983 Minimum Cost For Tickets.py

Author: rajeevranjancom

983 Minimum Cost For Tickets.py

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+#!/usr/bin/python3
+"""
+In a country popular for train travel, you have planned some train travelling
+one year in advance.  The days of the year that you will travel is given as an
+array days.  Each day is an integer from 1 to 365.
+
+Train tickets are sold in 3 different ways:
+
+a 1-day pass is sold for costs[0] dollars;
+a 7-day pass is sold for costs[1] dollars;
+a 30-day pass is sold for costs[2] dollars.
+The passes allow that many days of consecutive travel.  For example, if we get
+a 7-day pass on day 2, then we can travel for 7 days: day 2, 3, 4, 5, 6, 7, and
+8.
+
+Return the minimum number of dollars you need to travel every day in the given
+list of days.
+
+Example 1:
+
+Input: days = [1,4,6,7,8,20], costs = [2,7,15]
+Output: 11
+Explanation:
+For example, here is one way to buy passes that lets you travel your travel plan:
+On day 1, you bought a 1-day pass for costs[0] = $2, which covered day 1.
+On day 3, you bought a 7-day pass for costs[1] = $7, which covered days 3, 4, ..., 9.
+On day 20, you bought a 1-day pass for costs[0] = $2, which covered day 20.
+In total you spent $11 and covered all the days of your travel.
+Example 2:
+
+Input: days = [1,2,3,4,5,6,7,8,9,10,30,31], costs = [2,7,15]
+Output: 17
+Explanation:
+For example, here is one way to buy passes that lets you travel your travel plan:
+On day 1, you bought a 30-day pass for costs[2] = $15 which covered days 1, 2, ..., 30.
+On day 31, you bought a 1-day pass for costs[0] = $2 which covered day 31.
+In total you spent $17 and covered all the days of your travel.
+
+Note:
+
+1 <= days.length <= 365
+1 <= days[i] <= 365
+days is in strictly increasing order.
+costs.length == 3
+1 <= costs[i] <= 1000
+"""
+from typing import List
+
+
+class Solution:
+    def mincostTickets(self, days: List[int], costs: List[int]) -> int:
+        """
+        Iterate backward.
+
+        Why does iterate backward work? Currrent min depends on the future mins
+
+        Let F[i] be the min cost at day i, covering all trips from i to 365
+        F[i] = min(F[i + d] + c for d, c in zip([1, 7, 30], costs))
+        If day i is not travel day, then wait until i + k that is a travel day
+
+        O(365)
+        """
+        F = [float("inf") for _ in range(366 + 30)]
+        for i in range(366, 366 + 30):
+            F[i] = 0
+
+        days_set = set(days)
+        for i in range(365, 0, -1):
+            if i not in days_set:
+                F[i] = F[i+1]
+            else:
+                F[i] = min(
+                    c + F[i+d]
+                    for d, c in zip([1, 7, 30], costs)
+                )
+
+        return F[1]
+
+    def mincostTickets_error(self, days: List[int], costs: List[int]) -> int:
+        """
+        Iterate backward on days
+        O(30 * |days|)
+
+        Iterate throughout the year is more elegant
+        Need buffer day
+        """
+        n = len(days)
+        F = [float("inf") for _ in range(n)]
+        F[-1] = costs[0]
+        for i in range(n-2, -1, -1):
+            for j in range(i+1, n):
+                delta = days[j] - days[i]
+                if delta <= 1:
+                    F[i] = min(F[i], costs[0] + F[j])
+                if delta <= 7:
+                    F[i] = min(F[i], costs[1] + F[j])
+                if delta <= 30:
+                    F[i] = min(F[i], costs[2] + F[j])
+                else:
+                    break
+        return F[0]
+
+    def mincostTickets_error(self, days: List[int], costs: List[int]) -> int:
+        """
+        dp
+        Let F[i] be the min cost at day i, covering all trips from day 1 to i
+        For 30-day ticiekt, iterate forward all 30 days?
+        How to express idle date? Same as previous.
+
+        Why does iterate forward fail? Because future min does not depends on the
+        current min. Current higher cost may contribtue to future lower cost.
+        """
+        F = [float("inf") for _ in range(365 + 1)]
+        F[0] = 0
+        days_set = set(days)
+        for i in range(1, 366):
+            if i not in days_set:
+                F[i] = F[i-1]
+            else:
+                # iterate forward does not work
+                F[i] = min(F[i], F[i-1] + costs[0])
+
+
+if __name__ == "__main__":
+    assert Solution().mincostTickets([1,4,6,7,8,20], [2,7,15]) == 11