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# List of 100+ Dynamic Programming Problems

#### Dynamic Programming (DP) Algorithms Culture Get this book -> Problems on Array: For Interviews and Competitive Programming

This is the List of 100+ Dynamic Programming (DP) Problems along with different types of DP problems such as Mathematical DP, Combination DP, String DP, Tree DP, Standard DP and Advanced DP optimizations.

1. Mathematical DP
2. Combination DP
3. String DP
4. Tree DP
5. Standard DP

The list of problems in each category of Dynamic Programming is as follows:

# Combinations DP

• Subset Sum Problem
• Same Sum Subset
• Number of ways to pair elements
• number of subsets of an array having a given XOR value
• number of subsets with given Bitwise OR value
• Number of non unique Partitions of an Integer
• Number of unique partitions of an integer
• Number of ways to reach a given number using increments of 1 and 2
• Number of ways to reach a number using increments of 1 and 2 (consecutive 2s are not allowed)
• Number of ways to reach a number using increments of 1 and 2 (consecutive 1s are not allowed)
• Number of ordered pairs such that (A[i] & A[j])=0
• number of sub matrices having sum divisible by K
• number of subsets with sum divisible by given number M

# Tree DP

• Minimum Cost Path in 2D matrix (+)

• Maximum Cost Path in 2D matrix (+)

• Maximum average value path in a 2D matrix (Restricted)

• Minimum average value path in a 2D matrix (Restricted)

• Count paths from Top Left to Bottom Right of a Matrix

• Minimum Cost for Triangulation of a Convex Polygon

• Largest Independent Set in Binary Tree

• Number of paths with k edges

• Shortest Path with k edges

• Vertex Cover Problem

• Binary Lifting with k-th ancestor

• Minimum number of Nodes to be removed such that no subtree has more than K nodes

• Minimum number of nodes to be deleted so that at most k leaves are left

• Minimum number of nodes to be deleted so that k leaves are left (*)

# Standard DP

• Knuth's optimization
• Breaking string with cost
• Divide and Conquer Optimization
• Group people to reduce unfamiliarity 