Find the Lexicographically Smallest Valid Sequence

Problem Description

You are given two strings word1 and word2. A string x is called almost equal to y if you can change at most one character in x to make it identical to y. A sequence of indices seq is called valid if:

• The indices are sorted in ascending order.
• Concatenating the characters at these indices in word1 in the same order results in a string that is almost equal to word2.

Return an array of size word2.length representing the lexicographically smallest valid sequence of indices. If no such sequence of indices exists, return an empty array.

Key Insights

• A valid sequence should match the length of word2.
• The resulting characters from word1 need to be almost equal to word2 with at most one character change.
• The sequence needs to be lexicographically smallest, implying we should prioritize earlier indices when forming the sequence.

Space and Time Complexity

Time Complexity: O(n) - We traverse word1 and word2 linearly to find a valid sequence. Space Complexity: O(m) - We store the indices of the valid sequence, where m is the length of word2.

Solution

To solve the problem, we can use a greedy approach combined with two pointers. We iterate through word1 and use a pointer to track our position in word2. For each character in word1, we check if it can contribute to forming word2. We maintain a list of indices, ensuring that we only change one character if necessary. Finally, we return the lexicographically smallest sequence of indices that forms a valid match.

Code Solutions