2976. Minimum Cost to Convert String I

Description

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].

 

Example 1:

Input: 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]
Output: 28
Explanation: To convert the string "abcd" to string "acbe":
- Change value at index 1 from 'b' to 'c' at a cost of 5.
- Change value at index 2 from 'c' to 'e' at a cost of 1.
- Change value at index 2 from 'e' to 'b' at a cost of 2.
- Change value at index 3 from 'd' to 'e' at a cost of 20.
The total cost incurred is 5 + 1 + 2 + 20 = 28.
It can be shown that this is the minimum possible cost.

Example 2:

Input: source = "aaaa", target = "bbbb", original = ["a","c"], changed = ["c","b"], cost = [1,2]
Output: 12
Explanation: 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.

Example 3:

Input: source = "abcd", target = "abce", original = ["a"], changed = ["e"], cost = [10000]
Output: -1
Explanation: It is impossible to convert source to target because the value at index 3 cannot be changed from 'd' to 'e'.

 

Constraints:

• 1 <= source.length == target.length <= 105
• source, target consist of lowercase English letters.
• 1 <= cost.length == original.length == changed.length <= 2000
• original[i], changed[i] are lowercase English letters.
• 1 <= cost[i] <= 106
• original[i] != changed[i]

 

Solutions

Solution: Floyd-Warshall's algorithm

• Time complexity: O(26³+n+m)
• Space complexity: O(26²)

 

JavaScript

/**
 * @param {string} source
 * @param {string} target
 * @param {character[]} original
 * @param {character[]} changed
 * @param {number[]} cost
 * @return {number}
 */
const minimumCost = function (source, target, original, changed, cost) {
  const BASE_CODE = 'a'.charCodeAt(0);
  const n = source.length;
  const m = cost.length;
  const dist = Array.from({ length: 26 }, () => {
    return new Array(26).fill(Number.MAX_SAFE_INTEGER);
  });
  let result = 0;

  for (let index = 0; index < m; index++) {
    const a = original[index].charCodeAt(0) - BASE_CODE;
    const b = changed[index].charCodeAt(0) - BASE_CODE;

    dist[a][b] = Math.min(cost[index], dist[a][b]);
  }

  for (let k = 0; k < 26; k++) {
    for (let a = 0; a < 26; a++) {
      if (dist[a][k] === Number.MAX_SAFE_INTEGER) continue;

      for (let b = 0; b < 26; b++) {
        if (dist[k][b] === Number.MAX_SAFE_INTEGER) continue;

        dist[a][b] = Math.min(dist[a][k] + dist[k][b], dist[a][b]);
      }
    }
  }

  for (let index = 0; index < n; index++) {
    if (source[index] === target[index]) continue;

    const a = source[index].charCodeAt(0) - BASE_CODE;
    const b = target[index].charCodeAt(0) - BASE_CODE;

    if (dist[a][b] === Number.MAX_SAFE_INTEGER) return -1;

    result += dist[a][b];
  }

  return result;
};