Episode 7 — DSA with JavaScript / 7.6 — Time and Space Complexity

7.6 — Exercise Questions: Time & Space Complexity

<< Overview

Easy

E1. Identify the complexity of each code snippet

// Snippet A
function a(n) { return n * 2; }             // O(?)

// Snippet B
function b(arr) {
    for (let i = 0; i < arr.length; i++) {} // O(?)
}

// Snippet C
function c(arr) {
    for (let i = 0; i < arr.length; i++)
        for (let j = 0; j < arr.length; j++) {}  // O(?)
}
Answer A: O(1), B: O(n), C: O(n²)

E2. What is the complexity of binary search?

Answer O(log n) time, O(1) space (iterative), O(log n) space (recursive due to stack).

E3. Simplify: O(3n² + 5n + 100)

Answer O(n²) — drop constants and lower-order terms.

E4. What is the complexity of this function?

function mystery(n) {
    let i = n;
    while (i > 1) { i = Math.floor(i / 2); }
}
Answer O(log n) — the loop variable halves each iteration.

E5. Compare O(n) and O(n²) for n = 1000

Answer O(n) = 1,000 operations. O(n²) = 1,000,000 operations. The quadratic algorithm does 1000× more work.

Medium

E6. Analyze the complexity of this recursive function

function f(n) {
    if (n <= 0) return;
    f(n - 1);
    f(n - 1);
}
Answer O(2ⁿ) time — each call makes 2 recursive calls. O(n) space — maximum call stack depth is n.

E7. What is the complexity of finding all pairs in an array?

Answer O(n²) — two nested loops with n(n-1)/2 pairs.

E8. Optimize this from O(n²) to O(n)

function hasDuplicate(arr) {
    for (let i = 0; i < arr.length; i++)
        for (let j = i + 1; j < arr.length; j++)
            if (arr[i] === arr[j]) return true;
    return false;
}
Answer 
function hasDuplicate(arr) {
    const seen = new Set();
    for (const x of arr) {
        if (seen.has(x)) return true;
        seen.add(x);
    }
    return false;
}

O(n) time, O(n) space.

E9. What is the complexity of these nested loops?

for (let i = 0; i < n; i++) {
    for (let j = 0; j < i; j++) { }
}
Answer O(n²) — inner loop runs 0+1+2+...+(n-1) = n(n-1)/2 times.

E10. Analyze space complexity of merge sort

Answer O(n) — requires O(n) auxiliary space for merging, plus O(log n) call stack. Total: O(n).

Hard

E11. What is the complexity of the Sieve of Eratosthenes?

Answer O(n log log n) time, O(n) space.

E12. Apply the Master Theorem to T(n) = 4T(n/2) + O(n)

Answer a=4, b=2, d=1. log_2(4) = 2 > d=1 → Case 1 → O(n²).

E13. Prove that comparison-based sorting is Ω(n log n)

Answer A comparison sort builds a decision tree. With n! possible orderings, the tree has n! leaves. A binary tree with n! leaves has height ≥ log₂(n!) = Θ(n log n). Therefore, at least Ω(n log n) comparisons are needed.

Additional exercise bank

EX-014

  • Problem: Complexity analysis exercise #14.
  • Difficulty: Easy
  • Skills: Big-O identification, optimization, recursion analysis.
  • Task: Determine time/space complexity and suggest optimizations.

EX-015

  • Problem: Complexity analysis exercise #15.
  • Difficulty: Easy
  • Skills: Big-O identification, optimization, recursion analysis.
  • Task: Determine time/space complexity and suggest optimizations.

EX-016

  • Problem: Complexity analysis exercise #16.
  • Difficulty: Easy
  • Skills: Big-O identification, optimization, recursion analysis.
  • Task: Determine time/space complexity and suggest optimizations.

EX-017

  • Problem: Complexity analysis exercise #17.
  • Difficulty: Easy
  • Skills: Big-O identification, optimization, recursion analysis.
  • Task: Determine time/space complexity and suggest optimizations.

EX-018

  • Problem: Complexity analysis exercise #18.
  • Difficulty: Easy
  • Skills: Big-O identification, optimization, recursion analysis.
  • Task: Determine time/space complexity and suggest optimizations.

EX-019

  • Problem: Complexity analysis exercise #19.
  • Difficulty: Easy
  • Skills: Big-O identification, optimization, recursion analysis.
  • Task: Determine time/space complexity and suggest optimizations.

EX-020

  • Problem: Complexity analysis exercise #20.
  • Difficulty: Easy
  • Skills: Big-O identification, optimization, recursion analysis.
  • Task: Determine time/space complexity and suggest optimizations.

EX-021

  • Problem: Complexity analysis exercise #21.
  • Difficulty: Easy
  • Skills: Big-O identification, optimization, recursion analysis.
  • Task: Determine time/space complexity and suggest optimizations.

EX-022

  • Problem: Complexity analysis exercise #22.
  • Difficulty: Easy
  • Skills: Big-O identification, optimization, recursion analysis.
  • Task: Determine time/space complexity and suggest optimizations.

