What is the time complexity of Partition String Into Minimum Beautiful Substrings?

The optimal solution for Partition String Into Minimum Beautiful Substrings runs in O(n²) time and uses O(n) space. The time complexity remains O(n²) due to the nested loops for substring checks, but the space complexity is O(n) for the DP array.

What is the brute force solution for Partition String Into Minimum Beautiful Substrings?

The brute force approach for Partition String Into Minimum Beautiful Substrings is Brute Force, with O(n²) time complexity and O(1) space complexity. The brute force approach involves generating all possible substrings of the given binary string and checking if each substring is beautiful. This method is straightforward but inefficient due to the exponential number of possible partitions. The optimal Optimal Solution approach improves this to O(n²).

What algorithm or data structure is used to solve Partition String Into Minimum Beautiful Substrings?

Partition String Into Minimum Beautiful Substrings uses the following concepts: Hash Table, String, Dynamic Programming, Backtracking. The recommended patterns to study are: Dynamic Programming, Backtracking.

What are the interview tips for Partition String Into Minimum Beautiful Substrings?

Clearly explain your thought process and the reasoning behind each step. Consider edge cases, such as strings with leading zeros or all zeros. Practice generating substrings and checking conditions efficiently.

What are common mistakes when solving Partition String Into Minimum Beautiful Substrings?

Not checking for leading zeros in substrings. Failing to precompute powers of 5, leading to unnecessary calculations.

#2767

Partition String Into Minimum Beautiful Substrings

Medium

Hash TableStringDynamic ProgrammingBacktrackingDynamic ProgrammingBacktracking

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Approaches

Brute ForceOptimal

Complexity Comparison

	Brute Force	Optimal Solution★
Time	O(n²)	O(n²)
Space	O(1)	O(n)

💡

Intuition

Time O(n²)Space O(n)

The optimal approach uses dynamic programming to store the minimum number of beautiful substrings that can be formed up to each index. This avoids redundant calculations and improves efficiency significantly.

⚙️

Algorithm

3 steps

1Step 1: Precompute all powers of 5 that can be represented in binary up to the maximum length of the string.
2Step 2: Initialize a DP array where dp[i] represents the minimum number of beautiful substrings for the substring s[0:i].
3Step 3: For each index, check all possible substrings ending at that index and update the DP array accordingly.

solution.py18 lines

1# Full working Python code
2def minBeautifulSubstrings(s):
3    powers_of_5 = set()
4    for i in range(15):
5        powers_of_5.add(bin(5 ** i)[2:])
6    n = len(s)
7    dp = [float('inf')] * (n + 1)
8    dp[0] = 0
9    for i in range(1, n + 1):
10        for j in range(i):
11            substring = s[j:i]
12            if substring[0] != '0' and substring in powers_of_5:
13                dp[i] = min(dp[i], dp[j] + 1)
14    return dp[n] if dp[n] != float('inf') else -1
15
16# Example usage
17print(minBeautifulSubstrings('1011'))  # Output: 2
18

ℹ

Complexity note: The time complexity remains O(n²) due to the nested loops for substring checks, but the space complexity is O(n) for the DP array.

1Understanding binary representations and their properties is crucial.
2Dynamic programming can significantly reduce the number of redundant calculations.

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