Dp Pattern Library

dp-pattern-library

A specialized skill for dynamic programming pattern recognition, matching problems to known DP patterns, generating template code, and providing optimization guidance for DP solutions.

Purpose

Assist with dynamic programming by:

• Matching problems to 50+ classic DP patterns
• Generating template code for matched patterns
• Detecting problem variants (knapsack variants, LCS variants, etc.)
• Providing state design recommendations
• Suggesting optimization techniques

Capabilities

Core Features

1. Pattern Recognition

   • Analyze problem statement for DP indicators
   • Match to known pattern categories
   • Identify problem variants and transformations
   • Suggest state representation

2. Pattern Categories

   • Linear DP (1D array)
   • Grid/Matrix DP (2D paths)
   • String DP (LCS, edit distance)
   • Interval DP (ranges, parenthesization)
   • Tree DP (subtree problems)
   • Bitmask DP (subset enumeration)
   • Digit DP (number counting)
   • Knapsack variants
   • DP with state machine

3. Code Generation

   • Template code for recognized patterns
   • Multiple language support (Python, C++, Java)
   • Comments explaining state and transitions
   • Space-optimized variants

4. Optimization Guidance

   • Rolling array technique
   • Convex hull trick
   • Divide and conquer optimization
   • Monotonic queue/stack optimization
   • Knuth optimization

Pattern Library

Linear DP Patterns

String DP Patterns

Knapsack Patterns

Grid DP Patterns

Interval DP Patterns

Tree DP Patterns

Bitmask DP Patterns

Usage

Pattern Matching

# Match problem to DP pattern
dp-pattern-library match --problem "Given an array of integers, find the longest increasing subsequence"

# Output:
# Pattern: Linear DP - Longest Increasing Subsequence (LIS)
# State: dp[i] = length of LIS ending at index i
# Transition: dp[i] = max(dp[j] + 1) for all j < i where arr[j] < arr[i]
# Time: O(n^2) naive, O(n log n) with binary search
# Space: O(n)

Template Generation

# Generate template code
dp-pattern-library template --pattern "lis" --language python

# Output:
def lengthOfLIS(nums):
    if not nums:
        return 0

    n = len(nums)
    # dp[i] = length of LIS ending at index i
    dp = [1] * n

    for i in range(1, n):
        for j in range(i):
            if nums[j] < nums[i]:
                dp[i] = max(dp[i], dp[j] + 1)

    return max(dp)

Optimization Suggestions

# Get optimization recommendations
dp-pattern-library optimize --pattern "lis"

# Output:
# Current: O(n^2) time, O(n) space
# Optimizations:
# 1. Binary Search: O(n log n) time
#    - Maintain sorted list of smallest tail elements
#    - Binary search for insertion point
# 2. Segment Tree: O(n log n) time
#    - For coordinate compression + range max query

Output Schema

{
  "match": {
    "pattern": "Linear DP - LIS",
    "confidence": 0.95,
    "category": "linear",
    "variants": ["LIS", "LDS", "LNDS"]
  },
  "state": {
    "description": "dp[i] = length of LIS ending at index i",
    "dimensions": 1,
    "meaning": "LIS length ending at position i"
  },
  "transition": {
    "formula": "dp[i] = max(dp[j] + 1) for j < i, arr[j] < arr[i]",
    "baseCase": "dp[i] = 1 for all i",
    "order": "left to right"
  },
  "complexity": {
    "time": "O(n^2)",
    "space": "O(n)",
    "optimized": {
      "time": "O(n log n)",
      "technique": "binary search on patience sort"
    }
  },
  "template": {
    "python": "...",
    "cpp": "...",
    "java": "..."
  },
  "similarProblems": [
    "Longest Increasing Subsequence",
    "Number of Longest Increasing Subsequence",
    "Russian Doll Envelopes",
    "Maximum Length of Pair Chain"
  ]
}

Integration with Processes

This skill enhances:

• dp-pattern-matching - Core pattern matching workflow
• dp-state-optimization - State space optimization
• dp-transition-derivation - Deriving transitions
• leetcode-problem-solving - DP problem identification
• classic-dp-library - Building a personal DP library

Pattern Recognition Indicators

References

• Dynamic Programming Patterns
• DP Visualization Tools
• LeetCode DP Patterns
• CP Algorithms - DP
• CSES DP Section

Error Handling

Best Practices

1. Start with brute force - Understand recurrence before optimizing
2. Draw state diagram - Visualize transitions
3. Verify base cases - Most DP bugs are in base cases
4. Check state uniqueness - Each state should be uniquely defined
5. Consider space optimization - Often can reduce dimension
6. Test with small inputs - Trace through by hand