Memoization to Optimize Recursion in DSA Go - Interactive Practice

Practice - 5 Tasks

1fill in blank

easy

Complete the code to declare the memo map for caching results.

DSA Go

var memo = make(map[int]int[1])

Drag options to blanks, or click blank then click option'

A<>

B[]

C()

D{}

Attempts:

3 left

💡 Hint

Common Mistakes

Using square brackets [] instead of curly braces {}

Using parentheses () which is invalid for map initialization

The memo map is initialized with curly braces {} to create an empty map.

2fill in blank

medium

Complete the code to check if the result for n is already cached in memo.

DSA Go

if val, ok := memo[[1]]; ok {
    return val
}

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Amemo

Bn

Cresult

Dval

Attempts:

3 left

💡 Hint

Common Mistakes

Checking memo[result] instead of memo[n]

Using memo[val] which is incorrect

We check if the input n is already in the memo map to avoid recomputation.

3fill in blank

hard

Fix the error in the recursive call to fib by adding memoization.

DSA Go

memo[n] = fib([1], memo) + fib(n-2, memo)

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An

Bn+1

Cn-1

Dn-2

Attempts:

3 left

💡 Hint

Common Mistakes

Using fib(n) causing infinite recursion

Using fib(n+1) which is incorrect

The recursive call should be fib(n-1, memo) to compute the previous Fibonacci number.

4fill in blank

hard

Fill both blanks to complete the memoized Fibonacci function signature and base case check.

DSA Go

func fib([1] int, [2] map[int]int) int {
    if n <= 1 {
        return n
    }

Drag options to blanks, or click blank then click option'

An

Bmemo

Ccache

Dval

Attempts:

3 left

💡 Hint

Common Mistakes

Using wrong parameter names like val or cache

Missing the memo parameter

The function takes n as int and memo as map[int]int for caching.

5fill in blank

hard

Fill all three blanks to complete the memoized Fibonacci function body.

DSA Go

if val, ok := [1][n]; ok {
    return val
}
memo[n] = fib(n-1, [2]) + fib(n-2, [3])
return memo[n]

Drag options to blanks, or click blank then click option'

Amemo

Dcache

Attempts:

3 left

💡 Hint

Common Mistakes

Using different variable names instead of memo

Not passing memo in recursive calls

The memo map is used to check and store computed Fibonacci values.

Practice

1. What is the main purpose of memoization in recursive functions?

easy

A. To store results of expensive function calls and reuse them

B. To make the function run slower by adding extra steps

C. To remove recursion and use loops instead

D. To increase the memory usage without any benefit

Solution

1. Step 1: Understand what memoization does

   Memoization saves the results of function calls so they don't need to be recalculated.

2. Step 2: Identify the benefit of memoization

   By reusing saved results, the function runs faster and avoids repeated work.

3. Final Answer:

   To store results of expensive function calls and reuse them -> Option A

4. Quick Check:

   Memoization = Store and reuse results [OK]

Hint: Memoization saves repeated work by caching results [OK]

Common Mistakes:

• Thinking memoization slows down the function
• Confusing memoization with removing recursion
• Ignoring the memory benefit of caching

2. Which of the following Go code snippets correctly declares a memo map for memoization of integer keys and values?

easy

A. memo := new(map[int]int)

B. memo := make(map[int]int)

C. memo := make([]int, 10)

D. memo := map[string]int{}

Solution

1. Step 1: Identify correct map declaration syntax

   In Go, make(map[int]int) creates a map with int keys and int values.

2. Step 2: Check other options

   memo := map[string]int{} uses string keys, not int; memo := make([]int, 10) creates a slice, not a map; memo := new(map[int]int) creates a pointer to a map but does not initialize it.

3. Final Answer:

   memo := make(map[int]int) -> Option B

4. Quick Check:

   Correct map syntax = make(map[int]int) [OK]

Hint: Use make(map[int]int) to create int-to-int map [OK]

Common Mistakes:

• Using slice instead of map for memo
• Using wrong key type in map
• Declaring pointer to map without initialization

3. What will be the output of the following Go code using memoization for Fibonacci numbers?

package main
import "fmt"

func fib(n int, memo map[int]int) int {
    if n <= 1 {
        return n
    }
    if val, ok := memo[n]; ok {
        return val
    }
    memo[n] = fib(n-1, memo) + fib(n-2, memo)
    return memo[n]
}

func main() {
    memo := make(map[int]int)
    fmt.Println(fib(5, memo))
}

medium

A. 8

B. Error

C. 3

D. 5

Solution

1. Step 1: Understand Fibonacci calculation with memo

   fib(5) = fib(4) + fib(3), and memo stores intermediate results to avoid repeats.

2. Step 2: Calculate fib(5) step-by-step

   fib(0)=0, fib(1)=1, fib(2)=1, fib(3)=2, fib(4)=3, fib(5)=5.

3. Final Answer:

   5 -> Option D

4. Quick Check:

   fib(5) = 5 [OK]

Hint: Memoized fib(5) returns 5 quickly [OK]

Common Mistakes:

• Confusing fib(5) with fib(6)
• Ignoring memo and recalculating
• Expecting error due to map usage

4. Identify the error in this Go recursive function with memoization for factorial:

func fact(n int, memo map[int]int) int {
    if n == 0 {
        return 1
    }
    if val, ok := memo[n]; ok {
        return val
    }
    memo[n] = n * fact(n-1, memo)
    return memo[n]
}

func main() {
    memo := make(map[int]int)
    fmt.Println(fact(-1, memo))
}

medium

A. Compilation error due to map usage

B. No error, output is 1

C. Infinite recursion for negative input

D. Returns 0 for negative input

Solution

1. Step 1: Analyze base case and input

   Base case is n == 0, but input is -1, so base case never reached.

2. Step 2: Understand recursion behavior

   For n = -1, function calls fact(-2), then fact(-3), causing infinite recursion.

3. Final Answer:

   Infinite recursion for negative input -> Option C

4. Quick Check:

   Negative input causes infinite recursion [OK]

Hint: Check base case covers all inputs to avoid infinite recursion [OK]

Common Mistakes:

• Assuming negative input returns 1
• Ignoring infinite recursion possibility
• Expecting compilation error incorrectly

5. You want to optimize a recursive function that calculates the number of ways to climb n stairs taking 1 or 2 steps at a time using memoization in Go. Which approach below correctly applies memoization to avoid repeated calculations?

hard

A. Pass a map[int]int as a parameter to the function and store intermediate results in it

B. Use a slice of size n and fill it after recursion completes

C. Use a global variable to store results and update it inside the function

D. Call the recursive function twice without storing results

Solution

1. Step 1: Understand memoization with parameters

   Passing a map as a parameter allows storing and reusing results during recursion.

2. Step 2: Evaluate options for memoization

   Pass a map[int]int as a parameter to the function and store intermediate results in it correctly uses a map parameter; Use a global variable to store results and update it inside the function uses global state which is less safe; Use a slice of size n and fill it after recursion completes fills after recursion, not during; Call the recursive function twice without storing results repeats work without memo.

3. Final Answer:

   Pass a map[int]int as a parameter to the function and store intermediate results in it -> Option A

4. Quick Check:

   Memo map parameter stores intermediate results [OK]

Hint: Pass memo map as argument to cache results during recursion [OK]

Common Mistakes:

• Using global variables instead of parameters
• Filling memo after recursion ends
• Not storing results causing repeated work