Create find-minimum-time-to-finish-all-jobs.py

Author: kamyu104

Python/find-minimum-time-to-finish-all-jobs.py

@@ -0,0 +1,59 @@
+# Time:  O(k^n * logr), the real complexity shoud be much less, but hard to analyze
+# Space: O(n + k)
+
+class Solution(object):
+    def minimumTimeRequired(self, jobs, k):
+        """
+        :type jobs: List[int]
+        :type k: int
+        :rtype: int
+        """
+        def backtracking(jobs, i, cap, counts):
+            if i == len(jobs):
+                return True
+            for j in xrange(len(counts)):
+                if counts[j]+jobs[i] <= cap:
+                    counts[j] += jobs[i]
+                    if backtracking(jobs, i+1, cap, counts):
+                        return True
+                    counts[j] -= jobs[i]
+                if counts[j] == 0:
+                    break
+            return False
+
+        jobs.sort(reverse=True)
+        left, right = max(jobs), sum(jobs)
+        while left <= right:
+            mid = left + (right-left)//2
+            if backtracking(jobs, 0, mid, [0]*k):
+                right = mid-1
+            else:
+                left = mid+1
+        return left
+
+
+# Time:  O(k * k^n), the real complexity shoud be less, but hard to analyze
+# Space: O(n + k)
+class Solution2(object):
+    def minimumTimeRequired(self, jobs, k):
+        """
+        :type jobs: List[int]
+        :type k: int
+        :rtype: int
+        """
+        def backtracking(jobs, i, counts, result):
+            if i == len(jobs):
+                result[0] = min(result[0], max(counts))
+                return
+            for j in xrange(len(counts)):
+                if counts[j]+jobs[i] <= result[0]:
+                    counts[j] += jobs[i]
+                    backtracking(jobs, i+1, counts, result)
+                    counts[j] -= jobs[i]
+                if counts[j] == 0:
+                    break
+
+        jobs.sort(reverse=False)
+        result = [sum(jobs)]
+        backtracking(jobs, 0, [0]*k, result)
+        return result[0]