Create minimum-time-to-eat-all-grains.py

Author: kamyu104

Python/minimum-time-to-eat-all-grains.py

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+# Time:  O(mlogm + nlogn + (m + n) * logr), r = 2*(max(max(hens), max(grains))-min(min(hens), min(grains))
+# Space: O(1)
+
+# binary search, greedy
+class Solution(object):
+    def minimumTime(self, hens, grains):
+        """
+        :type hens: List[int]
+        :type grains: List[int]
+        :rtype: int
+        """
+        def check(x):
+            i = 0
+            for h in hens:
+                if h-grains[i] > x:
+                    return False
+                elif h-grains[i] > 0:
+                    d = h-grains[i]
+                    c = max(x-2*d, (x-d)//2)  # max(go left then right, go right then left)
+                else:
+                    c = x                   
+                while i < len(grains) and grains[i] <= h+c:
+                    i += 1
+                if i == len(grains):
+                    return True
+            return False
+    
+        hens.sort()
+        grains.sort()
+        left, right = 0, 2*(max(grains[-1], hens[-1])-min(grains[0], hens[0]))
+        while left <= right:
+            mid = left+(right-left)//2
+            if check(mid):
+                right = mid-1
+            else:
+                left = mid+1
+        return left
+