Dynamic Programming Questions
The Maximum Sum of Subsequence with No Thirty-One Consecutive Elements problem is a dynamic programming problem that involves finding the maximum sum of a subsequence from a given sequence, where no consecutive elements in the subsequence can sum up to 31.
To solve this problem using dynamic programming, we can use an array to store the maximum sum of subsequences ending at each index. Let's call this array dp.
We initialize dp[0] and dp[1] with the first two elements of the sequence. Then, for each subsequent element at index i, we have two options:
1. Exclude the current element: In this case, the maximum sum of subsequences ending at index i is equal to the maximum sum of subsequences ending at index i-1, which is stored in dp[i-1].
2. Include the current element: In this case, we need to make sure that the sum of the current element and the element at index i-2 (to avoid having consecutive elements sum up to 31) is less than or equal to 31. If it is, then the maximum sum of subsequences ending at index i is equal to the sum of the current element and the maximum sum of subsequences ending at index i-2, which is stored in dp[i-2].
We can then update dp[i] as the maximum value between the two options mentioned above.
Finally, the maximum sum of subsequences with no thirty-one consecutive elements will be the maximum value in the dp array.
By using this dynamic programming approach, we can efficiently solve the Maximum Sum of Subsequence with No Thirty-One Consecutive Elements problem.