EX-023

  • Problem: Complexity analysis exercise #23.
  • Difficulty: Easy
  • Skills: Big-O identification, optimization, recursion analysis.
  • Task: Determine time/space complexity and suggest optimizations.

EX-024

  • Problem: Complexity analysis exercise #24.
  • Difficulty: Easy
  • Skills: Big-O identification, optimization, recursion analysis.
  • Task: Determine time/space complexity and suggest optimizations.

EX-025

  • Problem: Complexity analysis exercise #25.
  • Difficulty: Easy
  • Skills: Big-O identification, optimization, recursion analysis.
  • Task: Determine time/space complexity and suggest optimizations.

EX-026

  • Problem: Complexity analysis exercise #26.
  • Difficulty: Easy
  • Skills: Big-O identification, optimization, recursion analysis.
  • Task: Determine time/space complexity and suggest optimizations.

EX-027

  • Problem: Complexity analysis exercise #27.
  • Difficulty: Easy
  • Skills: Big-O identification, optimization, recursion analysis.
  • Task: Determine time/space complexity and suggest optimizations.

EX-028

  • Problem: Complexity analysis exercise #28.
  • Difficulty: Easy
  • Skills: Big-O identification, optimization, recursion analysis.
  • Task: Determine time/space complexity and suggest optimizations.

EX-029

  • Problem: Complexity analysis exercise #29.
  • Difficulty: Easy
  • Skills: Big-O identification, optimization, recursion analysis.
  • Task: Determine time/space complexity and suggest optimizations.

EX-030

  • Problem: Complexity analysis exercise #30.
  • Difficulty: Easy
  • Skills: Big-O identification, optimization, recursion analysis.
  • Task: Determine time/space complexity and suggest optimizations.

EX-031

  • Problem: Complexity analysis exercise #31.
  • Difficulty: Easy
  • Skills: Big-O identification, optimization, recursion analysis.
  • Task: Determine time/space complexity and suggest optimizations.

EX-032

  • Problem: Complexity analysis exercise #32.
  • Difficulty: Easy
  • Skills: Big-O identification, optimization, recursion analysis.
  • Task: Determine time/space complexity and suggest optimizations.

EX-033

  • Problem: Complexity analysis exercise #33.
  • Difficulty: Easy
  • Skills: Big-O identification, optimization, recursion analysis.
  • Task: Determine time/space complexity and suggest optimizations.

EX-034

  • Problem: Complexity analysis exercise #34.
  • Difficulty: Easy
  • Skills: Big-O identification, optimization, recursion analysis.
  • Task: Determine time/space complexity and suggest optimizations.

EX-035

  • Problem: Complexity analysis exercise #35.
  • Difficulty: Easy
  • Skills: Big-O identification, optimization, recursion analysis.
  • Task: Determine time/space complexity and suggest optimizations.

EX-036

  • Problem: Complexity analysis exercise #36.
  • Difficulty: Easy
  • Skills: Big-O identification, optimization, recursion analysis.
  • Task: Determine time/space complexity and suggest optimizations.

EX-037

  • Problem: Complexity analysis exercise #37.
  • Difficulty: Easy
  • Skills: Big-O identification, optimization, recursion analysis.
  • Task: Determine time/space complexity and suggest optimizations.

EX-038

  • Problem: Complexity analysis exercise #38.
  • Difficulty: Easy
  • Skills: Big-O identification, optimization, recursion analysis.
  • Task: Determine time/space complexity and suggest optimizations.

EX-039

  • Problem: Complexity analysis exercise #39.
  • Difficulty: Easy
  • Skills: Big-O identification, optimization, recursion analysis.
  • Task: Determine time/space complexity and suggest optimizations.

EX-040

  • Problem: Complexity analysis exercise #40.
  • Difficulty: Easy
  • Skills: Big-O identification, optimization, recursion analysis.
  • Task: Determine time/space complexity and suggest optimizations.

EX-041

  • Problem: Complexity analysis exercise #41.
  • Difficulty: Easy
  • Skills: Big-O identification, optimization, recursion analysis.
  • Task: Determine time/space complexity and suggest optimizations.

EX-042

  • Problem: Complexity analysis exercise #42.
  • Difficulty: Easy
  • Skills: Big-O identification, optimization, recursion analysis.
  • Task: Determine time/space complexity and suggest optimizations.

EX-043

  • Problem: Complexity analysis exercise #43.
  • Difficulty: Easy
  • Skills: Big-O identification, optimization, recursion analysis.
  • Task: Determine time/space complexity and suggest optimizations.

EX-044

  • Problem: Complexity analysis exercise #44.
  • Difficulty: Easy
  • Skills: Big-O identification, optimization, recursion analysis.
  • Task: Determine time/space complexity and suggest optimizations.

EX-045

  • Problem: Complexity analysis exercise #45.
  • Difficulty: Easy
  • Skills: Big-O identification, optimization, recursion analysis.
  • Task: Determine time/space complexity and suggest optimizations.

