Are you going to appear for a FAANG interview? Then, the one quintessential topic that you must not miss is Dynamic Programming (DP). This concept can be intimidating to many aspirants. However, several tech interview analyses have depicted this as the core differentiator between strong and weak candidates.
Therefore, to give your FAANG interview prep a more structured and strategic approach, this is a step-by-step roadmap to understand its core concepts, transform your problem-solving skills, apply a universal solving framework, and dramatically increase your confidence. So, let’s get started.
Demystifying the core concepts of DP
Dynamic Programming is mainly an optimization paradigm that breaks down complex problems into simpler subproblems, solving each only once, and storing their solutions. This is a technique called “memoization.”
Now, this technique has two primary implementation methods:
- Top-Down (Memoization): This is a recursive problem-solving method with a cache. Starting from the original problem, you gradually work downwards. Whenever you solve a subproblem, you record its answer in a memo (like an array or dictionary). This helps prevent needless, expensive computations later.
- Bottom-Up (Tabulation): This is more of an iterative, table-driven method. Opposite of the Top-Down approach, here you start from the smallest, simplest subproblems and systematically build up to the solution for the original problem. This implementation is considered more efficient since it avoids potential recursion stack limits.
So, how do you recognize if a problem is solvable by DP? You need to look for these two key properties in the problem:
- Overlapping subproblems: A problem can be broken down into subproblems whose solutions are reused multiple times. A perfect example is computing the Fibonacci sequence, where the value of `fib(3)` is needed repeatedly.
- Optimal substructure: The optimal solution to the main problem can be constructed from the optimal solutions of its subproblems. For example, if the shortest path from point A to point C goes through point B, then the path from A to B and B to C must also be the shortest paths.
A universal framework for solving DP problems
You can resolve any DP problem by following this step-by-step framework:
Step 1: Categorize the problem
First, you need to recognize the problem’s pattern correctly. Common categories include:
- 1D/2D Array: Fibonacci, Climbing Stairs, Unique Paths.
- Knapsack: Partition Equal Subset Sum, Coin Change.
- String/Palindrome: Longest Common Subsequence, Longest Palindromic Substring.
- Interval: Matrix Chain Multiplication.
Step 2: Define the State and DP table
After categorizing the problem correctly, identify the state (a set of parameters that define a subproblem) and the DP array (table to store the solution for that state) of the problem.
- Ask yourself: “What information do I need to know at each step?” For instance, for `dp[i]` in “Climbing Stairs,” the state is the step number `i`, and the value is the number of ways to reach it.
Step 3: Formulate the recurrence relation
Recurrence relation is the core of any DP solution. It’s an equation that defines how to calculate a larger solution from smaller, already-solved subproblems.
- Pseudocode first: “The ways to reach step `i` equals the summation of ways to reach step `i-1` and step `i-2`.”
- Then, in code language: `dp[i] = dp[i-1] + dp[i-2]`.
Step 4: Establish Base Cases
You can easily solve base cases without any further decomposition, as they are the simplest, smallest subproblems. They anchor the entire solution and prevent infinite loops.
- For climbing stairs problems: `dp[0] = 1` (one way to be on the ground), `dp[1] = 1`.
Step 5: Implement and optimize
- Implementation: Choose the Top-Down method for clarity or the Bottom-Up method for efficiency in your solution. During interviews, express that you can do both, but implement only the most efficient one.
- Optimization: To get the most optimal solution, analyze space complexity. Can you reduce a 2D table to a 1D array? Can you replace an array with just a few variables?
Walkthrough: The “Coin Change” problem
Let’s understand the framework better by applying it to the classic Coin Change problem.
The problem: You are given coins of different denominations and a total amount. Write a function to compute the fewest number of coins needed to make that amount.
Let’s apply our framework:
Step 1: Categorize: An Unbounded Knapsack Problem
Step 2: Define State: dp[i] = minimum number of coins needed to make up the amount i.
Step 3: Recurrence Relation: For each amount i, iterate through each coin. If, coin ≤ i, then dp[i] = min(dp[i], 1 + dp[i – coin])
Step 4: Base Case: dp[0] = 0. Making an amount 0 requires 0 coins. Initialize all other dp[i] to a large number (e.g., amount + 1) to represent an initially impossible state.
Step 5: Implement (Bottom-Up):
def coinChange(coins, amount):
dp = [amount + 1] * (amount + 1)
dp[0] = 0
for i in range(1, amount + 1):
for coin in coins:
if coin <= i:
dp[i] = min(dp[i], 1 + dp[i – coin])
return dp[amount] if dp[amount] != amount + 1 else -1
Time complexity: O(amount * len(coins)),
Space complexity: O(amount).
The Non-negotiable: Practice with curated questions
To master DP, theory alone is insufficient; you need a deliberate, pattern-focused practice. You cannot master algorithms and data structures by solving random questions. This is why practicing with hand-picked questions is a must-have resource. For example, AlgoCademy’s well-curated, hand-picked question bank provides a structured path through the entire DP landscape.
- Cover all fundamental patterns (Knapsack, LCS, LIS, etc.), no duplicates.
- Attempt problems of varying difficulty, from “Climbing Stairs” to “Edit Distance.”
- Heighten the muscle memory needed to quickly and accurately recognize the problem’s category and state in a time-bound, pressured interview setting.
Building this efficiency is the most critical skill for success in a FAANG interview. Further, to be able to solve coding questions under pressure, you must first learn to internalize these patterns through systematic repetition.
Final thoughts
Learning Dynamic Programming is a journey. You need patience, consistent practice, and a solid strategy. By following the above approach, you will be able to master this overwhelming subject and make it your most powerful interview strength.
Sandra Larson is a writer with the personal blog at ElizabethanAuthor and an academic coach for students. Her main sphere of professional interest is the connection between AI and modern study techniques. Sandra believes that digital tools are a way to a better future in the education system.