Refactor the collatz conjecture with memoization and safety limits

Author: Facelessism

math/Collatz-Conjecture/Collatz-Conjecture.py

@@ -8,35 +8,90 @@
 print("- Continue until you reach 1")
 print("=" * 50)
 
+MAX_STEPS = 100000
+MAX_VALUE = 10**18
+MAX_INPUT = 10**12
+steps_cache = {1: 0}
+
+def collatz_next(n):
+    return n // 2 if n % 2 == 0 else 3 * n + 1
+
+def get_remaining_sequence(n):
+    seq = []
+    while n != 1:
+        n = collatz_next(n)
+        seq.append(n)
+    return seq
+def collatz_sequence(start):
+    if start in steps_cache:
+        n = start
+        yield n
+        while n != 1:
+            n = collatz_next(n)
+            yield n
+        return
+
+    n = start
+    path = [n]
+    steps = 0
+
+    yield n
+
+    while n != 1 and steps < MAX_STEPS:
+        n = collatz_next(n)
+        steps += 1
+
+        if n > MAX_VALUE:
+            print("\n\n⚠ Computation stopped: safety limit reached")
+            break
+
+        yield n
+        path.append(n)
+
+        if n in steps_cache:
+            for remaining in get_remaining_sequence(n):
+                yield remaining
+            steps += steps_cache[n]
+            break
+
+    total = steps_cache.get(n, 0)
+    for value in reversed(path):
+        total += 1
+        steps_cache[value] = total
+
 while True:
     try:
         number = int(input("\nEnter a positive integer to start: "))
         if number > 0:
+            if number > MAX_INPUT:
+                print(f"Input too large! Maximum allowed: {MAX_INPUT:,}")
+                continue
             break
         else:
             print("Please enter a positive integer!")
     except ValueError:
         print("Please enter a valid number!")
 
 original_number = number
-sequence = [number]
-steps = 0
 
 print(f"\nStarting with: {number}")
 print("\nSequence:")
-print(number, end="")
-
-while number != 1:
-    if number % 2 == 0:
-        number = number // 2
-    else:
-        number = 3 * number + 1
-    
-    sequence.append(number)
+
+sequence = []
+steps = 0
+max_value = number
+
+gen = collatz_sequence(number)
+
+first = next(gen)
+print(first, end="")
+sequence.append(first)
+
+for num in gen:
+    sequence.append(num)
     steps += 1
-    
-    print(f" → {number}", end="")
-    
+    max_value = max(max_value, num)
+    print(f" → {num}", end="")
     if steps % 10 == 0:
         print()
 
@@ -46,7 +101,7 @@
 print(f"Starting number: {original_number}")
 print(f"Total steps: {steps}")
 print(f"Sequence length: {len(sequence)}")
-print(f"Highest number reached: {max(sequence)}")
+print(f"Highest number reached: {max_value}")
 
 if len(sequence) <= 100:
     view_details = input("\nWould you like to see step-by-step details? (yes/no): ").lower()