Add solution for the euler project problem 111.

Author: mindaugl

project_euler/problem_111/__init__.py

@@ -0,0 +1,100 @@
+"""
+Project Euler Problem 111: https://projecteuler.net/problem=111
+
+Primes with Runs
+
+First, note that for sequence of 10 digits, M(4,d) is 8 or 9.
+Start by constructing prime list up to sqrt(n), which are used to check if
+number is prime.
+Then iterate over possible combinations of numbers checking each if prime.
+
+"""
+
+from numpy import sqrt
+
+
+def generate_primes(n: int):
+    """
+    Calculates the list of primes up to and including n.
+
+    >>> generate_primes(6)
+    [2, 3, 5]
+    """
+    primes = [True] * (n + 1)
+    primes[0] = primes[1] = False
+    for i in range(2, int(sqrt(n + 1)) + 1):
+        if primes[i]:
+            j = i * i
+            while j <= n:
+                primes[j] = False
+                j += i
+    primes_list = []
+    for i in range(2, len(primes)):
+        if primes[i]:
+            primes_list += [i]
+    return primes_list
+
+
+def is_prime(n, primes_all):
+    """
+    Check in int n is prime using primes_all list of relatively small primes
+    compared to n.
+
+    >>> is_prime(5, [2, 3])
+    True
+    """
+    return all(n % p != 0 for p in primes_all)
+
+
+def solution(n: int = 10000000000) -> int:
+    """
+    Check each possible combination if it is prime.
+
+
+    >>> solution(10000)
+    273700
+    """
+    primes_all = generate_primes(int(sqrt(n)) + 1)
+    total = 0
+
+    n_zeros = len(str(n)) - 3
+    for i in range(1, 10):
+        for j in range(1, 10):
+            num = int(str(i) + "0" * n_zeros + str(j))
+            if is_prime(num, primes_all):
+                total += num
+
+    one_digit = set()
+    n_dig = len(str(n)) - 2
+    for i in range(1, 10):
+        for j in range(n_dig + 1):
+            for k in range(10):
+                num = int(str(i) * j + str(k) + str(i) * (n_dig - j))
+                if is_prime(num, primes_all):
+                    one_digit.add(i)
+                    total += num
+
+    n_dig = len(str(n)) - 3
+    two_dig = {1, 2, 3, 4, 5, 6, 7, 8, 9} - one_digit
+    for i in list(two_dig):  # main digit
+        for j in range(n_dig + 1):
+            for k in range(n_dig + 1 - j):
+                for m1 in range(10):  # first changing digit
+                    if m1 == 0 and j == 0:
+                        continue
+                    for m2 in range(10):  # second changing digit
+                        num = int(
+                            str(i) * j
+                            + str(m1)
+                            + str(i) * k
+                            + str(m2)
+                            + str(i) * (n_dig - j - k)
+                        )
+                        if is_prime(num, primes_all):
+                            total += num
+
+    return total
+
+
+if __name__ == "__main__":
+    print(f"{solution() = }")