Topic: dynamic-programming-problem / Level: beginner

• 1. Find the nth Fibonacci number using dynamic programming.
• 2. Solve the staircase problem where you can take either 1 or 2 steps.
• 3. Find the minimum cost path in a grid (only moves allowed are right or down).
• 4. Solve the 0/1 Knapsack problem for a given set of weights and values.
• 5. Determine if a subset of a given set can sum to a target value.
• 6. Find the number of distinct ways to reach the nth step of a staircase.
• 7. Compute the number of ways to climb a staircase with a maximum of 3 steps.
• 8. Given an array of coins and an amount, find how many ways you can make the amount.
• 9. Determine the maximum sum of non-adjacent numbers from an array.
• 10. Calculate the minimum number of edits (insertions, deletions, substitutions) to transform one string into another (Levenshtein distance).
• 11. Find the number of ways to make change for a given amount using unlimited coins.
• 12. Solve the climbing stairs problem with a variable number of steps allowed (up to k steps).
• 13. Compute the nth Tribonacci number where the sum of the last three numbers forms the next number.
• 14. Find the minimum number of jumps required to reach the end of an array where each element represents the maximum jump length.
• 15. Determine if a string can be segmented into a space-separated sequence of dictionary words.
• 16. Solve the "House Robber Problem," where adjacent houses cannot be robbed, and you need to maximize the loot.
• 17. Calculate the number of unique paths in a grid where some cells are blocked.
• 18. Determine the minimum sum path in a triangle of numbers.
• 19. Solve the "Longest Substring Without Repeating Characters" problem using dynamic programming.
• 20. Find the maximum sum of a contiguous subarray (Kadane’s Algorithm).
• 21. Count the number of binary strings of length n without consecutive 1s.
• 22. Solve the problem of cutting a rod to maximize the profit, where the lengths and prices are given.
• 23. Compute the maximum value that can be obtained by cutting a rod into pieces.
• 24. Find the number of ways to decode a message where A is represented as 1, B as 2, ..., and Z as 26.
• 25. Determine the minimum number of deletions required to make a string a palindrome.
• 26. Find the number of distinct subsequences of a string that match a given pattern.
• 27. Solve the "Wildcard Matching Problem" to determine if a string matches a given pattern.
• 28. Compute the minimum cost to convert one string to another using only insertions, deletions, and substitutions.
• 29. Find the number of ways to paint a fence with n posts using k colors, ensuring no more than two adjacent posts have the same color.
• 30. Solve the "Partition Problem" to determine if an array can be divided into two subsets of equal sum.
• 31. Find the number of ways to tile a 2 x n grid using 2 x 1 tiles.
• 32. Compute the nth Catalan number using dynamic programming.
• 33. Determine if a string can be rearranged into a palindrome.
• 34. Find the minimum path sum from top to bottom in a triangle of numbers.
• 35. Solve the "Jump Game" problem where each element in the array represents the maximum jump length.
• 36. Calculate the minimum number of cuts required to partition a string such that every substring is a palindrome.
• 37. Solve the "Unique Binary Search Trees" problem, counting the number of structurally unique BSTs that store values 1 to n.
• 38. Determine the maximum number of ways to cut a piece of rope into segments of lengths a, b, and c.
• 39. Solve the "Dice Roll Problem" where you need to compute the number of ways to get a sum n using a given number of dice.
• 40. Find the number of ways to fill a 3xN grid with dominoes.
• 41. Find the maximum sum of increasing subsequence in an array.
• 42. Solve the "Maximal Square Problem" where you need to find the largest square made of 1s in a binary matrix.
• 43. Compute the maximum profit from a single buy and sell in a stock prices array.
• 44. Find the number of ways to climb a staircase where you can take 1, 2, or 3 steps at a time.
• 45. Solve the "Knapsack Problem" with repetition allowed.
• 46. Find the minimum number of deletions required to make two strings identical.
• 47. Compute the number of distinct ways to distribute n candies among k people.
• 48. Solve the "Flood Fill Problem" where you need to fill connected regions of a grid with a specific color.
• 49. Determine the number of unique paths in a grid with some obstacles.
• 50. Find the longest increasing path in a matrix using dynamic programming.

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