LeetCode #2976 — MEDIUM

Minimum Cost to Convert String I

Move from brute-force thinking to an efficient approach using array strategy.

Solve on LeetCode
The Problem

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]

Roadmap

  1. Brute Force Baseline
  2. Core Insight
  3. Algorithm Walkthrough
  4. Edge Cases
  5. Full Annotated Code
  6. Interactive Study Demo
  7. Complexity Analysis
Step 01

Brute Force Baseline

Problem summary: 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].

Baseline thinking

Start with the most direct exhaustive search. That gives a correctness anchor before optimizing.

Pattern signal: Array

Example 1

"abcd"
"acbe"
["a","b","c","c","e","d"]
["b","c","b","e","b","e"]
[2,5,5,1,2,20]

Example 2

"aaaa"
"bbbb"
["a","c"]
["c","b"]
[1,2]

Example 3

"abcd"
"abce"
["a"]
["e"]
[10000]

Related Problems

  • Can Convert String in K Moves (can-convert-string-in-k-moves)
  • Minimum Moves to Convert String (minimum-moves-to-convert-string)
Step 02

Core Insight

What unlocks the optimal approach

  • Construct a graph with each letter as a node, and construct an edge <code>(a, b)</code> with weight <code>c</code> if we can change from character <code>a</code> to letter <code>b</code> with cost <code>c</code>. (Keep the one with the smallest cost in case there are multiple edges between <code>a</code> and <code>b</code>).
  • Calculate the shortest path for each pair of characters <code>(source[i], target[i])</code>. The sum of cost over all <code>i</code> in the range <code>[0, source.length - 1]</code>. If there is no path between <code>source[i]</code> and <code>target[i]</code>, the answer is <code>-1</code>.
  • Any shortest path algorithms will work since we only have <code>26</code> nodes. Since we only have at most <code>26 * 26</code> pairs, we can save the result to avoid re-calculation.
  • We can also use Floyd Warshall's algorithm to precompute all the results.
Interview move: turn each hint into an invariant you can check after every iteration/recursion step.
Step 03

Algorithm Walkthrough

Iteration Checklist

  1. Define state (indices, window, stack, map, DP cell, or recursion frame).
  2. Apply one transition step and update the invariant.
  3. Record answer candidate when condition is met.
  4. Continue until all input is consumed.
Use the first example testcase as your mental trace to verify each transition.
Step 04

Edge Cases

Minimum Input
Single element / shortest valid input
Validate boundary behavior before entering the main loop or recursion.
Duplicates & Repeats
Repeated values / repeated states
Decide whether duplicates should be merged, skipped, or counted explicitly.
Extreme Constraints
Upper-end input sizes
Re-check complexity target against constraints to avoid time-limit issues.
Invalid / Corner Shape
Empty collections, zeros, or disconnected structures
Handle special-case structure before the core algorithm path.
Step 05

Full Annotated Code

Source-backed implementations are provided below for direct study and interview prep.

// Accepted solution for LeetCode #2976: Minimum Cost to Convert String I
class Solution {
    public long minimumCost(
        String source, String target, char[] original, char[] changed, int[] cost) {
        final int inf = 1 << 29;
        int[][] g = new int[26][26];
        for (int i = 0; i < 26; ++i) {
            Arrays.fill(g[i], inf);
            g[i][i] = 0;
        }
        for (int i = 0; i < original.length; ++i) {
            int x = original[i] - 'a';
            int y = changed[i] - 'a';
            int z = cost[i];
            g[x][y] = Math.min(g[x][y], z);
        }
        for (int k = 0; k < 26; ++k) {
            for (int i = 0; i < 26; ++i) {
                for (int j = 0; j < 26; ++j) {
                    g[i][j] = Math.min(g[i][j], g[i][k] + g[k][j]);
                }
            }
        }
        long ans = 0;
        int n = source.length();
        for (int i = 0; i < n; ++i) {
            int x = source.charAt(i) - 'a';
            int y = target.charAt(i) - 'a';
            if (x != y) {
                if (g[x][y] >= inf) {
                    return -1;
                }
                ans += g[x][y];
            }
        }
        return ans;
    }
}
Step 06

Interactive Study Demo

Use this to step through a reusable interview workflow for this problem.

Press Step or Run All to begin.
Step 07

Complexity Analysis

Time
O(m + n + |\Sigma|^3)
Space
O(|\Sigma|^2)

Approach Breakdown

BRUTE FORCE
O(n²) time
O(1) space

Two nested loops check every pair or subarray. The outer loop fixes a starting point, the inner loop extends or searches. For n elements this gives up to n²/2 operations. No extra space, but the quadratic time is prohibitive for large inputs.

OPTIMIZED
O(n) time
O(1) space

Most array problems have an O(n²) brute force (nested loops) and an O(n) optimal (single pass with clever state tracking). The key is identifying what information to maintain as you scan: a running max, a prefix sum, a hash map of seen values, or two pointers.

Shortcut: If you are using nested loops on an array, there is almost always an O(n) solution. Look for the right auxiliary state.
Coach Notes

Common Mistakes

Review these before coding to avoid predictable interview regressions.

Off-by-one on range boundaries

Wrong move: Loop endpoints miss first/last candidate.

Usually fails on: Fails on minimal arrays and exact-boundary answers.

Fix: Re-derive loops from inclusive/exclusive ranges before coding.