Add Egg Drop algorithm

dynamic_programming/egg_drop.py

@@ -0,0 +1,46 @@
+"""
+Egg Dropping Problem is a well-known problem in computer science.
+The task is to find the minimum number of attempts required in the
+worst case to find the highest floor from which an egg can be dropped
+without breaking, given a certain number of floors and eggs.
+
+Wikipedia: https://en.wikipedia.org/wiki/Dynamic_programming#Egg_dropping_puzzle
+"""
+
+
+def egg_drop(eggs: int, floors: int) -> int:
+    """
+    Calculate the minimum number of attempts required in the worst case
+    to determine the highest floor from which an egg can be dropped
+    without breaking it.
+
+    Parameters:
+    eggs (int): Number of eggs available.
+    floors (int): Number of floors to test.
+
+    Returns:
+    int: Minimum number of attempts required in the worst case.
+
+    Example:
+    >>> egg_drop(2, 10)
+    4
+
+    >>> egg_drop(3, 14)
+    4
+    """
+    # Initialize dp table with integers
+    dp = [[0 for _ in range(floors + 1)] for _ in range(eggs + 1)]
+
+    # Fill dp table for one egg (we have to try all floors)
+    for i in range(1, floors + 1):
+        dp[1][i] = i
+
+    # Fill the rest of the dp table
+    for e in range(2, eggs + 1):
+        for f in range(1, floors + 1):
+            dp[e][f] = floors + 1  # Start with an arbitrary large integer
+            for k in range(1, f + 1):
+                res = 1 + max(dp[e - 1][k - 1], dp[e][f - k])
+                dp[e][f] = min(dp[e][f], res)
+
+    return dp[eggs][floors]