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

Find All Possible Stable Binary Arrays II (LeetCode #3130) can be solved using Brute Force or Optimal Solution. The optimal approach is Optimal Solution with O(zero * one * limit) time complexity and O(zero * one) space complexity. Key insight: Dynamic programming can significantly reduce the time complexity by avoiding redundant calculations.

What is the time complexity of Find All Possible Stable Binary Arrays II?

The optimal solution for Find All Possible Stable Binary Arrays II runs in O(zero * one * limit) time and uses O(zero * one) space. This complexity arises from filling a 3D DP table based on the number of zeros, ones, and the limit, leading to a polynomial time complexity.

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

The brute force approach for Find All Possible Stable Binary Arrays II is Brute Force, with O(2^(zero + one)) time complexity and O(1) space complexity. We can generate all possible binary arrays of given lengths and check if they meet the stability criteria. This approach is straightforward but inefficient due to the exponential number of combinations. The optimal Optimal Solution approach improves this to O(zero * one * limit).

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

Find All Possible Stable Binary Arrays II 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 II?

Clearly explain your thought process while transitioning from brute force to optimal solutions. Practice writing DP solutions, as they are common in interviews. Always consider edge cases, such as the smallest inputs for zero, one, and limit.

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

Not initializing the base cases correctly in the DP table. Overlooking the limit condition when filling the DP table.

#3130

Find All Possible Stable Binary Arrays II

Hard

Dynamic ProgrammingPrefix SumDynamic ProgrammingPrefix Sum

LeetCode ↗

Approaches

Brute ForceOptimal

Complexity Comparison

	Brute Force	Optimal Solution★
Time	O(2^(zero + one))	O(zero * one * limit)
Space	O(1)	O(zero * one)

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Intuition

Time O(zero * one * limit)Space O(zero * one)

We can use dynamic programming to efficiently count the valid stable arrays by breaking the problem into smaller subproblems. This avoids the need to generate all combinations.

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Algorithm

3 steps

1Step 1: Define a DP table dp[x][y][z] where x is the number of zeros, y is the number of ones, and z indicates the last element (0 or 1).
2Step 2: Initialize base cases for dp where only one '1' is present.
3Step 3: Fill the DP table by considering adding groups of zeros or ones, ensuring they do not violate the limit condition.

solution.py12 lines

1def countStableArrays(zero, one, limit):
2    MOD = 10**9 + 7
3    dp = [[[0, 0] for _ in range(one + 1)] for _ in range(zero + 1)]
4    dp[0][1][1] = 1  # Base case: one '1'
5    for x in range(zero + 1):
6        for y in range(1, one + 1):
7            for k in range(1, limit + 1):
8                if x >= k:
9                    dp[x][y][1] = (dp[x][y][1] + dp[x - k][y][0]) % MOD
10                if y > 1:
11                    dp[x][y][0] = (dp[x][y][0] + dp[x][y - 1][1]) % MOD
12    return (dp[zero][one][0] + dp[zero][one][1]) % MOD

ℹ

Complexity note: This complexity arises from filling a 3D DP table based on the number of zeros, ones, and the limit, leading to a polynomial time complexity.

1Dynamic programming can significantly reduce the time complexity by avoiding redundant calculations.
2Understanding the constraints helps in designing the DP state transitions effectively.

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