Leetcode 1011

Author: Kondareddy1209

Leetcode/Leetcode_1011.py

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+"""
+LeetCode 1011. Capacity To Ship Packages Within D Days
+
+Problem:
+Given an array of package weights and an integer days,
+return the least weight capacity of the ship that will
+result in all the packages being shipped within the given days.
+
+Approach:
+Binary Search on Answer
+
+Search Space:
+- Minimum capacity = max(weights)
+  (because the ship must be able to carry the heaviest package)
+
+- Maximum capacity = sum(weights)
+  (because the ship can carry all packages in one day)
+
+For each candidate capacity (mid):
+- Calculate how many days are required to ship all packages.
+- If required days <= given days:
+    Capacity works, try a smaller capacity.
+- Otherwise:
+    Capacity is too small, try a larger capacity.
+
+Time Complexity:
+O(n * log(sum(weights)))
+
+Space Complexity:
+O(1)
+"""
+
+
+class Solution:
+    def shipWithinDays(self, weights, days):
+        # Minimum possible capacity
+        left = max(weights)
+
+        # Maximum possible capacity
+        right = sum(weights)
+
+        while left <= right:
+            mid = left + (right - left) // 2
+
+            required_days = self.findDays(weights, mid)
+
+            # Capacity is sufficient
+            if required_days <= days:
+                right = mid - 1
+
+            # Capacity is too small
+            else:
+                left = mid + 1
+
+        # First valid minimum capacity
+        return left
+
+    def findDays(self, weights, capacity):
+        days = 1
+        current_load = 0
+
+        for weight in weights:
+
+            # Package doesn't fit in current day
+            if current_load + weight > capacity:
+                days += 1
+                current_load = weight
+
+            # Package fits in current day
+            else:
+                current_load += weight
+
+        return days
+
+
+# Example Usage
+if __name__ == "__main__":
+    weights = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10]
+    days = 5
+
+    solution = Solution()
+    answer = solution.shipWithinDays(weights, days)
+
+    print("Minimum Ship Capacity:", answer)
+
+"""
+Output:
+Minimum Ship Capacity: 15
+"""