Dynamic Programming Questions
The Maximum Sum of Subsequence with No Twenty-Five 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 have a difference of 25 or more.
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] as the first element of the sequence, and dp[1] as the maximum of the first two elements. For each subsequent index i, we have two options:
1. Include the current element: In this case, the maximum sum of the subsequence ending at index i is the sum of the current element and the maximum sum of the subsequence ending at index i-2 (dp[i-2]). This is because we cannot include the previous element (i-1) in the subsequence due to the constraint of no consecutive elements with a difference of 25 or more.
2. Exclude the current element: In this case, the maximum sum of the subsequence ending at index i is the same as the maximum sum of the subsequence ending at index i-1 (dp[i-1]).
Therefore, we can calculate dp[i] as the maximum of these two options: dp[i] = max(dp[i-2] + sequence[i], dp[i-1]).
Finally, the maximum sum of the subsequence with no twenty-five 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 Twenty-Five Consecutive Elements problem.