From e7002254e2b434f0b87f9371d7496df795f74758 Mon Sep 17 00:00:00 2001
From: Felix Martin <mail@felixm.de>
Date: Fri, 14 May 2021 20:17:59 -0400
Subject: [PATCH] Solve problem 98

---
 python/e098.py | 88 ++++++++++++++++++++++++++++++++++++++++++++++++++
 1 file changed, 88 insertions(+)
 create mode 100644 python/e098.py

diff --git a/python/e098.py b/python/e098.py
new file mode 100644
index 0000000..258d6db
--- /dev/null
+++ b/python/e098.py
@@ -0,0 +1,88 @@
+
+def get_words():
+    with open("../txt/e098.txt", "r") as f:
+        words = list(map(lambda w: w.strip().lower(), f.readlines()))
+    words.sort(key=len, reverse=True)
+    return words
+
+
+def get_pair_subsets(xs):
+    """ Returns all subsets of size two. """
+    r = [(xs[i], xs[j])
+            for i in range(len(xs))
+            for j in range(i + 1, len(xs))]
+    return r
+
+
+def find_anagrams(xs):
+    anagrams = {}
+    for x in xs:
+        x_tuple = tuple(sorted(x))
+        try:
+            anagrams[x_tuple].append(x)
+        except KeyError:
+            anagrams[x_tuple] = [x]
+    anagrams = [a for a in anagrams.values() if len(a) > 1]
+    return anagrams
+
+
+def find_anagram_pairs(xs):
+    anagrams = find_anagrams(xs)
+    r = [pair
+         for anagram in anagrams
+         for pair in get_pair_subsets(anagram)]
+    return r
+
+
+def words_match_numbers(words, numbers):
+    letters_a, letters_b = words
+    digits_a, digits_b = numbers
+
+    digit_to_letter = {}
+    for l, d in zip(letters_a, digits_a):
+        if d in digit_to_letter and digit_to_letter[d] != l:
+            # Each digit can only be assigned to one letter
+            return False
+        digit_to_letter[d] = l
+
+
+    letter_to_digit = {l: d for l, d in zip(letters_a, digits_a)}
+    for l, d in zip(letters_b, digits_b):
+        if letter_to_digit[l] != d:
+            return False
+    return True
+
+
+def find_pairs(words, squares):
+    pairs = []
+    anagram_pairs = find_anagram_pairs(words)
+    square_pairs = find_anagram_pairs(squares)
+    for word_pair in anagram_pairs:
+        for number_pair in square_pairs:
+            if words_match_numbers(word_pair, number_pair):
+                # pairs.append([word_pair, number_pair])
+                pairs.append(number_pair)
+    return pairs
+
+
+def euler_098():
+    squares = [str(i * i) for i in range(200000)]
+    words = get_words()
+
+    largest_number = 0
+    for i in range(3, 9):
+        words_i = list(filter(lambda w: len(w) == i, words))
+        squares_i = list(filter(lambda w: len(w) == i, squares))
+        pairs = find_pairs(words_i, squares_i)
+        for pair in pairs:
+            n = max(map(int, pair))
+            if n > largest_number:
+                largest_number = n
+    return largest_number
+
+
+if __name__ == "__main__":
+    solution = euler_098()
+    print("e098.py: " + str(solution))
+    assert(solution == 18769)
+