add dp up - down minimum cost for tickets (#7934)

* add dp up - down minimum cost for tickets

* add typints

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* add new tests and checks.

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* add more tests

* add types for the dp function

* Update dynamic_programming/minimum_tickets_cost.py

Co-authored-by: Christian Clauss <cclauss@me.com>

* fix review notes

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* small fix

* Update dynamic_programming/minimum_tickets_cost.py

Co-authored-by: Christian Clauss <cclauss@me.com>

* Update dynamic_programming/minimum_tickets_cost.py

Co-authored-by: Christian Clauss <cclauss@me.com>

* [pre-commit.ci] auto fixes from pre-commit.com hooks

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* fix tests

* Update dynamic_programming/minimum_tickets_cost.py

Co-authored-by: Christian Clauss <cclauss@me.com>

* Update dynamic_programming/minimum_tickets_cost.py

Co-authored-by: pre-commit-ci[bot] <66853113+pre-commit-ci[bot]@users.noreply.github.com>
Co-authored-by: Christian Clauss <cclauss@me.com>

dynamic_programming/minimum_tickets_cost.py

@@ -0,0 +1,129 @@
+"""
+Author  : Alexander Pantyukhin
+Date    : November 1, 2022
+
+Task:
+Given a list of days when you need to travel. Each day is integer 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.
+
+Runtime complexity: O(n)
+
+The implementation was tested on the
+leetcode: https://leetcode.com/problems/minimum-cost-for-tickets/
+
+
+Minimum Cost For Tickets
+Dynamic Programming: up -> down.
+"""
+
+from functools import lru_cache
+
+
+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
+
+    >>> mincost_tickets([2], [2, 90, 150])
+    2
+
+    >>> mincost_tickets([], [2, 90, 150])
+    0
+
+    >>> mincost_tickets('hello', [2, 90, 150])
+    Traceback (most recent call last):
+     ...
+    ValueError: The parameter days should be a list of integers
+
+    >>> mincost_tickets([], 'world')
+    Traceback (most recent call last):
+     ...
+    ValueError: The parameter costs should be a list of three integers
+
+    >>> mincost_tickets([0.25, 2, 3, 4, 5, 6, 7, 8, 9, 10, 30, 31], [2, 90, 150])
+    Traceback (most recent call last):
+     ...
+    ValueError: The parameter days should be a list of integers
+
+    >>> mincost_tickets([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 30, 31], [2, 0.9, 150])
+    Traceback (most recent call last):
+     ...
+    ValueError: The parameter costs should be a list of three integers
+
+    >>> mincost_tickets([-1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 30, 31], [2, 90, 150])
+    Traceback (most recent call last):
+     ...
+    ValueError: All days elements should be greater than 0
+
+    >>> mincost_tickets([2, 367], [2, 90, 150])
+    Traceback (most recent call last):
+     ...
+    ValueError: All days elements should be less than 366
+
+    >>> mincost_tickets([2, 3, 4, 5, 6, 7, 8, 9, 10, 30, 31], [])
+    Traceback (most recent call last):
+     ...
+    ValueError: The parameter costs should be a list of three integers
+
+    >>> mincost_tickets([], [])
+    Traceback (most recent call last):
+     ...
+    ValueError: The parameter costs should be a list of three integers
+
+    >>> mincost_tickets([2, 3, 4, 5, 6, 7, 8, 9, 10, 30, 31], [1, 2, 3, 4])
+    Traceback (most recent call last):
+     ...
+    ValueError: The parameter costs should be a list of three integers
+    """
+
+    # Validation
+    if not isinstance(days, list) or not all(isinstance(day, int) for day in days):
+        raise ValueError("The parameter days should be a list of integers")
+
+    if len(costs) != 3 or not all(isinstance(cost, int) for cost in costs):
+        raise ValueError("The parameter costs should be a list of three integers")
+
+    if len(days) == 0:
+        return 0
+
+    if min(days) <= 0:
+        raise ValueError("All days elements should be greater than 0")
+
+    if max(days) >= 366:
+        raise ValueError("All days elements should be less than 366")
+
+    days_set = set(days)
+
+    @lru_cache(maxsize=None)
+    def dynamic_programming(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 dynamic_programming(1)
+
+
+if __name__ == "__main__":
+    import doctest
+
+    doctest.testmod()