Memoization Top Down DP in DSA C - Cheat Sheet & Quick Revision

Recall & Review

beginner

What is memoization in the context of dynamic programming?

Memoization is a technique where we store the results of expensive function calls and reuse them when the same inputs occur again, avoiding repeated calculations.

beginner

How does top-down dynamic programming differ from bottom-up dynamic programming?

Top-down DP solves the problem by breaking it down recursively and storing results (memoization), while bottom-up DP solves smaller subproblems first and builds up to the solution iteratively.

beginner

In C, what data structure is commonly used to store memoized results for top-down DP?

An array or a 2D array is commonly used to store memoized results, where each index corresponds to a subproblem's input parameters.

intermediate

Why is memoization important in recursive solutions for problems like Fibonacci numbers?

Without memoization, recursive solutions recompute the same subproblems many times, causing exponential time. Memoization reduces this to linear time by storing and reusing results.

intermediate

What is a key step to implement memoization in a top-down DP function in C?

Initialize a memo array with a special value (like -1) to indicate uncomputed states, then check this array before computing a subproblem to reuse stored results.

What does memoization help avoid in recursive DP solutions?

A Using extra memory

B Repeated calculations of the same subproblems

C Writing recursive functions

D Using loops

Memoization stores results of subproblems to avoid recalculating them multiple times.

In top-down DP, when do we store the result of a subproblem?

A Before solving the subproblem

B We never store results

C Only for the final answer

D After solving the subproblem

We store the result after computing a subproblem to reuse it later.

Which of these is a common initial value to mark uncomputed states in memo arrays?

A 0

B 1

C -1

D 100

Using -1 helps identify which states have not been computed yet.

What is the time complexity improvement when using memoization for Fibonacci numbers?

A From O(2^n) to O(n)

B No improvement

C From O(n) to O(1)

D From O(n^2) to O(n)

Memoization reduces exponential time O(2^n) to linear time O(n) for Fibonacci.

Which programming construct is essential for top-down DP?

A Recursion

B Iteration with for loops

C Switch statements

D Goto statements

Top-down DP uses recursion to break down problems.

Explain how memoization works in a top-down dynamic programming approach.

Think about how you remember answers to avoid solving the same problem twice.

Describe the steps to implement memoization for a recursive Fibonacci function in C.

Focus on how you use an array to save and reuse results.