Dynamic Programming is an algorithmic technique with the following properties.
- It is mainly an optimization over plain recursion. Wherever we see a recursive solution that has repeated calls for the same inputs, we can optimize it using Dynamic Programming.
- The idea is to simply store the results of subproblems so that we do not have to re-compute them when needed later. This simple optimization typically reduces time complexities from exponential to polynomial.
- Some popular problems solved using Dynamic Programming are Fibonacci Numbers, Diff Utility (Longest Common Subsequence), Bellman–Ford Shortest Path, Floyd Warshall, Edit Distance and Matrix Chain Multiplication.
Basic of DP
Basic Problems
- Fibonacci numbers
- Tribonacci Numbers
- Lucas Numbers
- Climbing Stairs
- Climbing Stairs with 3 Moves
- Weighted Climbing Stairs
- Maximum Segments
- nth Catalan Number
- Count Unique BSTs
- Count Valid Parenthesis
- Ways to Triangulate a Polygon
- Min Sum in a Triangle
- Minimum Perfect Squares
- Ways to Partition a Set
- Binomial Coefficient
- Pascal's Triangle
- Nth Row of Pascal Triangle
- Min Sum in a Triangle
Easy Problems
- House Robber
- Min Cost Path
- Decode Ways
- Subset Sum Problem
- Coin change problem - Count Ways
- Coin Change – Minimum Coins to Make Sum
- Painting Fence Algorithm
- Cutting a Rod
- Jump Game
- Longest Common Substring
- Count all paths in a Grid
- Paths in a Grid with Obstacles
- Permutations with K Inversions
- Max A's using Special Keyboard
Medium Problems
- Water Overflow
- Longest Common Subsequence
- Longest Increasing Subsequence
- Edit Distance
- Largest Divisible Subset
- Weighted Job Schedulling
- 0-1 Knapsack Problem
- Printing Items in 0/1 Knapsack
- Unbounded Knapsack
- Word Break Problem
- Tile Stacking Problem
- Box-Stacking Problem
- Partition Problem
- Longest Palindromic Subsequence
- Longest Common Increasing Subsequence (LCS + LIS)
- All distinct subset (or subsequence) sums
- Count Derangements
- Minimum insertions for palindrome
- Wildcard Pattern Matching
- Regular Expression Matching
- Arrange Balls with adjacent of different types
- Longest Subsequence with 1 adjacent difference
- Maximum size square sub-matrix with all 1s
- Bellman–Ford Algorithm
- Floyd Warshall Algorithm
- Maximum Tip Calculator
Hard Problems
- Largest X Bordered Square
- Egg Dropping Problem
- Palindrome Partitioning
- Palindromic Substring Count
- Word Wrap Problem
- Optimal Strategy for a Game
- The painter’s partition problem
- Program for Bridge and Torch problem
- Matrix Chain Multiplication
- Printing Matrix Chain Multiplication
- Maximum sum rectangle
- Stock Buy and Sell - At-Most k Times
- Stock Buy and Sell - At Most 2 Times
- Min cost to sort strings using Reversals
- Count of AP Subsequences
- DP on Trees
- Max Height of Tree when any Node can be Root
- Longest repeating and non-overlapping substring
- Palindrome Substrings Count
Problems Sorted by Topic / Dimensions
- DP Standard Problems and Variations.
- DP Problems Dimension Wise (1D, 2D and 3D)
- DP Problems Topic Wise
