Lexicographically Smallest String After Operations With Constraint

Lexicographically Smallest String After Operations With Constraint

What is this problem about?

The "Lexicographically Smallest String After Operations With Constraint interview question" is a greedy string problem. You are given a string and a maximum number of "points" (distance) you can use. You can change any character to any other character, but the "cost" is the distance between them in the alphabet (e.g., 'a' to 'c' costs 2). You want to reach the lexicographically smallest string without exceeding your total points. This "Lexicographically Smallest String After Operations With Constraint coding problem" is about optimizing your budget to get the best possible prefix.

Why is this asked in interviews?

This problem tests a candidate's "Greedy interview pattern" skills and their ability to manage a resource (points). Companies like ServiceNow use it to see if you understand that characters at the beginning of the string are much more important for lexicographical order than characters at the end. It evaluates your ability to make the best possible change at the earliest possible index.

Algorithmic pattern used

The strategy is to iterate from the first character to the last. For each character, try to change it to 'a'. Calculate the distance from the current character to 'a'. If your remaining points are enough, change the character to 'a' and subtract the cost from your points. If not, change the character to the smallest possible character you can afford (current character - remaining points). Once your points are zero, you stop modifying characters.

Example explanation

String: "zbbz", Points: 3

1. Index 0 ('z'): Distance to 'a' is 25. Too expensive (3 < 25).
2. Greedy adjustment: We have 3 points. Change 'z' to 'z' - 3 = 'w'. Points left: 0.
3. Result: "wbbz". If we had 100 points, we'd change the first 'z' to 'a', then move to 'b', change it to 'a', and so on.

Common mistakes candidates make

• Spending points on the wrong index: Changing a later character to 'a' while an earlier character could have been improved.
• Incorrect distance calculation: Not handling the "wrap around" if the problem allows 'z' to 'a' as a distance of 1 (though most don't, always check).
• Overspending: Not correctly subtracting the cost and ending up with a negative point balance.

Interview preparation tip

In lexicographical problems, the importance of an index is exponential. Improving index 0 is almost always better than improving all other indices combined. Always spend your "budget" as early as possible.