Maximize outfits with distinct colors
Problem: Maximize Outfits with Distinct Colors
YouYou are provided with item counts categorized by color. Your objective is to assemble the maximum possible number of outfits, subject to the following rules:
- Each outfit must contain exactly three items.
- All three items within an outfit must be of distinct colors.
- Once an item is used in an outfit, it cannot be reused in any subsequent outfit.
Input Formats
The input will be given in one of two formats:
- An array
counts, wherecounts[i]denotes the number of items available for colori(colors are 0-indexed). - A multiset of color labels (e.g.,
['red', 'red', 'blue', 'green', ...]).
Tasks
- Calculate Maximum Outfits: Determine and return the total maximum number of outfits that can be created.
- Construct Assignment: Generate and return one valid assignment for the first
min(10, answer)outfits. This assignment should specify the three distinct colors chosen for each of these outfits.
Constraints & Requirements
- Time Complexity: Your algorithm must achieve an optimal time complexity of O(C log C), where C represents the number of distinct colors.
- Space Complexity: Your algorithm must utilize O(C) extra space.
- Total Items: The sum of all items across all colors can be up to 10^6.
- Optimality Proof: You are required to either formally prove the optimality of your algorithm or provide a compelling argument for why it guarantees the maximum number of outfits. A greedy approach, likely involving a max-heap to manage remaining counts, is suggested. Pay particular attention to pathological distributions (e.g.,
[100, 1, 1, ...]) that could challenge simpler greedy strategies. - Edge Cases: Your solution must robustly handle various edge cases, including:
- Scenarios where fewer than three non-zero colors are initially available.
- Extremely skewed distributions of item counts among colors.
- Situations with many distinct colors, each having only one item.
Example
counts = [3, 2, 2, 1]
- Expected Maximum Outfits: 2
- One Valid Assignment:
[(color0, color1, color2), (color0, color1, color3)]
AI interview prep
Core dilemma
The central engineering conflict is balancing the immediate greedy choice (which three colors to pick for the current outfit) against the long-term goal of maximizing total outfits, especially when facing highly skewed resource distributions. The challenge is to ensure the greedy strategy doesn't prematurely exhaust a critical color, thereby limiting future outfit possibilities, while adhering to distinct color and item reuse constraints.
3 tradeoffs and 3 stress tests locked
Interview prep
Unlock the interviewer X-Ray rubric, tradeoff matrix, stress tests, clarifying questions, and key concepts.
Maximize outfits with distinct colors
Problem: Maximize Outfits with Distinct Colors
YouYou are provided with item counts categorized by color. Your objective is to assemble the maximum possible number of outfits, subject to the following rules:
- Each outfit must contain exactly three items.
- All three items within an outfit must be of distinct colors.
- Once an item is used in an outfit, it cannot be reused in any subsequent outfit.
Input Formats
The input will be given in one of two formats:
- An array
counts, wherecounts[i]denotes the number of items available for colori(colors are 0-indexed). - A multiset of color labels (e.g.,
['red', 'red', 'blue', 'green', ...]).
Tasks
- Calculate Maximum Outfits: Determine and return the total maximum number of outfits that can be created.
- Construct Assignment: Generate and return one valid assignment for the first
min(10, answer)outfits. This assignment should specify the three distinct colors chosen for each of these outfits.
Constraints & Requirements
- Time Complexity: Your algorithm must achieve an optimal time complexity of O(C log C), where C represents the number of distinct colors.
- Space Complexity: Your algorithm must utilize O(C) extra space.
- Total Items: The sum of all items across all colors can be up to 10^6.
- Optimality Proof: You are required to either formally prove the optimality of your algorithm or provide a compelling argument for why it guarantees the maximum number of outfits. A greedy approach, likely involving a max-heap to manage remaining counts, is suggested. Pay particular attention to pathological distributions (e.g.,
[100, 1, 1, ...]) that could challenge simpler greedy strategies. - Edge Cases: Your solution must robustly handle various edge cases, including:
- Scenarios where fewer than three non-zero colors are initially available.
- Extremely skewed distributions of item counts among colors.
- Situations with many distinct colors, each having only one item.
Example
counts = [3, 2, 2, 1]
- Expected Maximum Outfits: 2
- One Valid Assignment:
[(color0, color1, color2), (color0, color1, color3)]