How do you solve Shortest String That Contains Three Strings on LeetCode?

Shortest String That Contains Three Strings (LeetCode #2800) can be solved using Brute Force or Optimal Solution. The optimal approach is Optimal Solution with O(n!) time complexity and O(n) space complexity. Key insight: Permutations help explore all possible orders of strings.

What is the brute force solution for Shortest String That Contains Three Strings?

The brute force approach for Shortest String That Contains Three Strings is Brute Force, with O(n²) time complexity and O(1) space complexity. The brute-force approach involves generating all possible permutations of the three strings and checking each permutation to find the shortest string that contains all three as substrings. This is straightforward but inefficient as it explores many unnecessary combinations. The optimal Optimal Solution approach improves this to O(n!).

What algorithm or data structure is used to solve Shortest String That Contains Three Strings?

Shortest String That Contains Three Strings uses the following concepts: String, Greedy, Enumeration. The recommended patterns to study are: String Manipulation, Permutations.

What are the interview tips for Shortest String That Contains Three Strings?

Explain your thought process clearly while discussing permutations. Be ready to discuss time and space complexity trade-offs. Practice merging strings with overlaps to gain confidence.

What are common mistakes when solving Shortest String That Contains Three Strings?

Not considering all permutations of the strings. Failing to check for lexicographical order in case of ties.

#2800

Shortest String That Contains Three Strings

Medium

StringGreedyEnumerationString ManipulationPermutations

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 approach leverages permutations and efficient merging of strings while ensuring overlaps are maximized. This reduces unnecessary computations and ensures we find the shortest and lexicographically smallest string efficiently.

⚙️

Algorithm

3 steps

1Step 1: Generate all permutations of the three strings a, b, and c.
2Step 2: For each permutation, calculate the merged string using maximum overlaps.
3Step 3: Track the shortest merged string and ensure it is lexicographically smallest in case of ties.

solution.py19 lines

1from itertools import permutations
2
3def merge_strings(s1, s2):
4    max_overlap = 0
5    for i in range(1, min(len(s1), len(s2)) + 1):
6        if s1[-i:] == s2[:i]:
7            max_overlap = i
8    return s1 + s2[max_overlap:]
9
10
11def shortest_superstring(a, b, c):
12    min_length = float('inf')
13    result = ''
14    for perm in permutations([a, b, c]):
15        merged = merge_strings(merge_strings(perm[0], perm[1]), perm[2])
16        if (len(merged) < min_length) or (len(merged) == min_length and merged < result):
17            min_length = len(merged)
18            result = merged
19    return result

ℹ

Complexity note: The time complexity is O(n!) due to the permutations of the three strings, where n is the number of strings (3 in this case). The space complexity is O(n) for storing the merged strings.

1Permutations help explore all possible orders of strings.
2Maximizing overlaps reduces the length of the resulting string.

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