Common Dynamic Programming Problems

Dynamic programming is a powerful technique that can be applied to a wide range of problems. It allows us to break down complex problems into smaller subproblems and solve them independently, eliminating redundant computations.

In programming interviews, dynamic programming is often used to solve optimization problems efficiently. These optimization problems have a well-defined objective and require finding the best solution among a set of possible solutions.

Let's take a look at some common dynamic programming problems:

1. Fibonacci Sequence: The Fibonacci sequence is a classic example that showcases the power of dynamic programming. The nth Fibonacci number can be calculated using dynamic programming by storing the results of previous subproblems.

2. Longest Common Subsequence: Given two sequences, find the length of the longest subsequence present in both. Dynamic programming can be used to solve this problem efficiently by breaking it down into smaller subproblems.

3. Knapsack Problem: Given a set of items with weights and values, determine the maximum value that can be obtained by selecting a subset of items with a total weight not exceeding a given limit. Dynamic programming can be used to find the optimal subset of items to maximize the value.

4. Coin Change: Given a target amount and a set of coin denominations, find the minimum number of coins required to make the target amount. Dynamic programming can be used to solve this problem by considering all possible coin combinations.

These are just a few examples of the many problems that can be efficiently solved using dynamic programming. By understanding the underlying principles and techniques of dynamic programming, you can confidently approach and solve a wide range of programming problems in interviews and real-world scenarios.

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}

using System;

​

public class DynamicProgrammingProblems

{

    public static long Fibonacci(int n)

    {

        long[] dp = new long[n + 1];

        dp[0] = 0;

        dp[1] = 1;

​

        for (int i = 2; i <= n; i++)

        {

            dp[i] = dp[i - 1] + dp[i - 2];

        }

​

        return dp[n];

    }

​

    public static int LongestCommonSubsequence(string text1, string text2)

    {

        int m = text1.Length;

        int n = text2.Length;

​

        int[,] dp = new int[m + 1, n + 1];

​

        for (int i = 1; i <= m; i++)

        {

            for (int j = 1; j <= n; j++)

            {