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math/README.md

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+## math, logic, dynamic programming
+
+<br>
+
+### dynamic programming
+
+<br>
+
+* take a recursive algorithm and cache overlapping problems (repeated calls).
+* the runtime is given by the number of calls.
+* **top-down**: how can we divide the problem into sub-problems?
+    * top-down dynamic programming is called **memoization**.
+* **bottom-up**: solve for a simple case, then figure out for more elements.
+
+<br>
+
+---
+
+### examples
+
+<br>
+
+```python
+python3 fibonacci.py
+
+Testing fibonacci
+Fibonacci of 10: 55
+```
+
+<br>
+
+```python
+python playing_with_math.py
+
+Greatest common divider of 21 and 7 is 7
+Prime factors of 21 are [3, 7]
+```

math/check_sudoku_board.py

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+#!/usr/bin/env python3
+# -*- coding: utf-8 -*-
+# author: bt3gl
+
+
+```
+Determine if a 9 x 9 Sudoku board is valid. Only the filled cells need to be validated according to the following rules:
+
+- Each row must contain the digits 1-9 without repetition.
+- Each column must contain the digits 1-9 without repetition.
+- Each of the nine 3 x 3 sub-boxes of the grid must contain the digits 1-9 without repetition.
+
+Input: board = 
+[["5","3",".",".","7",".",".",".","."]
+,["6",".",".","1","9","5",".",".","."]
+,[".","9","8",".",".",".",".","6","."]
+,["8",".",".",".","6",".",".",".","3"]
+,["4",".",".","8",".","3",".",".","1"]
+,["7",".",".",".","2",".",".",".","6"]
+,[".","6",".",".",".",".","2","8","."]
+,[".",".",".","4","1","9",".",".","5"]
+,[".",".",".",".","8",".",".","7","9"]]
+Output: true
+```
+
+def is_valid_sudoku(board) -> bool:
+        
+  N = 9
+
+  rows = [set() for _ in range(N)]
+  cols = [set() for _ in range(N)]
+  boxes = [set() for _ in range(N)]
+            
+  for r in range(N):
+    for c in range(N):
+      val = board[r][c]
+      if val == '.':
+        continue
+                
+      if val in rows[r]:
+        return False
+      rows[r].add(val)
+
+      if val in cols[c]:
+        return False
+      cols[c].add(val)
+
+      index = (r // 3) * 3 + c // 3
+      if val in boxes[index]:
+        return False
+      boxes[index].add(val)
+        
+  return True

math/fibonacci.py

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+#!/usr/bin/env python3
+# -*- coding: utf-8 -*-
+# author: bt3gl
+
+def fibonacci(n):
+    """ Calculate the nth Fibonacci number """
+    if n == 0 or n == 1:
+        return n
+    return fibonacci(n - 1) + fibonacci(n - 2)
+
+
+if __name__ == '__main__':
+
+    print('Testing fibonacci')
+    n = 10
+    print(f'Fibonacci of {n}: {fibonacci(n)}')

math/happy_number.py

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+#!/usr/bin/env python3
+# -*- coding: utf-8 -*-
+# author: bt3gl
+
+
+def get_next(n):
+  
+  total_sum = 0
+  while n > 0:
+    n, digit = divmod(n, 10)
+    total_sum += digit**2
+
+  return total_sum
+
+
+def is_happy(self, n: int) -> bool:
+
+  seen = set()
+  while n != 1 and n not in seen:
+    seen.add(n)
+    n = get_next(n)
+
+  return n == 1
+    

math/playing_with_math.py

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+#!/usr/bin/env python3
+# -*- coding: utf-8 -*-
+# author: bt3gl
+
+
+import math
+import random
+
+
+def find_greatest_common_divider(a, b) -> int:
+    '''Implements the greatest common divider algorithm '''
+    
+    while(b != 0):
+        result = b
+        a, b = b, a % b
+        
+    return result
+
+
+def _is_prime(number) -> bool:
+    '''Check if a number is prime '''
+
+    if number < 2:
+        return False
+
+    for i in range(2, int(math.sqrt(number))):
+        if number % i == 0:
+            return False
+    
+    return True
+
+
+def find_prime_factors(number) -> list:
+    '''Find prime factors of a number '''
+    
+    divisors = [d for d in range(2, number//2 + 1) if number % d == 0]
+    primes = [d for d in divisors if _is_prime(d)]
+
+    return primes
+
+
+
+if __name__ == '__main__':
+
+    n1 = 21
+    n2 = 7
+
+    print(f'Greatest common divider of {n1} and {n2} is {find_greatest_common_divider(n1, n2)}')
+    print(f'Prime factors of {n1} are {find_prime_factors(n1)}')
+
+