost) {\n\n }\n}", "__typename": "CodeSnippetNode" }, { "lang": "JavaScript", "langSlug": "javascript", "code": "/**\n * @param {string} source\n * @param {string} target\n * @param {string[]} original\n * @param {string[]} changed\n * @param {number[]} cost\n * @return {number}\n */\nvar minimumCost = function(source, target, original, changed, cost) {\n\n};", "__typename": "CodeSnippetNode" }, { "lang": "TypeScript", "langSlug": "typescript", "code": "function minimumCost(source: string, target: string, original: string[], changed: string[], cost: number[]): number {\n \n};", "__typename": "CodeSnippetNode" }, { "lang": "PHP", "langSlug": "php", "code": "class Solution {\n\n /**\n * @param String $source\n * @param String $target\n * @param String[] $original\n * @param String[] $changed\n * @param Integer[] $cost\n * @return Integer\n */\n function minimumCost($source, $target, $original, $changed, $cost) {\n\n }\n}", "__typename": "CodeSnippetNode" }, { "lang": "Swift", "langSlug": "swift", "code": "class Solution {\n func minimumCost(_ source: String, _ target: String, _ original: [String], _ changed: [String], _ cost: [Int]) -> Int {\n\n }\n}", "__typename": "CodeSnippetNode" }, { "lang": "Kotlin", "langSlug": "kotlin", "code": "class Solution {\n fun minimumCost(source: String, target: String, original: Array, changed: Array, cost: IntArray): Long {\n\n }\n}", "__typename": "CodeSnippetNode" }, { "lang": "Dart", "langSlug": "dart", "code": "class Solution {\n int minimumCost(String source, String target, List original, List changed, List cost) {\n \n }\n}", "__typename": "CodeSnippetNode" }, { "lang": "Go", "langSlug": "golang", "code": "func minimumCost(source string, target string, original []string, changed []string, cost []int) int64 {\n\n}", "__typename": "CodeSnippetNode" }, { "lang": "Ruby", "langSlug": "ruby", "code": "# @param {String} source\n# @param {String} target\n# @param {String[]} original\n# @param {String[]} changed\n# @param {Integer[]} cost\n# @return {Integer}\ndef minimum_cost(source, target, original, changed, cost)\n\nend", "__typename": "CodeSnippetNode" }, { "lang": "Scala", "langSlug": "scala", "code": "object Solution {\n def minimumCost(source: String, target: String, original: Array[String], changed: Array[String], cost: Array[Int]): Long = {\n\n }\n}", "__typename": "CodeSnippetNode" }, { "lang": "Rust", "langSlug": "rust", "code": "impl Solution {\n pub fn minimum_cost(source: String, target: String, original: Vec, changed: Vec, cost: Vec) -> i64 {\n\n }\n}", "__typename": "CodeSnippetNode" }, { "lang": "Racket", "langSlug": "racket", "code": "(define/contract (minimum-cost source target original changed cost)\n (-> string? string? (listof string?) (listof string?) (listof exact-integer?) exact-integer?)\n )", "__typename": "CodeSnippetNode" }, { "lang": "Erlang", "langSlug": "erlang", "code": "-spec minimum_cost(Source :: unicode:unicode_binary(), Target :: unicode:unicode_binary(), Original :: [unicode:unicode_binary()], Changed :: [unicode:unicode_binary()], Cost :: [integer()]) -> integer().\nminimum_cost(Source, Target, Original, Changed, Cost) ->\n .", "__typename": "CodeSnippetNode" }, { "lang": "Elixir", "langSlug": "elixir", "code": "defmodule Solution do\n @spec minimum_cost(source :: String.t, target :: String.t, original :: [String.t], changed :: [String.t], cost :: [integer]) :: integer\n def minimum_cost(source, target, original, changed, cost) do\n \n end\nend", "__typename": "CodeSnippetNode" } ], "stats": "{\"totalAccepted\": \"1.6K\", \"totalSubmission\": \"6K\", \"totalAcceptedRaw\": 1587, \"totalSubmissionRaw\": 5977, \"acRate\": \"26.6%\"}", "hints": [ "Give each unique string in original and changed arrays a unique id. There are at most 2 * m unique strings in total where m is the length of the arrays. We can put them into a hash map to assign ids.", "We can pre-compute the smallest costs between all pairs of unique strings using Floyd Warshall algorithm in O(m ^ 3) time complexity.", "Let dp[i] be the smallest cost to change the first i characters (prefix) of source into target, leaving the suffix untouched.\r\nWe have dp[0] = 0.\r\ndp[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).\r\nIf neither of the two conditions is satisfied, dp[i] = infinity.", "We can use Trie to check for the second condition in O(1).", "The answer is dp[n] where n is source.length." ], "solution": null, "status": null, "sampleTestCase": "\"abcd\"\n\"acbe\"\n[\"a\",\"b\",\"c\",\"c\",\"e\",\"d\"]\n[\"b\",\"c\",\"b\",\"e\",\"b\",\"e\"]\n[2,5,5,1,2,20]", "metaData": "{\n \"name\": \"minimumCost\",\n \"params\": [\n {\n \"name\": \"source\",\n \"type\": \"string\"\n },\n {\n \"type\": \"string\",\n \"name\": \"target\"\n },\n {\n \"type\": \"string[]\",\n \"name\": \"original\"\n },\n {\n \"type\": \"string[]\",\n \"name\": \"changed\"\n },\n {\n \"type\": \"integer[]\",\n \"name\": \"cost\"\n }\n ],\n \"return\": {\n \"type\": \"long\"\n }\n}", "judgerAvailable": true, "judgeType": "large", "mysqlSchemas": [], "enableRunCode": true, "envInfo": "{\"cpp\":[\"C++\",\"

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