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Problem solution · Python

Maximum Sum of Three Numbers Divisible by Three

Maximum Sum of Three Numbers Divisible by Three: a Python solution using sorting and greedy selection. Learn the idea, check the complexity, and read the full code, with credit to Kamyu LeetCode Solutions.

Technique
Sorting and greedy selection
Source
Kamyu LeetCode Solutions
Length
50 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

Sorting and greedy selection

For Maximum Sum of Three Numbers Divisible by Three, the implementation first exposes a useful order, then scans that order while making locally justified choices.

  1. Choose the key that reveals the greedy or grouping structure.
  2. Sort the relevant records by that key.
  3. Scan in order, maintaining the invariant that makes each local choice safe.

Code notes

  • 50 lines of Python from the credited upstream file maximum-sum-of-three-numbers-divisible-by-three.py.
  • The implementation visibly relies on sequence storage.
  • No explicit loop blocks detected.

Complexity

Sorting is typically the dominant term unless the subsequent scan uses a more expensive nested operation.

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 codeMaximum Sum of Three Numbers Divisible by Three · PythonPython
Use this to learn the idea, then write your own version.
# Time:  O(n)# Space: O(1) # sort, mathclass Solution(object):    def maximumSum(self, nums):        """        :type nums: List[int]        :rtype: int        """        def add(arr, x):            for i in xrange(len(arr)):                if x > arr[i]:                    arr[i], x = x, arr[i]            if len(arr) != 3:                arr.append(x)         group = [[] for _ in xrange(3)]        for x in nums:            add(group[x%3], x)        result = 0        for g in group:            if len(g) == 3:                result = max(result, sum(g))        if group[0] and group[1] and group[2]:            result = max(result, group[0][0]+group[1][0]+group[2][0])        return result  # Time:  O(nlogn)# Space: O(n)# sort, mathclass Solution2(object):    def maximumSum(self, nums):        """        :type nums: List[int]        :rtype: int        """        group = [[] for _ in xrange(3)]        for x in nums:            group[x%3].append(x)        result = 0        for g in group:            g.sort(reverse=True)            if len(g) >= 3:                result = max(result, sum(g[i] for i in xrange(3)))        if group[0] and group[1] and group[2]:            result = max(result, group[0][0]+group[1][0]+group[2][0])        return result

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