Refresh PR #2216

DIRECTORY.md

@@ -206,8 +206,10 @@
   * [Heaps Algorithm](https://github.com/TheAlgorithms/Python/blob/master/divide_and_conquer/heaps_algorithm.py)
   * [Heaps Algorithm Iterative](https://github.com/TheAlgorithms/Python/blob/master/divide_and_conquer/heaps_algorithm_iterative.py)
   * [Inversions](https://github.com/TheAlgorithms/Python/blob/master/divide_and_conquer/inversions.py)
+  * [Kth Order Statistic](https://github.com/TheAlgorithms/Python/blob/master/divide_and_conquer/kth_order_statistic.py)
   * [Max Subarray Sum](https://github.com/TheAlgorithms/Python/blob/master/divide_and_conquer/max_subarray_sum.py)
   * [Mergesort](https://github.com/TheAlgorithms/Python/blob/master/divide_and_conquer/mergesort.py)
+  * [Peak](https://github.com/TheAlgorithms/Python/blob/master/divide_and_conquer/peak.py)
   * [Power](https://github.com/TheAlgorithms/Python/blob/master/divide_and_conquer/power.py)
   * [Strassen Matrix Multiplication](https://github.com/TheAlgorithms/Python/blob/master/divide_and_conquer/strassen_matrix_multiplication.py)
 
@@ -390,6 +392,7 @@
   * [Chudnovsky Algorithm](https://github.com/TheAlgorithms/Python/blob/master/maths/chudnovsky_algorithm.py)
   * [Collatz Sequence](https://github.com/TheAlgorithms/Python/blob/master/maths/collatz_sequence.py)
   * [Combinations](https://github.com/TheAlgorithms/Python/blob/master/maths/combinations.py)
+  * [Decimal Isolate](https://github.com/TheAlgorithms/Python/blob/master/maths/decimal_isolate.py)
   * [Entropy](https://github.com/TheAlgorithms/Python/blob/master/maths/entropy.py)
   * [Eulers Totient](https://github.com/TheAlgorithms/Python/blob/master/maths/eulers_totient.py)
   * [Explicit Euler](https://github.com/TheAlgorithms/Python/blob/master/maths/explicit_euler.py)
@@ -493,6 +496,7 @@
   * [Autocomplete Using Trie](https://github.com/TheAlgorithms/Python/blob/master/other/autocomplete_using_trie.py)
   * [Binary Exponentiation](https://github.com/TheAlgorithms/Python/blob/master/other/binary_exponentiation.py)
   * [Binary Exponentiation 2](https://github.com/TheAlgorithms/Python/blob/master/other/binary_exponentiation_2.py)
+  * [Davis–Putnam–Logemann–Loveland](https://github.com/TheAlgorithms/Python/blob/master/other/davis–putnam–logemann–loveland.py)
   * [Detecting English Programmatically](https://github.com/TheAlgorithms/Python/blob/master/other/detecting_english_programmatically.py)
   * [Dijkstra Bankers Algorithm](https://github.com/TheAlgorithms/Python/blob/master/other/dijkstra_bankers_algorithm.py)
   * [Doomsday](https://github.com/TheAlgorithms/Python/blob/master/other/doomsday.py)
@@ -582,6 +586,7 @@
   * Problem 014
     * [Sol1](https://github.com/TheAlgorithms/Python/blob/master/project_euler/problem_014/sol1.py)
     * [Sol2](https://github.com/TheAlgorithms/Python/blob/master/project_euler/problem_014/sol2.py)
+    * [Sol3](https://github.com/TheAlgorithms/Python/blob/master/project_euler/problem_014/sol3.py)
   * Problem 015
     * [Sol1](https://github.com/TheAlgorithms/Python/blob/master/project_euler/problem_015/sol1.py)
   * Problem 016
@@ -660,6 +665,8 @@
     * [Sol1](https://github.com/TheAlgorithms/Python/blob/master/project_euler/problem_048/sol1.py)
   * Problem 049
     * [Sol1](https://github.com/TheAlgorithms/Python/blob/master/project_euler/problem_049/sol1.py)
+  * Problem 050
+    * [Sol1](https://github.com/TheAlgorithms/Python/blob/master/project_euler/problem_050/sol1.py)
   * Problem 051
     * [Sol1](https://github.com/TheAlgorithms/Python/blob/master/project_euler/problem_051/sol1.py)
   * Problem 052
@@ -681,6 +688,8 @@
     * [Sol1](https://github.com/TheAlgorithms/Python/blob/master/project_euler/problem_062/sol1.py)
   * Problem 063
     * [Sol1](https://github.com/TheAlgorithms/Python/blob/master/project_euler/problem_063/sol1.py)
+  * Problem 064
+    * [Sol1](https://github.com/TheAlgorithms/Python/blob/master/project_euler/problem_064/sol1.py)
   * Problem 065
     * [Sol1](https://github.com/TheAlgorithms/Python/blob/master/project_euler/problem_065/sol1.py)
   * Problem 067
@@ -694,6 +703,7 @@
     * [Sol2](https://github.com/TheAlgorithms/Python/blob/master/project_euler/problem_072/sol2.py)
   * Problem 074
     * [Sol1](https://github.com/TheAlgorithms/Python/blob/master/project_euler/problem_074/sol1.py)
+    * [Sol2](https://github.com/TheAlgorithms/Python/blob/master/project_euler/problem_074/sol2.py)
   * Problem 075
     * [Sol1](https://github.com/TheAlgorithms/Python/blob/master/project_euler/problem_075/sol1.py)
   * Problem 076
@@ -718,6 +728,8 @@
     * [Sol1](https://github.com/TheAlgorithms/Python/blob/master/project_euler/problem_119/sol1.py)
   * Problem 120
     * [Sol1](https://github.com/TheAlgorithms/Python/blob/master/project_euler/problem_120/sol1.py)
+  * Problem 123
+    * [Sol1](https://github.com/TheAlgorithms/Python/blob/master/project_euler/problem_123/sol1.py)
   * Problem 125
     * [Sol1](https://github.com/TheAlgorithms/Python/blob/master/project_euler/problem_125/sol1.py)
   * Problem 173
@@ -726,12 +738,16 @@
     * [Sol1](https://github.com/TheAlgorithms/Python/blob/master/project_euler/problem_174/sol1.py)
   * Problem 191
     * [Sol1](https://github.com/TheAlgorithms/Python/blob/master/project_euler/problem_191/sol1.py)
+  * Problem 203
+    * [Sol1](https://github.com/TheAlgorithms/Python/blob/master/project_euler/problem_203/sol1.py)
   * Problem 206
     * [Sol1](https://github.com/TheAlgorithms/Python/blob/master/project_euler/problem_206/sol1.py)
   * Problem 207
     * [Sol1](https://github.com/TheAlgorithms/Python/blob/master/project_euler/problem_207/sol1.py)
   * Problem 234
     * [Sol1](https://github.com/TheAlgorithms/Python/blob/master/project_euler/problem_234/sol1.py)
+  * Problem 301
+    * [Sol1](https://github.com/TheAlgorithms/Python/blob/master/project_euler/problem_301/sol1.py)
   * Problem 551
     * [Sol1](https://github.com/TheAlgorithms/Python/blob/master/project_euler/problem_551/sol1.py)
 
