add dp up - down minimum cost for tickets

dynamic_programming/minimum_tickets_cost.py

@@ -0,0 +1,61 @@
+"""
+Author  : Alexander Pantyukhin
+Date    : November 1, 2022
+
+Task:
+Given a list of days when you need to travel. Each day is int from 1 to 365.
+You are able to use tickets for 1 day, 7 days and 30 days.
+Each ticket has a cost.
+
+Find the minimum cost you need to travel every day in the given list of days.
+
+Implementation notes:
+implementation Dynamic Programming up bottom approach.
+
+The implementation was tested on the
+leetcode: https://leetcode.com/problems/minimum-cost-for-tickets/
+"""
+
+from typing import List
+
+"""
+Minimum Cost For Tickets
+Dynamic Programming: up -> down.
+"""
+
+
+def mincost_tickets(days: list[int], costs: list[int]) -> int:
+    """
+    >>> mincost_tickets([1,4,6,7,8,20], [2,7,15])
+    11
+    >>> mincost_tickets([1,2,3,4,5,6,7,8,9,10,30,31], [2,7,15])
+    17
+    >>> mincost_tickets([1,2,3,4,5,6,7,8,9,10,30,31], [2,90,150])
+    24
+    """
+
+    from functools import lru_cache
+
+    days_set = set(days)
+
+    @lru_cache(maxsize=None)
+    def dp(index: int) -> int:
+        if index > 365:
+            return 0
+
+        if index not in days_set:
+            return dp(index + 1)
+
+        return min(
+            costs[0] + dp(index + 1),
+            costs[1] + dp(index + 7),
+            costs[2] + dp(index + 30),
+        )
+
+    return dp(1)
+
+
+if __name__ == "__main__":
+    import doctest
+
+    doctest.testmod()