Create make-k-subarray-sums-equal.py

Author: kamyu104

Python/make-k-subarray-sums-equal.py

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+# Time:  O(n)
+# Space: O(n)
+
+import random
+
+
+# math, greedy, quick select
+class Solution(object):
+    def makeSubKSumEqual(self, arr, k):
+        """
+        :type arr: List[int]
+        :type k: int
+        :rtype: int
+        """
+        def gcd(a, b):
+            while b:
+                a, b = b, a%b
+            return a
+
+        def nth_element(nums, n, left=0, 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
+            
+            right = 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
+
+        l = gcd(k, len(arr))
+        result = 0
+        for i in xrange(l):
+            vals = [arr[j] for j in xrange(i, len(arr), l)]
+            nth_element(vals, len(vals)//2)
+            result += sum(abs(v-vals[len(vals)//2]) for v in vals)
+        return result