You are given two 0-indexed strings source and target, both of length n and consisting of lowercase English letters. You are also given two 0-indexed character arrays original and changed, and an integer array cost, where cost[i] represents the cost of changing the character original[i] to the character changed[i].
You start with the string source. In one operation, you can pick a character x from the string and change it to the character y at a cost of z if there exists any index j such that cost[j] == z, original[j] == x, and changed[j] == y.
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.
Note that there may exist indices i, j such that original[j] == original[i] and changed[j] == changed[i].
\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 the string "abcd" to string "acbe":\n- Change value at index 1 from 'b' to 'c' at a cost of 5.\n- Change value at index 2 from 'c' to 'e' at a cost of 1.\n- Change value at index 2 from 'e' to 'b' at a cost of 2.\n- Change value at index 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 = "aaaa", target = "bbbb", original = ["a","c"], changed = ["c","b"], cost = [1,2]\nOutput: 12\nExplanation: To change the character 'a' to 'b' change the character 'a' to 'c' at a cost of 1, followed by changing the character 'c' to 'b' at a cost of 2, for a total cost of 1 + 2 = 3. To change all occurrences of 'a' to 'b', a total cost of 3 * 4 = 12 is incurred.\n\n\n
Example 3:
\n\n\nInput: source = "abcd", target = "abce", original = ["a"], changed = ["e"], cost = [10000]\nOutput: -1\nExplanation: It is impossible to convert source to target because the value at index 3 cannot be changed from 'd' to 'e'.\n\n\n
\n
Constraints:
\n\n1 <= source.length == target.length <= 105source, target consist of lowercase English letters.1 <= cost.length == original.length == changed.length <= 2000original[i], changed[i] are lowercase English letters.1 <= cost[i] <= 106original[i] != changed[i](a, b) with weight c if we can change from character a to letter b with cost c. (Keep the one with the smallest cost in case there are multiple edges between a and b).",
"Calculate the shortest path for each pair of characters (source[i], target[i]). The sum of cost over all i in the range [0, source.length - 1]. If there is no path between source[i] and target[i], the answer is -1.",
"Any shortest path algorithms will work since we only have 26 nodes. Since we only have at most 26 * 26 pairs, we can save the result to avoid re-calculation.",
"We can also use Floyd Warshall's algorithm to precompute all the results."
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