diff --git a/problems/3016/jeremymanning.md b/problems/3016/jeremymanning.md index a12adae..fa7341e 100644 --- a/problems/3016/jeremymanning.md +++ b/problems/3016/jeremymanning.md @@ -1,11 +1,64 @@ # [Problem 3016: Minimum Number of Pushes to Type Word II](https://leetcode.com/problems/minimum-number-of-pushes-to-type-word-ii/description/?envType=daily-question) ## Initial thoughts (stream-of-consciousness) +- We have 8 unique "keys" to work with (i.e., the numbers 2 -- 9) +- I think we should start by counting up the number of occurances of each character. We can store the counts in a hash table. This takes $O(n)$ time, where $n$ is the length of the word. +- Then we can sort characters in descending order of occurance. This takes $O(c \log c)$ time, where $c$ is the number of unique characters. At most $c$ could be 26, so this is (roughly) constant time. +- The first 8 most common characters get "primary" mappings +- The second 8 most common characters get "secondary" mappings +- The third 8 most common characters get "tertiary" mappings +- The remaining (up to 2) most common characters get "quaternary" mappings +- We can store the mappings (we just need the costs, not the actual key mappings) in a hash table +- Then we can count up (and then return) the final score using a running sum where we tally up each character's cost by looking it up in the cost hash table. This (again) takes $O(n)$ time, so the full algorithm is still $O(n)$. + - Actually-- we could just loop through the hash table of counts to do this more quickly (e.g., `total_cost += counts[c] * cost[c]`) +- The only somewhat tricky part is hashing out the mappings to get the costs. Let's think through how that could work... ## Refining the problem, round 2 thoughts +- Given the sorted (in descending order) unique characters, we can assign "costs" per character as follows: +```python +n_keys = 8 +costs = {} +for i, c in enumerate(sorted_chars): + costs[c] == (i // n_keys) + 1 +``` +- I think we have enough to implement the full solution... ## Attempted solution(s) ```python -class Solution: # paste your code here! - ... +class Solution: + def minimumPushes(self, word: str) -> int: + # first count the number of times each character appears + counts = {} + for c in word: + if c in counts: + counts[c] += 1 + else: + counts[c] = 1 + + # now sort characters in descending order of the number of instances + chars = [x[0] for x in sorted(counts.items(), key=lambda x: x[1], reverse=True)] + + # assign per-character costs + n_keys = 8 + costs = {} + for i, c in enumerate(chars): + costs[c] = (i // n_keys) + 1 + + # now compute the final cost + total_cost = 0 + for c, n in counts.items(): + total_cost += counts[c] * costs[c] + + return total_cost ``` +- Given test cases pass +- Let's make up some new test cases by choosing random characters: + - `word = "glnzwujbyhhnjbhilhtqjmhnktjtoarvcarpuqflubisaevaydpgngdagmumalrlxwbtnumoqiuisvkkdvclvuujlhdyblcgpjgh"`: pass + - `word = "bqtzntmeeoybtaucsoyjfoeoyqufggsqyqkifdxmgaadxobokbkcdvtdjdaoxusdkbalkbayhtimzhtvalbgiyeyvayforynicgzfkwcualncyeqqwoeatqrnwvsjfjzcfclqrujwbinigppeyhwgmzvhcsjwkhwaqyvkfjqdeyakuhzjqgkbotsaqhvaskyyeocghtlnlfrcisagtlegupjqgjwvmxvmrjbxsnwpgimhpowgjavxvofqfwvtufibnuxhvwcndzcudakdzrrvfeykbytffdbvtkulfagtzarkuxtmnodtfxixnxpqjumpkzwymvkfecajjlazejugqifidyfdajqfjpftbeqeaummnkgpvnqfdlmbaiueiyvrhdupgvwnianvnyilipnujmpfmhcrubdlvqdslsgdukncrqimafvomuhrtpxcwisqhjhwgnierrgjhxhehkqdfjignutuluimlgpgcerxzsuvjyhkrjomnsrbeilotthlahcwjxcziyrkexdhogrebxxmqcigxicypeujqgdelsbyojloomsgifvsqtdegtvswnznkrdchzxnvbojnahefduzsdouuiixsgbchapavipuuumbrpkgsuhfejmlwxvjxpruwsrjbhhpnkspwwvnzhotspudnnlaiqguqfobrrybbrfziqfcetgyyxyadlicaybjpvaqttwkialbfptbfgptlbbotkviyfgsmbjsliktconbkflqfaahzxawzeckbvrbpbfxqhrigqkpeuiehgrponiqibdhfevulnfwqsajdnxgiysikcsujmxvtwpvznrummysbnophmmqnxbqbnqovbahpdbpnqzwmlymsmjmximzvvtmxudgtvfcthzkvrrrlpyotgixtmbrxnryypjguuaxuvylfthigtospjnllmexfaspoiicrxqhyluveosigeidnijlhixmheholsdsvcpxunpoffyueri"`: pass + - `word = "jjkezznflnsqzlwxmzatthemwtmvogsiwbwfdmmvwyozulmpobukdrihiotnjtehdwqgxdjsunoggeeweqtipmsgnddonlkypowsurvvbimgreiwbeoznsapncruwuqymamydccuryjhceanjdhrpwugfhawuvdyqiwxrhycmzzvlucchabetsrrxmqnnxdiqzulduutatvxcogrgqqywfmjtraithkqqydmbbysjphgbzosufyicmprvrcvgggiznsqdgrplesewdvoqpeircehsbznddrxzxzxhhectjylmbexyazzredznxxcmnydbdkfwgaddvasixsijtulqzhoaxuubqnazfysbyoprmnqhoopndhwkmljsvnxkdufsldymchxqgqrgcutygfxurvtqnkyknfutprmhstayofmfnhdhbfegskxmnwujexzkbprhsadakiavnlrarfmwolsnzgozkmzzhdgihwfdzqnyqmrrjiemqvfckvvqsxnesslyzcakaalqhtqftpclepvyayvgrgqpngxgdznijgikqosuwvnnulhjtpeuxszvezujwvoymrcttmyftjuugcvjmdzlnsdeekvbqkhkvhgfokwtgpwqvymazibayinuseqmmxxfjrkysqeeqgkyoiqenkmgubnehuenrbywuqekvbgtuancusvxgofswpnhoiqqqlyisgnlzjezrswzbzhjfbpczieqsmbkyqjplqsrkpwhkeuxorwkewbctkuxvhuymgkfzvdpskkmukloriplwrowpbnfnogapxvqdyvfottvkjgxhcciqioadlxewinrxfwqprphgdiozpzivfkcpdswylaopcphpxzgrvqriezzuszagivuijwxgwcnqlmgbcyrnflhdefxqtdtysfqwfdmdsneiqswmxiwaiwkgcitgrjlllvxblvbeajrxkyjojdhcupnffobcimywtefmgnaeirrgganmue"`: pass +- Looks OK; submitting... + +![Screenshot 2024-08-05 at 10 34 21 PM](https://github.com/user-attachments/assets/94cb71f4-79f8-444f-9522-544b7a8c1810) + +I'm surprised it's so slow relative to other solutions...but I'll take it-- solved! +