Minimum Component Subset — Problem Statement & Solution Guide
Problem Description
Given a list of integers representing available components and a set of distinct integers representing required components, determine the minimum length of a contiguous subarray that contains all required components. If no such subarray exists, return -1.
Examples
Input
[1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10]
Output
20
Explanation: Step-by-step: with input [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10], we find the minimum length subarray that contains all required components. The required components are all present in the first 10 elements, but the minimum length subarray that contains all required components is actually the entire array with a length of 20.
Input
[1, 2, 3, 4, 5, 6, 7, 8, 9, 10]
Output
10
Explanation: Step-by-step: with input [1, 2, 3, 4, 5, 6, 7, 8, 9, 10], we find the minimum length subarray that contains all required components. The required components are all present in the first 10 elements, so the minimum length subarray that contains all required components is the entire array with a length of 10.
Constraints
- 1 <= length of ingredients list <= 1000
- 1 <= number of required components <= 100
Optimal Approach & Strategy
The optimal approach involves sorting the ingredients list and required components list, then using two pointers to track the current position in each list and find the minimum window that satisfies the given conditions, resulting in a time complexity of O(n log n).
Brute Force Approach
A naive approach would involve generating all possible subsets of the ingredients list and checking each subset to see if it contains all required components, resulting in a time complexity of O(2^n).
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