Today’s problem is 1647: Minimum Deletions to Make Character Frequencies Unique. Our goal is to write
n, an integer as the minimum number of deci-binary numbbers, e.g
32 = 10+11+11. There are multiple ways to write
32 as the sum of deci-binary numbers but we’re looking at the smallest.
This one is tricky, but has a very short solution. I simply tabulated values, noticing that single digit numbers are their own answer. Then, if I took a number, say
17, I’d need
1+1+1+1+1+1+11 which is
7 terms. Then, I looked at
39 = 11+11+11+(1+1+1+1+1+1) which is
9 terms. There is a pattern of the result being the largest digit in
n. The idea is that we’re going to need
k terms to build up that specific digit, and is the limiting factor.
class Solution:def minDeletions(self, s: str) -> int:count = 0seen = set()freqs = [0 for _ in range(26)]'''Count frequencies, decrement uniques till we have a slot'''for char in s:freqs[ord(char)-ord('a')] += 1for idx in range(26):while freqs[idx] and freqs[idx] in seen:freqs[idx] -= 1count += 1seen.add(freqs[idx])return count
It took a while to realise the pattern, and the independence of digits to the left/right of the largest digit. I also had considered a recursive solution but this is overkill, and would be too slow. There are similar such number related problems where you’ll need to look for a pattern to simplify your logic to $O(n)$. The idea: if you observe a pattern, run a few examples by hand and test it!