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Problem solution · Python

Maximum Number of Items from Sale II

Maximum Number of Items from Sale II: 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
40 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 Number of Items from Sale II, 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

  • 40 lines of Python from the credited upstream file maximum-number-of-items-from-sale-ii.py.
  • The implementation visibly relies on sequence storage, hash lookup.
  • 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 Number of Items from Sale II · PythonPython
Use this to learn the idea, then write your own version.
# Time:  O(rlogr + nlogn) = O(nlogn), r = max(f for f, _ in items) <= n# Space: O(r + n) = O(n) import collections  # freq table, sort, greedyclass Solution(object):    def maximumSaleItems(self, items, budget):        """        :type items: List[List[int]]        :type budget: int        :rtype: int        """        NEG_INF = float("-inf")        cnt = [0]*(max(f for f, _ in items)+1)        for f, _ in items:            cnt[f] += 1        total = [0]*len(cnt)        for i in xrange(1, len(total)):            if not cnt[i]:                continue            for j in xrange(i, len(total), i):                total[i] += cnt[j]        min_p = min(p for _, p in items)        group = collections.defaultdict(int)        for f, price in items:            if price >= 2*min_p:                continue            group[price] += total[f]-1        result = 0        for p in sorted(group):            c = min(group[p], budget//p)            result += 2*c            budget -= c*p            if not budget:                break        result += budget//min_p        return result

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