Hacktoberfest: Add a solution for Project Euler 50

DIRECTORY.md

@@ -635,6 +635,8 @@
     * [Sol1](https://github.com/TheAlgorithms/Python/blob/master/project_euler/problem_48/sol1.py)
   * Problem 49
     * [Sol1](https://github.com/TheAlgorithms/Python/blob/master/project_euler/problem_49/sol1.py)
+  * Problem 50
+    * [Sol1](https://github.com/TheAlgorithms/Python/blob/master/project_euler/problem_50/sol1.py)
   * Problem 52
     * [Sol1](https://github.com/TheAlgorithms/Python/blob/master/project_euler/problem_52/sol1.py)
   * Problem 53

project_euler/problem_50/sol1.py

@@ -0,0 +1,107 @@
+"""
+Consecutive prime sum
+
+Problem 50
+https://projecteuler.net/problem=50
+
+The prime 41, can be written as the sum of six consecutive primes:
+
+41 = 2 + 3 + 5 + 7 + 11 + 13
+
+This is the longest sum of consecutive primes that adds to
+a prime below one-hundred.
+
+The longest sum of consecutive primes below one-thousand that adds to a prime,
+contains 21 terms, and is equal to 953.
+
+Which prime, below one-million, can be written as the sum of
+the most consecutive primes?
+
+Solution:
+
+First of all, we need to generate all prime numbers
+from 2 to the closest prime number with 1000000.
+Then, use sliding window to get the answer.
+"""
+
+from math import floor, sqrt
+
+
+def is_prime(number: int) -> bool:
+    """
+    function to check whether a number is a prime or not.
+    >>> is_prime(2)
+    True
+    >>> is_prime(6)
+    False
+    >>> is_prime(1)
+    False
+    >>> is_prime(-7000)
+    False
+    >>> is_prime(104729)
+    True
+    """
+
+    if number < 2:
+        return False
+
+    for n in range(2, floor(sqrt(number)) + 1):
+        if number % n == 0:
+            return False
+
+    return True
+
+
+def solution(constraint: int = 10 ** 6):
+    """
+    Return the problem solution.
+    >>> solution(10000)
+    9521
+    >>> solution(1000)
+    953
+    >>> solution(50)
+    58
+    """
+
+    prime_list = [2] + [x for x in range(3, constraint, 2) if is_prime(x)]
+
+    cumulative_sum = []
+    tmp = 0
+    for prime in prime_list:
+        tmp += prime
+        if tmp < constraint:
+            cumulative_sum.append(tmp)
+        else:
+            break
+
+    upper_limit_idx = 0
+    for i in range(len(prime_list)):
+        if prime_list[i] < constraint:
+            upper_limit_idx = i
+        else:
+            break
+
+    max_count = -1
+    answer = 0
+    for number in reversed(cumulative_sum):
+        count_prime = cumulative_sum.index(number) + 1
+
+        if not is_prime(number):
+            tmp = number
+
+            for i in range(upper_limit_idx):
+                count_prime -= 1
+                tmp -= prime_list[i]
+
+                if is_prime(tmp) or tmp < 0:
+                    break
+
+        if max_count < count_prime:
+            max_count = count_prime
+            answer = tmp
+
+    return answer
+
+
+if __name__ == "__main__":
+    print(solution())