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Problem solution · Python

Minimum Operations to Equalize Subarrays

Minimum Operations to Equalize Subarrays: a Python solution using segment tree or range structure. Learn the idea, check the complexity, and read the full code, with credit to Kamyu LeetCode Solutions.

Technique
Segment tree or range structure
Source
Kamyu LeetCode Solutions
Length
78 lines
Start with the idea.

Try the problem first. If you get stuck, read the approach below, then write your own solution. The full code is at the bottom.

Approach

Segment tree or range structure

For Minimum Operations to Equalize Subarrays, the implementation stores interval information in a range-query data structure so updates and queries avoid rescanning the full input.

  1. Choose the aggregate stored for each interval or prefix.
  2. Build or initialize the structure from the input.
  3. Apply updates and combine the affected nodes to answer each query.

Code notes

  • 78 lines of Python from the credited upstream file minimum-operations-to-equalize-subarrays.py.
  • The implementation visibly relies on sequence storage, ordered lookup.
  • No explicit loop blocks detected.

Complexity

Count the build once, then multiply the logarithmic update or query path by the number of operations.

Check the problem constraints before deciding whether this complexity will pass.

Source

Code and credit

This code comes from Kamyu LeetCode Solutions by kamyu104 and is used under the MIT licence.

Open problem ↗Original source ↗
Full codeMinimum Operations to Equalize Subarrays · PythonPython
Use this to learn the idea, then write your own version.
# Time:  O((n + q) * logn)# Space: O(nlogn) # prefix sum, persistent segment tree, binary searchclass PersistentSegmentTree(object):    LEFT, RIGHT, CNT, TOTAL = range(4)     def __init__(self, vals):        self.sorted_unique_vals = sorted(set(vals))        self.val_to_idx = {x: i for i, x in enumerate(self.sorted_unique_vals)}        self.n = len(self.val_to_idx)        self.roots = []        self.__build(vals)     def __new_node(self):        return [None, None, 0, 0]     def __build(self, vals):        root = self.__new_node()        self.roots.append(root)        for x in vals:            root = root[:]            self.roots.append(root)            curr = root            left, right = 0, self.n-1            i = self.val_to_idx[x]            while left < right:                curr[self.CNT] += 1                curr[self.TOTAL] += x                mid = left+(right-left)//2                if i <= mid:                    curr[self.LEFT] = curr = curr[self.LEFT][:] if curr[self.LEFT] else self.__new_node()                    right = mid                else:                    curr[self.RIGHT] = curr = curr[self.RIGHT][:] if curr[self.RIGHT] else self.__new_node()                    left = mid+1            curr[self.CNT] += 1            curr[self.TOTAL] += x     def query(self, l, r):        a, b = self.roots[l], self.roots[r+1]        left_cnt = left_total = 0        med_cnt = (r-l+1)//2+1        left, right = 0, self.n-1        while left < right:            mid = left+(right-left)//2            cnt = ((b[self.LEFT][self.CNT] if b and b[self.LEFT] else 0)-                   (a[self.LEFT][self.CNT] if a and a[self.LEFT] else 0))            if med_cnt <= cnt:                a = a[self.LEFT] if a else None                b = b[self.LEFT] if b else None                right = mid            else:                med_cnt -= cnt                left_cnt += cnt                left_total += ((b[self.LEFT][self.TOTAL] if b and b[self.LEFT] else 0)-                               (a[self.LEFT][self.TOTAL] if a and a[self.LEFT] else 0))                a = a[self.RIGHT] if a else None                b = b[self.RIGHT] if b else None                left = mid+1        return ((self.sorted_unique_vals[left]*left_cnt-left_total)+((self.roots[r+1][self.TOTAL]-                self.roots[l][self.TOTAL]-left_total)-self.sorted_unique_vals[left]*((r-l+1)-left_cnt)))  class Solution(object):    def minOperations(self, nums, k, queries):        """        :type nums: List[int]        :type k: int        :type queries: List[List[int]]        :rtype: List[int]        """        prefix = [0]*(len(nums)+1)        for i, x in enumerate(nums):            prefix[i+1] = prefix[i]+(1 if i-1 >= 0 and nums[i]%k != nums[i-1]%k else 0)        pst = PersistentSegmentTree([x//k for x in nums])        return [pst.query(s, t) if prefix[t+1]-prefix[s+1] == 0 else -1 for s, t in queries]

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