#3106

Medium

auto_awesomeGreedy choice plus invariant validation

LeetCode Problem Workspace

Lexicographically Smallest String After Operations With Constraint

Minimize a string lexicographically using a series of operations constrained by a given integer k.

Problem Statement

You are given a string s and an integer k. Your task is to return the lexicographically smallest string that can be obtained by performing at most k operations, where each operation allows you to change one character of the string.

The distance between two strings s1 and s2 of the same length n is defined as the sum of the absolute differences of corresponding characters. For example, distance("ab", "cd") is 4, and distance("a", "z") is 1. You must make sure that the total distance of changes does not exceed k.

Examples

Example 1

Input: s = "zbbz", k = 3

Output: "aaaz"

Change s to "aaaz" . The distance between "zbbz" and "aaaz" is equal to k = 3 .

Example 2

Input: s = "xaxcd", k = 4

Output: "aawcd"

The distance between "xaxcd" and "aawcd" is equal to k = 4.

Example 3

Input: s = "lol", k = 0

Output: "lol"

It's impossible to change any character as k = 0 .

Constraints

1 <= s.length <= 100
0 <= k <= 2000
s consists only of lowercase English letters.

Solution Approach

Greedy Strategy for Lexicographical Minimization

Start from the leftmost character of the string and try to change it to 'a', the smallest possible character. Check whether the operation stays within the allowed distance constraint. If it does, perform the change and subtract the cost from k. Repeat this until either the string is fully minimized or you run out of operations.

Validating Constraints

After each operation, validate that the total accumulated distance does not exceed k. This requires careful tracking of the changes and ensuring that no operation violates the allowed number of steps. If at any point, the remaining allowed operations are insufficient to complete a change, stop and return the current string.

Efficient Implementation

The solution should efficiently iterate through the string, modifying characters and checking the distance against k. Given the constraints, a greedy approach that ensures the smallest lexicographical order will perform well. Consider edge cases where k is zero or when the string is already minimized.

Complexity Analysis

Metric	Value
Time	Depends on the final approach
Space	Depends on the final approach

The time complexity of the approach is O(n), where n is the length of the string. We iterate over the string once, performing constant-time operations for each character. The space complexity is O(1) as we only need a few variables to keep track of the current state.

What Interviewers Usually Probe

The problem can be solved greedily with careful validation of the operations.
Watch for edge cases like when k equals zero, where no operations can be performed.
Candidates should be able to explain the trade-off of minimizing the string while adhering to the distance constraint.

Common Pitfalls or Variants

Common pitfalls

Not handling the case where k equals zero and no changes can be made.
Misunderstanding the distance calculation or failing to properly track the allowed distance.
Not considering the edge case where the string is already the lexicographically smallest, requiring no operations.

Follow-up variants

What if the operations are unlimited? This would simplify the problem significantly.
Consider modifying the string to a fixed target rather than minimizing it.
What if we were allowed to change only specific positions in the string rather than all characters?

FAQ

What is the greedy approach in the Lexicographically Smallest String problem?

The greedy approach involves starting with the leftmost character and trying to change it to 'a', ensuring the total distance remains within the allowed k operations.

How do I calculate the distance between two strings?

The distance between two strings of the same length is the sum of the absolute differences of their corresponding characters' ASCII values.

What should I do when k equals zero?

If k equals zero, no changes can be made to the string, so the input string should be returned unchanged.

What is the time complexity of the solution?

The time complexity is O(n), where n is the length of the string, as we iterate through the string once.

Can I use a dynamic programming approach for this problem?

A dynamic programming approach is not necessary for this problem, as a greedy strategy with careful validation is more efficient.

terminal

Solution

Solution 1: Enumeration

We can traverse each position of the string $s$. For each position, we enumerate all characters less than the current character, calculate the cost $d$ to change to this character. If $d \leq k$, we change the current character to this character, subtract $d$ from $k$, end the enumeration, and continue to the next position.

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class Solution:
    def getSmallestString(self, s: str, k: int) -> str:
        cs = list(s)
        for i, c1 in enumerate(s):
            for c2 in ascii_lowercase:
                if c2 >= c1:
                    break
                d = min(ord(c1) - ord(c2), 26 - ord(c1) + ord(c2))
                if d <= k:
                    cs[i] = c2
                    k -= d
                    break
        return "".join(cs)

Continue Practicing

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