2976. Minimum Cost to Convert String I

Problem Statement

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]

Intuition

Approach:

Do Floydd warshall for finding all pairs shortest path

Links

https://leetcode.com/problems/minimum-cost-to-convert-string-i/description/

Video Links

Approach 1:

C++

class Solution {
public:
    long long minimumCost(string source, string target, vector<char>& original, vector<char>& changed, vector<int>& cost) {
        vector<vector<long long>> arr(26, vector<long long>(26, 1e9));
        for(int i=0; i<original.size(); i++){
            int x = original[i]-'a', y = changed[i]-'a';
            // Minimum to track for parallel edges
            arr[x][y] = min(arr[x][y], (long long)cost[i]);
        }
        // Constant 26*26*26
        for(int via = 0; via < 26; via++){
            for(int i = 0; i < 26; i++) {
                for(int j = 0; j < 26; j++) {
                    arr[i][j] = min( arr[i][j] , arr[i][via]+arr[via][j]);
                }
            }
        }

        long long ans = 0;
        for(int i=0; i<source.size(); i++){
            int x = source[i]-'a', y = target[i]-'a';
            if(x != y){
                long long dist = arr[x][y];
                if(dist == 1e9) 
                    return -1;
                ans += dist;
            }
        }

        return ans;
    }
};

Approach 2:

C++

Approach 3:

C++

Approach 4:

C++