What is the time complexity of Lexicographically Smallest String After Operations With Constraint?

The optimal solution for Lexicographically Smallest String After Operations With Constraint runs in O(n) time and uses O(n) space. The complexity is O(n) because we only iterate through the string once, making a constant-time decision for each character.

What is the brute force solution for Lexicographically Smallest String After Operations With Constraint?

The brute force approach for Lexicographically Smallest String After Operations With Constraint is Brute Force, with O(n²) time complexity and O(1) space complexity. In the brute force approach, we will try to change each character of the string to every possible character from 'a' to 'z'. For each character change, we will calculate the distance and check if it is within the allowed limit k. This method is straightforward but inefficient. The optimal Optimal Solution approach improves this to O(n).

What algorithm or data structure is used to solve Lexicographically Smallest String After Operations With Constraint?

Lexicographically Smallest String After Operations With Constraint uses the following concepts: String, Greedy. The recommended patterns to study are: Greedy, Dynamic Programming.

What are the interview tips for Lexicographically Smallest String After Operations With Constraint?

Always clarify the problem constraints and edge cases before jumping into coding. Think about the greedy nature of the problem and how you can minimize the result step by step. Practice writing clean and efficient code, as clarity can be just as important as correctness in interviews.

What are common mistakes when solving Lexicographically Smallest String After Operations With Constraint?

Not considering the distance calculation correctly, especially with cyclic characters. Failing to update the remaining distance k properly after each character change.

#3106

Lexicographically Smallest String After Operations With Constraint

Medium

StringGreedyGreedyDynamic Programming

LeetCode ↗

Approaches

Brute ForceOptimal

Complexity Comparison

	Brute Force	Optimal Solution★
Time	O(n²)	O(n)
Space	O(1)	O(n)

💡

Intuition

Time O(n)Space O(n)

The optimal solution uses a greedy approach to minimize the string lexicographically while keeping track of the distance. Instead of checking all characters for each position, we can directly compute the best character to change to based on the remaining distance.

⚙️

Algorithm

5 steps

1Step 1: Initialize an empty result string and a variable to track the total distance.
2Step 2: For each character in the input string, calculate the distance to 'a'.
3Step 3: If the distance is less than or equal to k, change the character to 'a' and reduce k by the distance.
4Step 4: If k is exhausted, keep the original character.
5Step 5: Continue until all characters are processed.

solution.py13 lines

1def distance(c1, c2):
2    return min((ord(c1) - ord(c2)) % 26, (ord(c2) - ord(c1)) % 26)
3
4def lexicographically_smallest_string(s, k):
5    result = ''
6    for char in s:
7        dist = distance(char, 'a')
8        if dist <= k:
9            result += 'a'
10            k -= dist
11        else:
12            result += char
13    return result

ℹ

Complexity note: The complexity is O(n) because we only iterate through the string once, making a constant-time decision for each character.

1Greedy approaches often yield optimal solutions for problems involving minimization or maximization under constraints.
2Understanding the cyclic nature of character distances helps in efficiently calculating the required transformations.

Solutions and explanations are original Tejav content. Problem titles © LeetCode — use the LeetCode button above for the full problem statement.