Which of the following dynamic programming problems can be solved in polynomial time?
Practice Questions
1 question
Q1
Which of the following dynamic programming problems can be solved in polynomial time?
Traveling Salesman Problem
Longest Increasing Subsequence
Hamiltonian Path
Graph Coloring
The Longest Increasing Subsequence problem can be solved in polynomial time using dynamic programming.
Questions & Step-by-step Solutions
1 item
Q
Q: Which of the following dynamic programming problems can be solved in polynomial time?
Solution: The Longest Increasing Subsequence problem can be solved in polynomial time using dynamic programming.
Steps: 6
Step 1: Understand what dynamic programming is. It is a method for solving complex problems by breaking them down into simpler subproblems.
Step 2: Identify the Longest Increasing Subsequence (LIS) problem. This problem involves finding the longest subsequence in a sequence of numbers where the elements are in increasing order.
Step 3: Recognize that the LIS problem can be solved using dynamic programming. This involves creating an array to store the lengths of the longest increasing subsequences found so far.
Step 4: Implement the dynamic programming solution. You will iterate through the array, comparing each element with the previous elements to build the longest subsequence.
Step 5: Analyze the time complexity of the LIS dynamic programming solution. It runs in O(n^2) time, which is polynomial time.
Step 6: Conclude that since the LIS problem can be solved in polynomial time using dynamic programming, it is a valid example of such a problem.
