Problem link I have seen the solution but i dont understand how the recurrance relation is dp[i]=dp[i-1]+dp[i-2]+2;
Can somebody explain it to me.
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Problem link I have seen the solution but i dont understand how the recurrance relation is dp[i]=dp[i-1]+dp[i-2]+2;
Can somebody explain it to me.
Название |
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dp[i] consists of the following:
So total is dp[i-1] + dp[i-2] + 2
Do you think it is a good idea to write down small cases and try to find a pattern to deduce the recurrence relation?
Yes, definitely. I solved this problem mostly by looking at the cases for n = 3 and 4. Especially pay attention to the new subsequences that actually use the last character.
By the way, there's an alternative solution (actually the first one I thought of) that counts the sequences ending with R and B separately. Then, if the ith character is R, dp[i][R] = dp[i-1][R] + dp[i-1][B] + 1 (you can take any red-ending subsequence of n-1 and leave it alone or any blue-ending subsequence of n-1 and add the last character or take just the last character), and dp[i][B] = dp[i-1][B]. If the ith character is B, then dp[i][B] = dp[i-1][R] + dp[i-1][B] + 1, and dp[i][R] = dp[i-1][R].