From e040ad2a01d2c7d7524682fb27da99aea663972b Mon Sep 17 00:00:00 2001
From: Iqrar Agalosi Nureyza <misteriqrar@gmail.com>
Date: Mon, 5 Oct 2020 09:57:09 +0700
Subject: [PATCH] Add a solution for Project Euler 49 (#2702)
* added doctests in modular_exponential.py
* added doctests in modular_exponential.py
* added URL link
* updating DIRECTORY.md
* Add problem 49 solution
* updating DIRECTORY.md
* Fix several mistakes
These fixes are intended to follow the CONTRIBUTING.md
* Move the import statements lower
* Update project_euler/problem_49/sol1.py
Co-authored-by: Dhruv <dhruvmanila@gmail.com>
Co-authored-by: github-actions <${GITHUB_ACTOR}@users.noreply.github.com>
Co-authored-by: Dhruv <dhruvmanila@gmail.com>
---
DIRECTORY.md | 2 +
project_euler/problem_49/__init__.py | 0
project_euler/problem_49/sol1.py | 139 +++++++++++++++++++++++++++
3 files changed, 141 insertions(+)
create mode 100644 project_euler/problem_49/__init__.py
create mode 100644 project_euler/problem_49/sol1.py
diff --git a/DIRECTORY.md b/DIRECTORY.md
index 1dd1289ab..a8d00f6cb 100644
--- a/DIRECTORY.md
+++ b/DIRECTORY.md
@@ -633,6 +633,8 @@
* [Sol1](https://github.com/TheAlgorithms/Python/blob/master/project_euler/problem_47/sol1.py)
* Problem 48
* [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 52
* [Sol1](https://github.com/TheAlgorithms/Python/blob/master/project_euler/problem_52/sol1.py)
* Problem 53
diff --git a/project_euler/problem_49/__init__.py b/project_euler/problem_49/__init__.py
new file mode 100644
index 000000000..e69de29bb
diff --git a/project_euler/problem_49/sol1.py b/project_euler/problem_49/sol1.py
new file mode 100644
index 000000000..6c3d69ad0
--- /dev/null
+++ b/project_euler/problem_49/sol1.py
@@ -0,0 +1,139 @@
+"""
+Prime permutations
+
+Problem 49
+
+The arithmetic sequence, 1487, 4817, 8147, in which each of
+the terms increases by 3330, is unusual in two ways:
+(i) each of the three terms are prime,
+(ii) each of the 4-digit numbers are permutations of one another.
+
+There are no arithmetic sequences made up of three 1-, 2-, or 3-digit primes,
+exhibiting this property, but there is one other 4-digit increasing sequence.
+
+What 12-digit number do you form by concatenating the three terms in this sequence?
+
+Solution:
+
+First, we need to generate all 4 digits prime numbers. Then greedy
+all of them and use permutation to form new numbers. Use binary search
+to check if the permutated numbers is in our prime list and include
+them in a candidate list.
+
+After that, bruteforce all passed candidates sequences using
+3 nested loops since we know the answer will be 12 digits.
+The bruteforce of this solution will be about 1 sec.
+"""
+
+from itertools import permutations
+from math import floor, sqrt
+
+
+def is_prime(number: int) -> bool:
+ """
+ function to check whether the number is prime or not.
+ >>> is_prime(2)
+ True
+ >>> is_prime(6)
+ False
+ >>> is_prime(1)
+ False
+ >>> is_prime(-800)
+ False
+ >>> is_prime(104729)
+ True
+ """
+
+ if number < 2:
+ return False
+
+ for i in range(2, floor(sqrt(number)) + 1):
+ if number % i == 0:
+ return False
+
+ return True
+
+
+def search(target: int, prime_list: list) -> bool:
+ """
+ function to search a number in a list using Binary Search.
+ >>> search(3, [1, 2, 3])
+ True
+ >>> search(4, [1, 2, 3])
+ False
+ >>> search(101, list(range(-100, 100)))
+ False
+ """
+
+ left, right = 0, len(prime_list) - 1
+ while left <= right:
+ middle = (left + right) // 2
+ if prime_list[middle] == target:
+ return True
+ elif prime_list[middle] < target:
+ left = middle + 1
+ else:
+ right = middle - 1
+
+ return False
+
+
+def solution():
+ """
+ Return the solution of the problem.
+ >>> solution()
+ 296962999629
+ """
+ prime_list = [n for n in range(1001, 10000, 2) if is_prime(n)]
+ candidates = []
+
+ for number in prime_list:
+ tmp_numbers = []
+
+ for prime_member in permutations(list(str(number))):
+ prime = int("".join(prime_member))
+
+ if prime % 2 == 0:
+ continue
+
+ if search(prime, prime_list):
+ tmp_numbers.append(prime)
+
+ tmp_numbers.sort()
+ if len(tmp_numbers) >= 3:
+ candidates.append(tmp_numbers)
+
+ passed = []
+ for candidate in candidates:
+ length = len(candidate)
+ found = False
+
+ for i in range(length):
+ for j in range(i + 1, length):
+ for k in range(j + 1, length):
+ if (
+ abs(candidate[i] - candidate[j])
+ == abs(candidate[j] - candidate[k])
+ and len(set([candidate[i], candidate[j], candidate[k]])) == 3
+ ):
+ passed.append(
+ sorted([candidate[i], candidate[j], candidate[k]])
+ )
+ found = True
+
+ if found:
+ break
+ if found:
+ break
+ if found:
+ break
+
+ answer = set()
+ for seq in passed:
+ answer.add("".join([str(i) for i in seq]))
+
+ return max([int(x) for x in answer])
+
+
+if __name__ == "__main__":
+ print(solution())