#1405

Medium

auto_awesomeGreedy choice plus invariant validation

LeetCode Problem Workspace

Longest Happy String

Solve the "Longest Happy String" problem using a greedy approach with validation of invariants for constructing the longest possible happy string.

string greedy heap priority queue

Problem Statement

You are given three integers a, b, and c representing the number of occurrences of the characters 'a', 'b', and 'c' respectively. The goal is to create the longest possible string with these characters such that no two consecutive characters are the same. If multiple longest strings are possible, any of them may be returned. If no valid string can be created, return an empty string.

A string is considered 'happy' if no two adjacent characters are the same. For instance, if a = 1, b = 1, and c = 7, a possible result would be 'ccaccbcc'. You are asked to form such a string given the constraints and using efficient strategies, particularly greedy algorithms with heap data structures.

Examples

Example 1

Input: a = 1, b = 1, c = 7

Output: "ccaccbcc"

"ccbccacc" would also be a correct answer.

Example 2

Input: a = 7, b = 1, c = 0

Output: "aabaa"

It is the only correct answer in this case.

Constraints

0 <= a, b, c <= 100
a + b + c > 0

Solution Approach

Greedy Approach with Heap

The key strategy is to use a greedy algorithm to repeatedly select the most frequent character that can be added without violating the 'no two consecutive characters' rule. A heap (priority queue) helps manage the characters by frequency, allowing efficient selection of the best character to add next.

Invariant Validation

To ensure the string remains valid, after adding a character, we must check that the newly chosen character is not the same as the last one added. The heap helps track the frequency of each character, ensuring that we can always pick the highest frequency character that fits the rules.

Edge Case Handling

Edge cases such as having one character with a significantly higher count than the others must be handled by checking if the frequency of one character exceeds the maximum allowed placements. If a string can't be formed due to this imbalance, we should return an empty string.

Complexity Analysis

Metric	Value
Time	O(a + b + c)
Space	O(1)

The time complexity is O(a + b + c) since each insertion and removal from the heap takes logarithmic time, and there are at most a + b + c operations. The space complexity is O(1) because we only use a constant amount of space for the heap and temporary variables.

What Interviewers Usually Probe

The candidate chooses the correct greedy strategy to handle character selection efficiently.
They successfully implement a heap to manage character frequencies, optimizing selection.
The candidate handles edge cases such as imbalances in character counts correctly, ensuring a valid string.

Common Pitfalls or Variants

Common pitfalls

Not managing the heap correctly, leading to inefficient or incorrect character selection.
Failing to check the validity of the string after each character is added, possibly leading to two consecutive characters.
Not handling edge cases where one character's count is too large to form a valid string, resulting in an empty string return.

Follow-up variants

Modify the problem to use more than three characters and still construct the longest happy string.
Change the problem to allow two consecutive identical characters but with a maximum count.
Implement the problem where the goal is to minimize the length of the string instead of maximizing it.

FAQ

What is the greedy strategy used in the "Longest Happy String" problem?

The greedy strategy involves always choosing the most frequent character that can be added to the string without violating the rule of no consecutive characters being the same.

How does the heap help in solving this problem?

The heap helps by efficiently managing the character frequencies, allowing us to quickly select the character with the highest count that is valid to add next.

What should I do if one character's count is too high to form a valid string?

If one character's count exceeds the allowable placements, it's impossible to form a valid string, and the solution should return an empty string.

Can the "Longest Happy String" problem have multiple correct solutions?

Yes, there can be multiple valid happy strings with the same maximum length, so any of them can be returned as the solution.

What is the time complexity of the "Longest Happy String" problem?

The time complexity is O(a + b + c), where a, b, and c are the counts of 'a', 'b', and 'c' respectively, due to heap operations.

terminal

Solution

Solution 1: Greedy + Priority Queue

The greedy strategy is to prioritize the selection of characters with the most remaining occurrences. By using a priority queue or sorting, we ensure that the character selected each time is the one with the most remaining occurrences (to avoid having three consecutive identical characters, in some cases, we need to select the character with the second most remaining occurrences).

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class Solution:
    def longestDiverseString(self, a: int, b: int, c: int) -> str:
        h = []
        if a > 0:
            heappush(h, [-a, 'a'])
        if b > 0:
            heappush(h, [-b, 'b'])
        if c > 0:
            heappush(h, [-c, 'c'])

        ans = []
        while len(h) > 0:
            cur = heappop(h)
            if len(ans) >= 2 and ans[-1] == cur[1] and ans[-2] == cur[1]:
                if len(h) == 0:
                    break
                nxt = heappop(h)
                ans.append(nxt[1])
                if -nxt[0] > 1:
                    nxt[0] += 1
                    heappush(h, nxt)
                heappush(h, cur)
            else:
                ans.append(cur[1])
                if -cur[0] > 1:
                    cur[0] += 1
                    heappush(h, cur)

        return ''.join(ans)

Continue Practicing

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