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# Dynamic Programming Interview Questions and Answers

### Ques 1. Fibonacci Series

The Fibonacci sequence is a series of numbers where each number is the sum of the two preceding ones.

Example:

`Fib(0) = 0, Fib(1) = 1, Fib(n) = Fib(n-1) + Fib(n-2)`

### Ques 2. Longest Increasing Subsequence (LIS)

Find the length of the longest subsequence of a given sequence such that all elements of the subsequence are sorted in increasing order.

Example:

`Input: [10, 22, 9, 33, 21, 50, 41, 60, 80], Output: 6`

### Ques 3. Coin Change Problem

Given a set of coin denominations, find the number of ways to make a certain amount of change.

Example:

`Input: coins=[1, 2, 5], amount=5, Output: 4`

### Ques 4. Edit Distance

Given two strings, find the minimum number of operations required to convert one string into the other.

Example:

`Input: word1 = "horse", word2 = "ros", Output: 3`

### Ques 5. Maximum Subarray Sum

Find the contiguous subarray with the largest sum.

Example:

`Input: [-2, 1, -3, 4, -1, 2, 1, -5, 4], Output: 6 (subarray [4, -1, 2, 1])`