The Partition String Into Minimum Beautiful Substrings problem asks you to partition a binary string into the minimum number of "beautiful" substrings, where a beautiful substring is a binary representation of a power of 5 (without leading zeros). This coding problem uses DP with precomputed beautiful string set. The hash table, backtracking, string, and dynamic programming interview pattern is demonstrated.
Google asks this to test DP on string partitioning where the "valid segment" condition involves number theory (powers of 5). Precomputing all powers of 5 representable in binary reduces the validation to a set lookup.
Precompute powers of 5 + partition DP. Generate all powers of 5 that fit within the string length (in binary: 1,101,11001,...). Store in a set. dp[i] = minimum beautiful partitions for s[0..i-1]. For each i, try all j ≤ i: if s[j..i-1] is in the beautiful set and no leading zeros, dp[i] = min(dp[i], dp[j]+1). Answer = dp[n] if reachable, else -1.
s="1011". Powers of 5 in binary: 1→"1", 5→"101", 25→"11001",...
String partition DP where validity involves number theory: precompute all valid patterns first, then apply standard partition DP. The valid-pattern precomputation is the non-trivial step. Practice generating binary representations of all powers of 5 up to length n: power = 1; while power's binary length ≤ n: add bin(power) to set; power *= 5. Then apply the standard DP template.
| Title | Difficulty | Topics | LeetCode |
|---|---|---|---|
| Longest Ideal Subsequence | Medium | Solve | |
| Split a String Into the Max Number of Unique Substrings | Medium | Solve | |
| Palindrome Partitioning | Medium | Solve | |
| Letter Combinations of a Phone Number | Medium | Solve | |
| Generate Parentheses | Medium | Solve |
