1011 Capacity To Ship Packages Within D Days.py

Author: rajeevranjancom

1011 Capacity To Ship Packages Within D Days.py

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+#!/usr/bin/python3
+"""
+A conveyor belt has packages that must be shipped from one port to another
+within D days.
+
+The i-th package on the conveyor belt has a weight of weights[i].  Each day, we
+load the ship with packages on the conveyor belt (in the order given by
+weights). We may not load more weight than the maximum weight capacity of the
+ship.
+
+Return the least weight capacity of the ship that will result in all the
+packages on the conveyor belt being shipped within D days.
+
+Example 1:
+
+Input: weights = [1,2,3,4,5,6,7,8,9,10], D = 5
+Output: 15
+Explanation:
+A ship capacity of 15 is the minimum to ship all the packages in 5 days like
+this:
+1st day: 1, 2, 3, 4, 5
+2nd day: 6, 7
+3rd day: 8
+4th day: 9
+5th day: 10
+
+Note that the cargo must be shipped in the order given, so using a ship of
+capacity 14 and splitting the packages into parts like (2, 3, 4, 5), (1, 6, 7),
+(8), (9), (10) is not allowed.
+Example 2:
+
+Input: weights = [3,2,2,4,1,4], D = 3
+Output: 6
+Explanation:
+A ship capacity of 6 is the minimum to ship all the packages in 3 days like
+this:
+1st day: 3, 2
+2nd day: 2, 4
+3rd day: 1, 4
+Example 3:
+
+Input: weights = [1,2,3,1,1], D = 4
+Output: 3
+Explanation:
+1st day: 1
+2nd day: 2
+3rd day: 3
+4th day: 1, 1
+
+Note:
+
+1 <= D <= weights.length <= 50000
+1 <= weights[i] <= 500
+"""
+from tying import List
+
+
+class Solution:
+    def shipWithinDays(self, weights: List[int], D: int) -> int:
+        """
+        Must respect conveyor's order
+
+        Binary search on value range (max, sum)
+        """
+        lo = max(weights)
+        hi = sum(weights)
+        while lo < hi:
+            mid = (lo + hi) // 2
+            cnt = 1
+            cur = 0
+            for w in weights:
+                cur += w
+                if cur > mid:
+                    cnt += 1
+                    cur = w
+                    
+            if cnt > D:
+                lo = mid + 1
+            else:
+                hi = mid
+
+        return lo