solve problem 32 in uiua

32/solution.uiua

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+# project euler #32
+
+# denote the digit distribution by a×b=c, where
+# a is the number of digits in the multiplicand,
+# b is the number of digits in the multiplier and
+# c is the number of digits in the product.
+# ⍉ 1×1=7
+# ⍉ 1×2=6 ≡ 2x1=6
+# ⍉ 1×3=5 ≡ 3x1=5
+# ⊚ 1×4=4 ≡ 4x1=4 only this
+# ⍉ 2×2=5
+# ⊚ 2×3=4 ≡ 3×2=4 and this
+# ⍉ 3×3=3
+# ⍉ ...
+# because the other digit distributions go over
+# or under too much.
+
+# get three numbers that form candidate
+# index_permutation ? factors_and_product
+n ← ⊕(⋕/⊂≡°⋕)⊙(+1⇡9)
+# check pandigital candidate numbers
+# factors_and_product ? is_pand_prod
+c ← =/×⊃↙₂⊣
+# permutes a number
+# n ? all_permutes_of_n
+p ← □⋕⧅≠∞°⋕
+# join all permutations
+# triple_baka ? combinations
+j ← ≡⇌♭₂⊞⊂°□⊣⟜(♭₂/◇⊞⊂↙2)
+
+# generate solution for given digit distribution
+# digit_distribution ? products
+s ← (
+  ◴⧅≠∞       # permutations of digits
+  ♭₂≡(j≡p n) # permute multiplicand, multiplier, product
+  ◴⊣⍉⊏⊸(⊚≡c) # check all hitherto permutations
+)
+s [2 2 2 2 1 1 1 0 0] # 2×3=5
+s [2 2 2 2 1 1 1 1 0] # 1×4=5
+/+◴⊂
+
+# my online pad solution can be found here:
+# https://uiua.org/pad?src=0_17_0-dev_2__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_IGlzX3BhbmRfcHJvZApjIOKGkCA9L8OX4oqD4oaZ4oKC4oqjCiMgcGVybXV0ZXMgYSBudW1iZXIKIyBuID8gYWxsX3Blcm11dGVzX29mX24KcCDihpAg4pah4ouV4qeF4omg4oiewrDii5UKIyBqb2luIGFsbCBwZXJtdXRhdGlvbnMKIyB0cmlwbGVfYmFrYSA_IGNvbWJpbmF0aW9ucwpqIOKGkCDiiaHih4zima3igoLiip7iioLCsOKWoeKKo-KfnCjima3igoIv4peH4oqe4oqC4oaZMikKCiMgZ2VuZXJhdGUgc29sdXRpb24gZm9yIGdpdmVuIGRpZ2l0IGRpc3RyaWJ1dGlvbgojIGRpZ2l0X2Rpc3RyaWJ1dGlvbiA_IHByb2R1Y3RzCnMg4oaQICgKICDil7Tip4XiiaDiiJ4gICAgICAgIyBwZXJtdXRhdGlvbnMgb2YgZGlnaXRzCiAg4pmt4oKC4omhKGriiaFwIG4pICMgcGVybXV0ZSBtdWx0aXBsaWNhbmQsIG11bHRpcGxpZXIsIHByb2R1Y3QKICDil7TiiqPijYniio_iirgo4oqa4omhYykgIyBjaGVjayBhbGwgaGl0aGVydG8gcGVybXV0YXRpb25zCikKcyBbMiAyIDIgMiAxIDEgMSAwIDBdICMgMsOXMz01CnMgWzIgMiAyIDIgMSAxIDEgMSAwXSAjIDHDlzQ9NQovK-KXtOKKggo=