@@ -740,6 +756,7 @@
   * [Half Adder](https://github.com/TheAlgorithms/Python/blob/master/quantum/half_adder.py)
   * [Not Gate](https://github.com/TheAlgorithms/Python/blob/master/quantum/not_gate.py)
   * [Quantum Entanglement](https://github.com/TheAlgorithms/Python/blob/master/quantum/quantum_entanglement.py)
+  * [Ripple Adder Classic](https://github.com/TheAlgorithms/Python/blob/master/quantum/ripple_adder_classic.py)
   * [Single Qubit Measure](https://github.com/TheAlgorithms/Python/blob/master/quantum/single_qubit_measure.py)
 
 ## Scheduling

project_euler/problem_014/sol3.py

@@ -0,0 +1,106 @@
+#!/usr/bin/env python
+from typing import Tuple
+
+"""
+Collatz conjecture: start with any positive integer n. Next term obtained from
+the previous term as follows:
+If the previous term is even, the next term is one half the previous term.
+If the previous term is odd, the next term is 3 times the previous term plus 1.
+The conjecture states the sequence will always reach 1 regardless of starting
+n.
+Problem Statement:
+The following iterative sequence is defined for the set of positive integers:
+    n → n/2 (n is even)
+    n → 3n + 1 (n is odd)
+Using the rule above and starting with 13, we generate the following sequence:
+    13 → 40 → 20 → 10 → 5 → 16 → 8 → 4 → 2 → 1
+It can be seen that this sequence (starting at 13 and finishing at 1) contains
+10 terms. Although it has not been proved yet (Collatz Problem), it is thought
+that all starting numbers finish at 1.
+Which starting number, under one million, produces the longest chain?
+"""
+
+# we are going to avoid repeat computations by creating a knowledge base
+# where we store the length of all collatz chains we calculated so far
+
+knowledge = {1: 1}
+
+
+# a single step in a collatz chain
+def collatz(n: int) -> int:
+    """
+    Calculates a single step in a collatz chain.
+
+    >>> collatz(13)
+    40
+    >>> collatz(40)
+    20
+    >>> collatz(5)
+    16
+    """
+    if n % 2 == 0:
+        return n // 2
+    else:
+        return 3 * n + 1
+
+
+def calculate_chain(n: int) -> None:
+    """
+    Calculates a collatz chain of a certain number. This calculation is halted
+    whenever we find a key with a known collatz chain in our knowledge base.
+    This function has no return value and doctests can't measure side effects,
+    so we can't do doctests on this function.
+    """
+    entries = []
+    while n not in knowledge:
+        entries.append(n)
+        n = collatz(n)
+    chain_size = knowledge[n]
+    for i in entries[::-1]:
+        chain_size += 1
+        knowledge[i] = chain_size
+
+
+def solution(m: int = 1000000, extra_info: bool = False) -> Tuple[int, int]:
+    """
+    Returns the number under n that generates the longest Collatz sequence.
+
+    >>> solution(1000000, True)
+    (837799, 525)
+    >>> solution(200, True)
+    (171, 125)
+    >>> solution(5000, True)
+    (3711, 238)
+    >>> solution(15000, True)
+    (13255, 276)
+    """
+    max_chain = (1, 1)
+    for i in range(1, m + 1):
+        calculate_chain(i)
+        # we can use knowledge[i] because calculate_chain
+        # by definition already adds the key we specified to the
+        # knowledge base
+        if max_chain[1] < knowledge[i]:
+            max_chain = (i, knowledge[i])
+
+    if extra_info:
+        return max_chain
+    else:
+        return max_chain[0]
+
+
+if __name__ == "__main__":
+    print(
+        """
+    calculate the number with the longest collatz chain
+    in the range between 1 and the following number:
+          """
+    )
+    input_number = int(input().strip())
+    number, chain_length = solution(input_number, True)
+    print(
+        f"""
+    the maximum collatz chain of all numbers between 1 and {input_number} is
+    {chain_length}, starting with the number {number}
+          """
+    )