mediumRecursionPattern: Mixed
Interleaved Recursive Sequences Solution
Problem Statement
Given two recursive sequences, a fuel sequence where each term is the sum of the previous two terms (starting with 23 and 17), and a resource sequence which alternates between the sum and difference of the previous two terms (starting with 11 and 7), implement a recursive function to find the nth term of the combined sequence where the fuel sequence and resource sequence are interleaved.
Examples
Example 1:
Input:1
Output:23
Explanation: First term of the fuel sequence.
Example 2:
Input:2
Output:11
Explanation: First term of the resource sequence.
Example 3:
Input:3
Output:17
Explanation: Second term of the fuel sequence.
Example 4:
Input:4
Output:7
Explanation: Second term of the resource sequence.
Example 5:
Input:5
Output:40
Explanation: Third term of the fuel sequence, which is the sum of the first two terms (23 + 17).
Constraints
- 1 <= n <= 20
- All terms are integers
Time: O(n) Space: O(n)
An optimized approach involves using memoization to store previously calculated terms, reducing the time complexity to O(n) by avoiding redundant calculations. This approach also uses a single recursive function to interleave the fuel and resource sequences.
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