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Bhanu Bisht

Template

Dynamic Programming Template: Pattern, Code & Cheat Sheet

The Dynamic Programming pattern is one of the most frequently tested coding interview patterns. Optimize recursive solutions with memoization and tabulation. This template gives you a reusable code skeleton, pseudocode, and implementation in multiple languages so you can solve 25+ problems using this single mental model.

Difficulty: Hard | Time Complexity: O(n²) typical | Space Complexity: O(n) to O(n²)

When to Use This Template

Use the Dynamic Programming template when you see these signals in a problem:

1.Optimization problems — Problems asking to optimization problems

2.Counting problems — Problems asking to counting problems

3.Decision problems — Problems asking to decision problems

Prerequisites: Recursion, Arrays

Problem count on W Code: 25 problems across Easy, Medium, and Hard difficulty levels.

If the problem does not match these signals, consider alternative patterns.

Pseudocode Template

function dpSolve(input):
    // 1. Define state: dp[i] = optimal answer for subproblem i
    dp = array of size (n + 1), filled with base_value
    
    // 2. Base case
    dp[0] = base_case_value
    
    // 3. Transition
    for i in range(1, n + 1):
        for each choice:
            dp[i] = optimize(dp[i], dp[prev_state] + cost)
    
    // 4. Answer
    return dp[n]

Python Implementation

python
def dp_solve(n: int, choices: list) -> int:
    dp = [0] * (n + 1)
    dp[0] = 0  # base case
    
    for i in range(1, n + 1):
        dp[i] = float("inf")
        for choice in choices:
            if i - choice >= 0:
                dp[i] = min(dp[i], dp[i - choice] + 1)
    
    return dp[n] if dp[n] != float("inf") else -1

Java Implementation

java
public Object solve(Object[] input) {
    // Dynamic Programming template
    // Implement core logic here
    return null;
}

C++ Implementation

cpp
auto solve(vector<int>& input) {
    // Dynamic Programming template
    // Implement core logic
    return result;
}

Variations & Adaptations

The Dynamic Programming pattern has several variations you should master:

Variation 1: 1D DP (linear)

This variation is useful when the problem specifically requires 1d dp (linear). Adapt the main template by modifying the core loop/recursion logic accordingly.

Variation 2: 2D DP (grid/string)

This variation is useful when the problem specifically requires 2d dp (grid/string). Adapt the main template by modifying the core loop/recursion logic accordingly.

Variation 3: Knapsack Variants

This variation is useful when the problem specifically requires knapsack variants. Adapt the main template by modifying the core loop/recursion logic accordingly.

Variation 4: Interval DP

This variation is useful when the problem specifically requires interval dp. Adapt the main template by modifying the core loop/recursion logic accordingly.

Variation 5: State Machine DP

This variation is useful when the problem specifically requires state machine dp. Adapt the main template by modifying the core loop/recursion logic accordingly.

Common Mistakes & Edge Cases

When implementing Dynamic Programming, watch out for:

1.Off-by-one errors — Carefully handle boundary conditions in loops

2.Missing base case — Ensure recursion terminates properly

3.Integer overflow — Use appropriate data types for large inputs

4.Empty input — Handle null/empty arrays, strings, or graphs

5.Single element — Test with minimal inputs

Edge cases to always test:

•Empty input → expected output

•Single element → correct result

•All same elements → no infinite loop

•Maximum constraints → within time limit

Step-by-Step Problem Solving Guide

1.Identify the pattern: Does the problem involve Optimization problems, Counting problems, Decision problems?

2.Choose the template: Select the variation from above that best fits

3.Define variables: Map problem-specific entities to template variables

4.Implement the core logic: Fill in the template skeleton

5.Handle edge cases: Add boundary checks

6.Verify with examples: Trace through sample inputs

7.Analyze complexity: Confirm O(n²) typical time and O(n) to O(n²) space

Frequently Asked Questions

What problems can I solve with the Dynamic Programming template?

The Dynamic Programming template applies to 25+ problems including: Optimization problems, Counting problems, Decision problems. Look for problems that involve optimize recursive solutions with memoization and tabulation..

What is the time complexity of Dynamic Programming?

The typical time complexity is O(n²) typical with space complexity of O(n) to O(n²). Some variations may differ.

What should I learn before Dynamic Programming?

Prerequisites include: Recursion, Arrays. Make sure you are comfortable with these concepts first.

How do I recognize a Dynamic Programming problem in an interview?

Key signals: the problem involves optimization problems; the problem involves counting problems; the problem involves decision problems. Practice identifying these cues by solving at least 10 problems using this pattern.

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