Dynamic Programming Questions
The Maximum Sum of Subsequence with No Five Consecutive Elements problem is a dynamic programming problem that involves finding the maximum sum of a subsequence from a given sequence, where no five consecutive elements are included in the subsequence.
To solve this problem using dynamic programming, we can use an array to store the maximum sum of subsequences up to a certain index. Let's denote this array as dp, where dp[i] represents the maximum sum of subsequences ending at index i.
The dynamic programming approach involves iterating through the given sequence and updating the dp array at each index. At each index i, we have two options:
1. Exclude the current element: In this case, the maximum sum of subsequences ending at index i is the same as the maximum sum of subsequences ending at index i-1. Therefore, we can set dp[i] = dp[i-1].
2. Include the current element: In this case, we need to make sure that the current element is not included in any five consecutive elements. Hence, we need to consider the maximum sum of subsequences ending at index i-2, i-3, i-4, and i-5. Therefore, we can set dp[i] = max(dp[i-2], dp[i-3], dp[i-4], dp[i-5]) + sequence[i].
After iterating through the entire sequence, the maximum sum of subsequences will be stored in dp[n-1], where n is the length of the sequence.
Therefore, the Maximum Sum of Subsequence with No Five Consecutive Elements problem can be solved using dynamic programming by following the above approach.