Dynamic Programming Explained for Beginners (With Simple Code Examples)

Dynamic Programming (DP) is one of the most powerful problem-solving techniques in computer science. If you are preparing for coding interviews, competitive programming, or learning Data Structures and Algorithms (DSA), then understanding Dynamic Programming is extremely important.

In this article, we will learn:

What is Dynamic Programming?
Why do we need it?
Overlapping subproblems
Optimal substructure
Memoization vs Tabulation
Beginner-friendly code examples
How to start practicing DP

If you are new to programming concepts, you may first read our guide on
👉 Understanding OOPS – Four Pillars of OOPS
to build strong fundamentals.

What is Dynamic Programming?

Dynamic Programming is an optimization technique used to solve problems by breaking them into smaller subproblems and storing the results of those subproblems to avoid recomputation.

Instead of solving the same problem again and again, we save the answer and reuse it.

This makes the algorithm much faster.

Why Do We Need Dynamic Programming?

Let’s understand with an example.

Suppose we want to calculate Fibonacci numbers:

F(0) = 0
F(1) = 1
F(n) = F(n-1) + F(n-2)

If we solve this using simple recursion, many values are calculated multiple times.

Example:

F(5) calls:

F(4)
F(3)

But F(4) again calls F(3).
So F(3) is calculated multiple times.

This is called Overlapping Subproblems.

Dynamic Programming solves this problem by storing already calculated results.

Two Important Properties of Dynamic Programming

1️⃣ Overlapping Subproblems

If a problem can be broken into smaller repeated subproblems, we can use DP.

2️⃣ Optimal Substructure

If the optimal solution of a problem depends on optimal solutions of its subproblems, DP can be applied.

Approaches in Dynamic Programming

There are two main approaches:

1️⃣ Memoization (Top-Down)

Uses recursion
Stores results in a cache (array/dictionary)
Avoids repeated computation

Example: Fibonacci Using Memoization (Python)

def fibonacci(n, dp):
    if n <= 1:
        return n
    
    if dp[n] != -1:
        return dp[n]
    
    dp[n] = fibonacci(n-1, dp) + fibonacci(n-2, dp)
    return dp[n]

n = 6
dp = [-1] * (n + 1)
print(fibonacci(n, dp))

Time Complexity: O(n)
Space Complexity: O(n)

2️⃣ Tabulation (Bottom-Up)

Uses iteration
No recursion
Builds solution from smallest subproblem

Example: Fibonacci Using Tabulation (Python)

def fibonacci(n):
    if n <= 1:
        return n
    
    dp = [0] * (n + 1)
    dp[1] = 1
    
    for i in range(2, n + 1):
        dp[i] = dp[i-1] + dp[i-2]
    
    return dp[n]

print(fibonacci(6))

Time Complexity: O(n)
Space Complexity: O(n)

Which One Should Beginners Use?

For beginners:

First understand recursion clearly
Then learn memoization
Finally practice tabulation

If you are also learning problem-solving basics, check:
👉 Time and Space Complexity Explained for Beginners
(Replace with your actual internal link if different)

Real-Life Example of Dynamic Programming

Imagine you are climbing stairs.

You can climb:

1 step
2 steps

How many ways can you reach step n?

This is also a DP problem because:

Ways(n) = Ways(n-1) + Ways(n-2)

This is again Fibonacci pattern.

Common Dynamic Programming Problems for Practice

Beginner Level:

Fibonacci
Climbing Stairs
Coin Change (basic)
Knapsack (0/1 basic)

Intermediate Level:

Longest Common Subsequence
Longest Increasing Subsequence
Matrix Chain Multiplication

How to Identify a DP Problem?

Ask yourself:

Can the problem be divided into smaller subproblems?
Are subproblems repeating?
Can I store results to avoid recalculation?

If YES → Try Dynamic Programming.

Dynamic Programming vs Recursion

Feature	Recursion	Dynamic Programming
Speed	Slow (repeated calls)	Fast
Memory	Less	More (stores results)
Efficiency	Poor for large input	Very efficient

Final Thoughts

Dynamic Programming may look difficult at first, but once you understand:

Overlapping subproblems
Optimal substructure
Memoization
Tabulation

It becomes much easier.

Start with small problems. Practice daily. Slowly move to advanced ones.

DP is one of the most important topics in coding interviews at top tech companies.

Dynamic Programming for Beginners: Easy Explanation with Code Examples (Python)