Actually recurrence relation is dp[n][0]= dp[n-1][0]+dp[n-1][1]

dp[n][1]=dp[n-1][0]

Here 0 denotes doesnt go while 1 denotes had gone to workout and n denotes day

answer is ans[n]= dp[n][0]+dp[n][1];

now how to use matrix exponentiation in this

Actually recurrence relation is dp[n][0]= dp[n-1][0]+dp[n-1][1]

dp[n][1]=dp[n-1][0]

Here 0 denotes doesnt go while 1 denotes had gone to workout and n denotes day

answer is ans[n]= dp[n][0]+dp[n][1];

now how to use matrix exponentiation in this

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Iâ€™ve explained them here.

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You are thinking more than needed.

If you check the answers for different N, you will get a sequence as follows:

0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, \cdots for 0 <= N <= 10^{18}.

Well, now you familiar with this sequence I think. Ring a Bell, itâ€™s a Fibonacci Sequence.

There are tons of articles out there to solve this problem which boils down to calculate the N^{th} term of the Fibonacci Sequence.

Recently @anon79763389 has posted a nice article related to different methods of calculating the Nth term of the Fibonacci Sequence.

You can refer to the article here: https://procoderforu.com/fibonacci-sequence/

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Thanks Very will explained

yeah i was just wondering how to form matrix