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Problem · Math

Count Ways to Select Fleet

● EasyAmazonOA

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You are given an integer representing a total count of wheels. Your task is to determine how many distinct ways you can form a group of vehicles using an unlimited supply of two-wheeled and four-wheeled types such that the sum of their wheels equals the given total.

Two arrangements are considered unique if the count of two-wheeled or four-wheeled vehicles used differs between them.

The function should return a list of integers, where each value corresponds to the number of valid combinations for the respective total in the input list.

Constraints

1 ≤ n ≤ 10^5
1 ≤ wheels[i] ≤ 10^9

Examples

01 · Example 1

wheels = [6, 3, 2]
return = [2, 0, 1]

For a total of 6 wheels: Option 1: One four-wheeled vehicle + one two-wheeled vehicle Option 2: Three two-wheeled vehicles Total combinations = 2 🦔 🦍 🐒 🐢 🐘 🦒 🐪 🦭 🦤 🪿 🦩 🦧 For 3 wheels: No possible arrangement can sum to 3 wheels using only 2- and 4-wheeled vehicles Total combinations = 0 🍓 🍉 🍊 🍋 🥑 🥝 🥭 🍅 🍋‍🟩 🍇 🥥 🍑 For 2 wheels: Only possible using one two-wheeler Total combinations = 1

02 · Example 2

wheels = [4, 5, 6]
return = [2, 0, 2]

For 4 wheels: either 1 four-wheeler or 2 two-wheelers. For 5 wheels: it is impossible. For 6 wheels: either 1 four-wheeler + 1 two-wheeler or 3 two-wheelers.