How do you solve Find All Possible Stable Binary Arrays I on LeetCode?

Find All Possible Stable Binary Arrays I (LeetCode #3129) can be solved using Brute Force or Optimal Solution. The optimal approach is Optimal Solution with O(n^3) time complexity and O(n^2) space complexity. Key insight: Dynamic programming can significantly reduce the complexity of counting problems.

What is the brute force solution for Find All Possible Stable Binary Arrays I?

The brute force approach for Find All Possible Stable Binary Arrays I is Brute Force, with O(n²) time complexity and O(n) space complexity. The brute force approach generates all possible binary arrays of given lengths and checks each one for stability. This method is straightforward but inefficient for larger inputs. The optimal Optimal Solution approach improves this to O(n^3).

What algorithm or data structure is used to solve Find All Possible Stable Binary Arrays I?

Find All Possible Stable Binary Arrays I uses the following concepts: Dynamic Programming, Prefix Sum. The recommended patterns to study are: Dynamic Programming, Prefix Sum.

What are the interview tips for Find All Possible Stable Binary Arrays I?

Explain your thought process clearly, especially when transitioning from brute force to optimal solutions. Discuss the time and space complexity of your solutions. Practice similar problems to get comfortable with dynamic programming.

What are common mistakes when solving Find All Possible Stable Binary Arrays I?

Not considering edge cases, such as when zero or one is zero. Failing to correctly implement the stability checks.

#3129

Find All Possible Stable Binary Arrays I

Medium

Dynamic ProgrammingPrefix SumDynamic ProgrammingPrefix Sum

LeetCode ↗

Approaches

Brute ForceOptimal

Complexity Comparison

	Brute Force	Optimal Solution★
Time	O(n²)	O(n^3)
Space	O(n)	O(n^2)

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Intuition

Time O(n^3)Space O(n^2)

Using dynamic programming, we can efficiently count stable binary arrays by building on previously computed results. This avoids the overhead of generating all permutations.

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Algorithm

3 steps

1Step 1: Define a DP table where dp[a][b][c][d] represents the number of stable arrays with 'a' 0s, 'b' 1s, and 'c' consecutive 0s or 1s at the end, with 'd' indicating if the last added number was a 0 or 1.
2Step 2: Initialize the DP table with base cases for 0s and 1s.
3Step 3: Iterate through the DP table and fill it based on the rules of stability, ensuring that no subarray exceeds the limit.

solution.py24 lines

1# Full working Python code
2MOD = 10**9 + 7
3
4def countStableBinaryArrays(zero, one, limit):
5    dp = [[[[0 for _ in range(2)] for _ in range(limit + 1)] for _ in range(one + 1)] for _ in range(zero + 1)]
6    dp[0][0][0][0] = 1  # Base case: empty array
7
8    for a in range(zero + 1):
9        for b in range(one + 1):
10            for c in range(limit + 1):
11                for d in range(2):
12                    if d == 0 and a > 0:
13                        dp[a][b][1][0] = (dp[a][b][1][0] + dp[a - 1][b][c][0]) % MOD
14                    if d == 1 and b > 0:
15                        dp[a][b][1][1] = (dp[a][b][1][1] + dp[a][b - 1][c][1]) % MOD
16                    if c < limit:
17                        if d == 0:
18                            dp[a][b][c + 1][0] = (dp[a][b][c + 1][0] + dp[a][b][c][0]) % MOD
19                        else:
20                            dp[a][b][c + 1][1] = (dp[a][b][c + 1][1] + dp[a][b][c][1]) % MOD
21
22    total_count = (dp[zero][one][0][0] + dp[zero][one][0][1]) % MOD
23    return total_count
24

ℹ

Complexity note: The time complexity is O(n^3) due to the nested loops iterating through the counts of 0s, 1s, and the limit. The space complexity is O(n^2) for storing the DP table.

1Dynamic programming can significantly reduce the complexity of counting problems.
2Understanding the constraints of the problem helps in designing efficient algorithms.

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