Create find-subsequence-of-length-k-with-the-largest-sum.py

Author: kamyu104

Python/find-subsequence-of-length-k-with-the-largest-sum.py

@@ -0,0 +1,50 @@
+# Time:  O(n)
+# Space: O(n)
+
+import random
+
+
+class Solution(object):
+    def maxSubsequence(self, nums, k):
+        """
+        :type nums: List[int]
+        :type k: int
+        :rtype: List[int]
+        """
+        def nth_element(nums, n, compare=lambda a, b: a < b):
+            def tri_partition(nums, left, right, target, compare):
+                mid = left
+                while mid <= right:
+                    if nums[mid] == target:
+                        mid += 1
+                    elif compare(nums[mid], target):
+                        nums[left], nums[mid] = nums[mid], nums[left]
+                        left += 1
+                        mid += 1
+                    else:
+                        nums[mid], nums[right] = nums[right], nums[mid]
+                        right -= 1
+                return left, right
+
+            left, right = 0, len(nums)-1
+            while left <= right:
+                pivot_idx = random.randint(left, right)
+                pivot_left, pivot_right = tri_partition(nums, left, right, nums[pivot_idx], compare)
+                if pivot_left <= n <= pivot_right:
+                    return
+                elif pivot_left > n:
+                    right = pivot_left-1
+                else:  # pivot_right < n.
+                    left = pivot_right+1
+
+        partition = nums[:]
+        nth_element(partition, k-1, compare=lambda a, b: a > b)
+        cnt = sum(partition[i] == partition[k-1] for i in xrange(k))
+        result = []
+        for x in nums:
+            if x > partition[k-1]:
+                result.append(x)
+            elif x == partition[k-1] and cnt > 0:
+                cnt -= 1
+                result.append(x)
+        return result