My solution for 3016

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!
+