Start by sorting the ice cream bar costs in ascending order. Buy each bar sequentially while coins last. This greedy approach ensures the invariant that buying cheaper bars first maximizes the total count without exceeding the available coins.
Problem Statement
A boy wants to buy as many ice cream bars as possible on a hot summer day. Each bar has a cost given in the array costs, and he has a limited number of coins.
He can purchase bars in any order, but the goal is to maximize the number of bars bought without exceeding his total coins. Determine the maximum bars he can purchase using an optimal strategy.
Examples
Example 1
Input: costs = [1,3,2,4,1], coins = 7
Output: 4
The boy can buy ice cream bars at indices 0,1,2,4 for a total price of 1 + 3 + 2 + 1 = 7.
Example 2
Input: costs = [10,6,8,7,7,8], coins = 5
Output: 0
The boy cannot afford any of the ice cream bars.
Example 3
Input: costs = [1,6,3,1,2,5], coins = 20
Output: 6
The boy can buy all the ice cream bars for a total price of 1 + 6 + 3 + 1 + 2 + 5 = 18.
Constraints
- costs.length == n
- 1 <= n <= 105
- 1 <= costs[i] <= 105
- 1 <= coins <= 108
Solution Approach
Sort Costs Ascending
Sort the array of ice cream bar costs from lowest to highest. This allows applying a greedy strategy by considering the cheapest bars first.
Greedy Purchase Loop
Iterate through the sorted costs and subtract each cost from coins if affordable. Stop when the next bar exceeds remaining coins, ensuring the invariant that coins are never overspent.
Counting Sort Optimization
For large n with bounded costs, use counting sort to avoid full comparison-based sorting. Iterate through the counts to purchase bars efficiently without breaking the greedy invariant.
Complexity Analysis
| Metric | Value |
|---|---|
| Time | Depends on the final approach |
| Space | Depends on the final approach |
Time complexity is O(n log n) with standard sort, or O(n + maxCost) with counting sort. Space complexity is O(n) for sorting or O(maxCost) for counting array. Iteration is O(n) in all cases.
What Interviewers Usually Probe
- Ask how to maximize purchases without overspending coins.
- Check if candidate recognizes greedy choice invariant with costs.
- Probe if counting sort can optimize large inputs efficiently.
Common Pitfalls or Variants
Common pitfalls
- Failing to sort costs before greedy selection leads to suboptimal purchases.
- Attempting to pick bars in arbitrary order can exceed coins early.
- Ignoring large cost values and limits may cause inefficiency or overflow.
Follow-up variants
- Compute maximum bars if each bar has a limit on quantity available.
- Determine maximum bars with a dynamic coin replenishment after each purchase.
- Maximize bars when only contiguous subarrays of costs can be purchased.
How GhostInterview Helps
- Provides step-by-step guidance to apply greedy choice and maintain the invariant.
- Highlights the importance of sorting or counting strategies for efficiency.
- Simulates coin tracking and decision-making to ensure maximal bar purchases.
Topic Pages
Related GhostInterview Pages
- LeetCode Interview Copilot - Use GhostInterview as a live solver when you want direct help with LeetCode-style coding questions.
- Coding Interview Assistant - See how GhostInterview supports array, string, linked list, graph, and tree interview workflows.
- How GhostInterview Works - Review the screenshot, reasoning, and answer flow before using the solver in a live interview.
FAQ
What is the main strategy for Maximum Ice Cream Bars problem?
The key strategy is greedy selection: always buy the cheapest available ice cream bar first to maximize the total count.
Can this problem be optimized without full sorting?
Yes, using counting sort for bounded costs allows linear-time iteration to achieve the greedy selection efficiently.
What should I watch out for when implementing this solution?
Ensure costs are sorted or counted correctly, track coins carefully, and stop purchasing before exceeding coins.
How does the greedy choice invariant apply here?
The invariant ensures that buying cheaper bars first never reduces the total number of bars obtainable, preserving optimality.
Are there variations of Maximum Ice Cream Bars I should consider?
Variants include limits on bar quantities, dynamic coins, or constraints on purchasing contiguous subarrays.
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