Add Egg Dropping Problem (Dynamic Programming)

dynamic_programming/egg_dropping.py

@@ -0,0 +1,60 @@
+"""
+Dynamic Programming - Egg Dropping Problem
+
+The Egg Dropping Puzzle:
+------------------------
+You are given k eggs and n floors. Find the minimum number of trials needed
+in the worst case to find the critical floor from which the egg starts breaking.
+
+Reference:
+https://en.wikipedia.org/wiki/Dynamic_programming#Egg_dropping_puzzle
+
+>>> egg_drop(1, 10)
+10
+>>> egg_drop(2, 10)
+4
+>>> egg_drop(3, 14)
+4
+"""
+
+from functools import cache
+
+
+@cache
+def egg_drop(eggs: int, floors: int) -> int:
+    """
+    Compute the minimum number of trials needed in the worst case with
+    a given number of eggs and floors.
+
+    Args:
+        eggs (int): number of eggs
+        floors (int): number of floors
+
+    Returns:
+        int: minimum number of trials required
+
+    >>> egg_drop(1, 5)
+    5
+    >>> egg_drop(2, 6)
+    3
+    >>> egg_drop(3, 14)
+    4
+    """
+    if floors in {0, 1}:
+        return floors
+    if eggs == 1:
+        return floors
+
+    min_trials = float("inf")
+    for floor in range(1, floors + 1):
+        # If egg breaks -> check below floor
+        # If egg doesn't break -> check above floor
+        trials = 1 + max(egg_drop(eggs - 1, floor - 1), egg_drop(eggs, floors - floor))
+        min_trials = min(min_trials, trials)
+    return int(min_trials)
+
+
+if __name__ == "__main__":
+    import doctest
+
+    doctest.testmod()