Decoded String at Index
What is this problem about?
The Decoded String at Index interview question involves a compressed string similar to "Decode String," but with a twist: you only need to find the character at a specific index k in the fully expanded version. The encoding is simple: characters are appended, and digits multiply the entire existing string. This Decoded String at Index coding problem is about calculating lengths without actually expanding the string.
Why is this asked in interviews?
Amazon and PhonePe use this to see if a candidate can handle potential memory overflows. The expanded string can have a length of 10^18 (quintillions), making it impossible to store in memory. It tests your ability to use modular arithmetic to work backwards from the final length to the desired character.
Algorithmic pattern used
This utilizes the String, Stack interview pattern, specifically working backwards.
- Forward Pass: Calculate the total length of the decoded string. If a char is a letter, length++. If it's a digit d, length *= d.
- Backward Pass: Iterate through the original string from right to left.
- Update k = k % length.
- If k == 0 and the current character is a letter, return that letter.
- If the current character is a digit d, update length /= d.
- Else, length--.
Example explanation
S = "leet2", k = 10.
- Length: 'l'(1), 'e'(2), 'e'(3), 't'(4), '2'(8). Total length = 8.
- Wait, k=10. Since the string is cyclic, k = 10 % 8 = 2.
- Backward Pass:
- Current: '2'. Length becomes 8/2 = 4. k = 2 % 4 = 2.
- Current: 't'. k=2 is not 0. Length becomes 4-1 = 3.
- Current: 'e'. k = 2 % 3 = 2. Not 0. Length becomes 3-1 = 2.
- Current: 'e'. k = 2 % 2 = 0. This is our character! Return 'e'.
Common mistakes candidates make
- Actually expanding the string: This will lead to a Memory Limit Exceeded error almost instantly for any non-trivial input.
- Off-by-one errors: Forgetting that k is usually 1-indexed in these problems and correctly handling the k % length == 0 case.
- Integer type: Using 32-bit integers for the length when it can clearly exceed 2^31-1.
Interview preparation tip
When a problem asks for an element at a specific index in a massive generated structure, always think about Modular Arithmetic. It allows you to map a large index back to a smaller, equivalent index within a base pattern.
