Update README.md

math/README.md

@@ -2,26 +2,173 @@
 
 <br>
 
+* when dealing with floating point numbers, take note of rounding mistakes. consider using epsilon comparisons instead of equality checks (`abs(x - y) <= 1e-6` instead of `x == y`).
+
 <br>
 
 ---
 
-### some examples in this dir
+### fibonnaci
+
+<br>
+
+* check the dynamic programming chapter to learn how to solve this with memoization.
 
 <br>
 
 ```python
-python3 fibonacci.py
+def fibonacci(n):
 
-Testing fibonacci
-Fibonacci of 10: 55
+    if n == 0 or n == 1:
+        return n
+    return fibonacci(n - 1) + fibonacci(n - 2)
 ```
 
 <br>
 
-```python
-python playing_with_math.py
+---
+
+### determine whether a sudoku board is valid
+
+<br>
+
+
+<br>
+
+```python
+
+'''
+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
 
-Greatest common divider of 21 and 7 is 7
-Prime factors of 21 are [3, 7]
+```
+
+<br>
+
+---
+
+### check if happy number
+
+<br>
+
+```python
+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
+```
+
+
+<br>
+
+---
+
+### get a row in a pascal triangle
+
+<br>
+
+```python
+def get_row(self, row: int) -> list[int]:
+        
+        if row == 0: 
+            return [1]
+	
+        result = self.get_row(row - 1)
+        
+        return [1] + [sum(_) for _ in zip(result, result[1:])] + [1]
+```
+
+<br>
+
+---
+
+### work with primes
+
+<br>
+
+```python
+import math
+import random
+
+
+def find_greatest_common_divider(a, b) -> int:
+    
+    while(b != 0):
+        result = b
+        a, b = b, a % b
+        
+    return result
+
+
+def _is_prime(number) -> bool:
+
+    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:
+    
+    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
 ```