Introduction

In this blog post, we will explore how to solve the LeetCode problem "2767" using AI. LeetCode is a popular platform for preparing for coding interviews, and with the help of AI tools like Chatmagic, we can generate solutions quickly and efficiently - helping you pass the interviews and get the job offer without having to study for months.

Problem Statement

Given a binary string s, partition the string into one or more substrings such that each substring is beautiful. A string is beautiful if: It doesn't contain leading zeros. It's the binary representation of a number that is a power of 5. Return the minimum number of substrings in such partition. If it is impossible to partition the string s into beautiful substrings, return -1. A substring is a contiguous sequence of characters in a string. Example 1: Input: s = "1011" Output: 2 Explanation: We can paritition the given string into ["101", "1"]. - The string "101" does not contain leading zeros and is the binary representation of integer 51 = 5. - The string "1" does not contain leading zeros and is the binary representation of integer 50 = 1. It can be shown that 2 is the minimum number of beautiful substrings that s can be partitioned into. Example 2: Input: s = "111" Output: 3 Explanation: We can paritition the given string into ["1", "1", "1"]. - The string "1" does not contain leading zeros and is the binary representation of integer 50 = 1. It can be shown that 3 is the minimum number of beautiful substrings that s can be partitioned into. Example 3: Input: s = "0" Output: -1 Explanation: We can not partition the given string into beautiful substrings. Constraints: 1 <= s.length <= 15 s[i] is either '0' or '1'.

Explanation

Here's a breakdown of the approach and the Python code:

• High-Level Approach:

  • Dynamic Programming: Use DP to store the minimum number of substrings needed to partition the string up to a given index.
  • Check for Beautiful Substrings: Iterate through all possible substrings and check if they represent a power of 5.
  • DP Update: If a substring is beautiful, update the DP array to reflect the minimum cuts needed.

• Complexity:

  • Runtime: O(n^2), where n is the length of the string s.
  • Storage: O(n)

Code

    def beautifulPartitions(s):
    n = len(s)
    dp = [float('inf')] * (n + 1)
    dp[0] = 0
    powers_of_5 = []
    power = 1
    while power <= int('1' * n, 2):
        powers_of_5.append(bin(power)[2:])
        power *= 5

    for i in range(1, n + 1):
        for j in range(i):
            sub = s[j:i]
            if sub[0] == '0' and len(sub) > 1:
                continue
            if sub in powers_of_5:
                dp[i] = min(dp[i], dp[j] + 1)

    if dp[n] == float('inf'):
        return -1
    else:
        return dp[n]