#984

Medium

auto_awesomeGreedy choice plus invariant validation

LeetCode Problem Workspace

String Without AAA or BBB

Solve the problem of constructing a string without consecutive 'AAA' or 'BBB' by applying a greedy approach with invariant checks.

string greedy

Problem Statement

Given two integers a and b, the goal is to construct any string s that uses exactly a occurrences of the character 'a' and b occurrences of the character 'b', and does not contain the substrings 'AAA' or 'BBB'. The string can start with either character, and the order does not have to be strictly alternating.

You are guaranteed that such a string always exists for the given values of a and b. The string should be as short as possible while still following these rules.

Examples

Example 1

Input: a = 1, b = 2

Output: "abb"

"abb", "bab" and "bba" are all correct answers.

Example 2

Input: a = 4, b = 1

Output: "aabaa"

Example details omitted.

Constraints

0 <= a, b <= 100
It is guaranteed such an s exists for the given a and b.

Solution Approach

Greedy Character Selection

To build the string, at each step, choose to append either 'a' or 'b' based on which character has a larger remaining count, but avoid appending more than two of the same character consecutively to prevent forming 'AAA' or 'BBB'.

Invariant Check

After each character addition, ensure the last two characters of the string are not the same as the next one that would cause an invalid sequence. This invariant check is essential for maintaining a valid string.

Termination Condition

The process continues until both 'a' and 'b' are fully used. The greedy choice ensures that the string is constructed without any violations of the 'AAA' or 'BBB' rule.

Complexity Analysis

Metric	Value
Time	O(A+B)
Space	O(A+B)

Time complexity is O(A + B) where A and B are the counts of 'a' and 'b', as we process each character once. Space complexity is O(A + B) since we need to store the resulting string, which will have a total length of A + B.

What Interviewers Usually Probe

The candidate demonstrates understanding of the greedy choice by selecting characters based on the remaining count while avoiding invalid sequences.
The candidate correctly applies the invariant check to ensure no invalid subsequences are formed.
The candidate shows efficiency in constructing the string without unnecessary operations or backtracking.

Common Pitfalls or Variants

Common pitfalls

Failing to implement the invariant check properly, leading to invalid strings.
Greedily appending too many of the same character, creating an invalid subsequence.
Overcomplicating the solution by considering unnecessary operations, when the problem can be solved by a simple greedy approach.

Follow-up variants

The number of 'a's and 'b's can be arbitrary within the constraint bounds, testing the generality of the greedy approach.
Handling very large inputs (A and B up to 100) tests the candidate's ability to construct the string efficiently.
Edge cases where one of A or B is zero, testing if the string can be formed with only one character type.

FAQ

How does the greedy approach work in this problem?

The greedy approach ensures that, at each step, the character with the larger remaining count is chosen, but no more than two consecutive characters of the same type are appended.

Why is it important to check the last two characters of the string?

Checking the last two characters ensures that the string does not contain any consecutive sequences of 'AAA' or 'BBB', which is prohibited in the problem constraints.

What happens if I append too many of the same character?

Appending too many of the same character will violate the problem's constraint, resulting in an invalid string that contains either 'AAA' or 'BBB'.

How can I handle edge cases where a or b is zero?

If either a or b is zero, the solution is trivial—simply return a string composed entirely of the other character, which is valid as long as it's within the problem constraints.

How does GhostInterview help with solving this problem?

GhostInterview provides step-by-step guidance on applying the greedy algorithm, ensuring the string construction avoids invalid subsequences and helps optimize the solution.

terminal

Solution

Solution 1

#### Python3

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class Solution:
    def strWithout3a3b(self, a: int, b: int) -> str:
        ans = []
        while a and b:
            if a > b:
                ans.append('aab')
                a, b = a - 2, b - 1
            elif a < b:
                ans.append('bba')
                a, b = a - 1, b - 2
            else:
                ans.append('ab')
                a, b = a - 1, b - 1
        if a:
            ans.append('a' * a)
        if b:
            ans.append('b' * b)
        return ''.join(ans)

Continue Practicing

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