11(May) Juggler Sequence

11. Juggler Sequence

The problem can be found at the following link: Question Link

Problem Description

Given a number (n), find the Juggler Sequence for this number as the first term of the sequence until it becomes 1. The Juggler Sequence is a series of integers generated using a recurrence relation.

Example: Input:

n = 9

Output:

9 27 140 11 36 6 2 1

Explanation: We start with 9 and use the Juggler Formula to generate the next terms until the sequence becomes 1.

My Approach

1. Initialization:

• Create a vector ans to store the Juggler Sequence.

• Push the initial term (n) into the vector.

1. Sequence Generation:

• Iterate until the last term of the sequence becomes 1.

• Calculate the next term of the sequence using the Juggler Formula:

  • If the current term is even, the next term is (\sqrt{\text{current term}}).

  • If the current term is odd, the next term is (\sqrt{\text{current term}}^3).

• Push the next term into the vector.

1. Return:

• Return the vector ans containing the Juggler Sequence.

Time and Auxiliary Space Complexity

• Expected Time Complexity: O(n), as we iterate until the last term of the sequence becomes 1.

• Expected Auxiliary Space Complexity: O(n), as we use a vector to store the Juggler Sequence.

Code (C++)

class Solution {
public:
    std::vector<long long> jugglerSequence(long long n) {
        std::vector<long long> res;
        res.push_back(n);

        while (n > 1) {
            if (n % 2)
                n = static_cast<long long>(std::sqrt(n) * n);
            else
                n = static_cast<long long>(std::sqrt(n));

            res.push_back(n);
        }

        return res;
    }
};

Contribution and Support

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