From fd4ff495d99dcb611aff57ca00d3b9c0d570d95f Mon Sep 17 00:00:00 2001
From: felixm <mail@felixm.de>
Date: Sun, 1 Oct 2023 20:19:41 +0200
Subject: [PATCH] Solve problem 111 and fix bug in lib prime.

---
 python/e111.py      | 46 +++++++++++++++++++++++++++++++++++++++++++++
 python/lib_prime.py |  7 ++++++-
 2 files changed, 52 insertions(+), 1 deletion(-)
 create mode 100644 python/e111.py

diff --git a/python/e111.py b/python/e111.py
new file mode 100644
index 0000000..14137c2
--- /dev/null
+++ b/python/e111.py
@@ -0,0 +1,46 @@
+from lib_prime import is_prime_rabin_miller as is_prime
+
+
+def get_permutations(number: str, number_permutations: int, start_index = 0):
+    """ Returns number permutated at number_permutations locations. """
+    if number_permutations == 0:
+        yield int(number)
+    else:
+        numbers = list("0123456789")
+        base = list(str(number))
+        for i in range(start_index, len(base)):
+            digit_stored = base[i]
+            for n in numbers:
+                if n == digit_stored:
+                    continue
+                base[i] = n
+                if base[0] == "0":
+                    continue
+                for p in get_permutations("".join(base), number_permutations - 1, i):
+                    yield p
+            base[i] = digit_stored
+
+
+def euler_111():
+    result = 0
+    n = 10
+    for d in range(10):
+        subresult = 0
+        base = "".join([str(d) for _ in range(n)])
+        for p in get_permutations(base, 1):
+            if is_prime(p):
+                subresult += p
+        if subresult == 0:
+            # d in [0, 2, 8] requires two permutations to yield at least one prime
+            for p in get_permutations(base, 2):
+                if is_prime(p):
+                    subresult += p
+        assert subresult > 0, "More than to permutations required to yield prime"
+        result += subresult
+    return result
+
+
+if __name__ == "__main__":
+    solution = euler_111()
+    print("e111.py: " + str(solution))
+    assert(solution == 612407567715)
diff --git a/python/lib_prime.py b/python/lib_prime.py
index 4d194c4..1a11b30 100644
--- a/python/lib_prime.py
+++ b/python/lib_prime.py
@@ -68,6 +68,11 @@ def is_prime(n):
 
 def is_prime_rabin_miller(number):
     """ Rabin-Miller Primality Test """
+    witnesses = [2, 3, 5, 7, 11, 13, 17, 23, 29, 31, 37, 41, 43, 47, 53]
+
+    if number in witnesses:
+        return True
+
     if number % 6 not in [1,5]:
         return False
 
@@ -76,7 +81,7 @@ def is_prime_rabin_miller(number):
         s //= 2
         r += 1
 
-    for witness in [2, 3, 5, 7, 11, 13, 17, 23, 29, 31, 37, 41, 43, 47, 53]:
+    for witness in witnesses:
         remainder = pow(witness, s, number)
         if remainder == 1:
             continue