Dynamic Programming Questions
The Maximum Sum of Subsequence with No Fifty-Five Consecutive Elements problem is a dynamic programming problem that involves finding the maximum sum of a subsequence from a given sequence, with the constraint that no two consecutive elements in the subsequence can be equal to 55.
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 all other indices i, we calculate dp[i] as the maximum of the following two options:
1. If the current element is not equal to 55, we can include it in the subsequence. In this case, dp[i] will be the sum of the current element and the maximum sum of the subsequence ending at the previous index (dp[i-1]).
2. If the current element is equal to 55, we cannot include it in the subsequence. In this case, dp[i] will be the maximum sum of the subsequence ending at the previous index (dp[i-1]).
Finally, the maximum sum of the subsequence with no fifty-five consecutive elements will be the maximum value in the dp array.
Here is the pseudocode for solving this problem using dynamic programming:
1. Initialize dp[0] as the first element of the sequence.
2. Initialize dp[1] as the maximum of the first two elements.
3. For i = 2 to n (where n is the length of the sequence):
a. If the current element is not equal to 55:
dp[i] = max(dp[i-1] + current element, dp[i-2] + current element)
b. If the current element is equal to 55:
dp[i] = dp[i-1]
4. Return the maximum value in the dp array.
By following this approach, we can efficiently solve the Maximum Sum of Subsequence with No Fifty-Five Consecutive Elements problem using dynamic programming.