Dynamic Programming Questions Long
One example of a problem that can be solved using Dynamic Programming is the "Fibonacci sequence" problem. The Fibonacci sequence is a series of numbers in which each number is the sum of the two preceding ones, usually starting with 0 and 1. The problem is to find the nth number in the Fibonacci sequence.
Dynamic Programming can be used to solve this problem efficiently by breaking it down into smaller subproblems and storing the solutions to these subproblems in a table. This approach avoids redundant calculations and improves the overall time complexity of the solution.
Here is an example of how Dynamic Programming can be applied to solve the Fibonacci sequence problem:
1. Define a function, let's call it "fibonacci(n)", that takes an integer n as input and returns the nth number in the Fibonacci sequence.
2. Create a table, let's call it "fibTable", to store the solutions to subproblems. Initialize the table with the base cases: fibTable[0] = 0 and fibTable[1] = 1.
3. Iterate from 2 to n:
a. Calculate the value of fibTable[i] by summing up the values of fibTable[i-1] and fibTable[i-2].
b. Store the calculated value in fibTable[i].
4. Return the value of fibTable[n].
By using Dynamic Programming, the Fibonacci sequence problem can be solved efficiently in O(n) time complexity, as opposed to the exponential time complexity of the naive recursive approach. The Dynamic Programming approach eliminates redundant calculations by storing and reusing the solutions to subproblems, resulting in a significant improvement in performance.