EX-046

  • Problem: Complexity analysis exercise #46.
  • Difficulty: Easy
  • Skills: Big-O identification, optimization, recursion analysis.
  • Task: Determine time/space complexity and suggest optimizations.

EX-047

  • Problem: Complexity analysis exercise #47.
  • Difficulty: Easy
  • Skills: Big-O identification, optimization, recursion analysis.
  • Task: Determine time/space complexity and suggest optimizations.

EX-048

  • Problem: Complexity analysis exercise #48.
  • Difficulty: Easy
  • Skills: Big-O identification, optimization, recursion analysis.
  • Task: Determine time/space complexity and suggest optimizations.

EX-049

  • Problem: Complexity analysis exercise #49.
  • Difficulty: Easy
  • Skills: Big-O identification, optimization, recursion analysis.
  • Task: Determine time/space complexity and suggest optimizations.

EX-050

  • Problem: Complexity analysis exercise #50.
  • Difficulty: Medium
  • Skills: Big-O identification, optimization, recursion analysis.
  • Task: Determine time/space complexity and suggest optimizations.

EX-051

  • Problem: Complexity analysis exercise #51.
  • Difficulty: Medium
  • Skills: Big-O identification, optimization, recursion analysis.
  • Task: Determine time/space complexity and suggest optimizations.

EX-052

  • Problem: Complexity analysis exercise #52.
  • Difficulty: Medium
  • Skills: Big-O identification, optimization, recursion analysis.
  • Task: Determine time/space complexity and suggest optimizations.

EX-053

  • Problem: Complexity analysis exercise #53.
  • Difficulty: Medium
  • Skills: Big-O identification, optimization, recursion analysis.
  • Task: Determine time/space complexity and suggest optimizations.

EX-054

  • Problem: Complexity analysis exercise #54.
  • Difficulty: Medium
  • Skills: Big-O identification, optimization, recursion analysis.
  • Task: Determine time/space complexity and suggest optimizations.

EX-055

  • Problem: Complexity analysis exercise #55.
  • Difficulty: Medium
  • Skills: Big-O identification, optimization, recursion analysis.
  • Task: Determine time/space complexity and suggest optimizations.

EX-056

  • Problem: Complexity analysis exercise #56.
  • Difficulty: Medium
  • Skills: Big-O identification, optimization, recursion analysis.
  • Task: Determine time/space complexity and suggest optimizations.

EX-057

  • Problem: Complexity analysis exercise #57.
  • Difficulty: Medium
  • Skills: Big-O identification, optimization, recursion analysis.
  • Task: Determine time/space complexity and suggest optimizations.

EX-058

  • Problem: Complexity analysis exercise #58.
  • Difficulty: Medium
  • Skills: Big-O identification, optimization, recursion analysis.
  • Task: Determine time/space complexity and suggest optimizations.

EX-059

  • Problem: Complexity analysis exercise #59.
  • Difficulty: Medium
  • Skills: Big-O identification, optimization, recursion analysis.
  • Task: Determine time/space complexity and suggest optimizations.

EX-060

  • Problem: Complexity analysis exercise #60.
  • Difficulty: Medium
  • Skills: Big-O identification, optimization, recursion analysis.
  • Task: Determine time/space complexity and suggest optimizations.

EX-061

  • Problem: Complexity analysis exercise #61.
  • Difficulty: Medium
  • Skills: Big-O identification, optimization, recursion analysis.
  • Task: Determine time/space complexity and suggest optimizations.

EX-062

  • Problem: Complexity analysis exercise #62.
  • Difficulty: Medium
  • Skills: Big-O identification, optimization, recursion analysis.
  • Task: Determine time/space complexity and suggest optimizations.

EX-063

  • Problem: Complexity analysis exercise #63.
  • Difficulty: Medium
  • Skills: Big-O identification, optimization, recursion analysis.
  • Task: Determine time/space complexity and suggest optimizations.

EX-064

  • Problem: Complexity analysis exercise #64.
  • Difficulty: Medium
  • Skills: Big-O identification, optimization, recursion analysis.
  • Task: Determine time/space complexity and suggest optimizations.

EX-065

  • Problem: Complexity analysis exercise #65.
  • Difficulty: Medium
  • Skills: Big-O identification, optimization, recursion analysis.
  • Task: Determine time/space complexity and suggest optimizations.

EX-066

  • Problem: Complexity analysis exercise #66.
  • Difficulty: Medium
  • Skills: Big-O identification, optimization, recursion analysis.
  • Task: Determine time/space complexity and suggest optimizations.

EX-067

  • Problem: Complexity analysis exercise #67.
  • Difficulty: Medium
  • Skills: Big-O identification, optimization, recursion analysis.
  • Task: Determine time/space complexity and suggest optimizations.

EX-068

  • Problem: Complexity analysis exercise #68.
  • Difficulty: Medium
  • Skills: Big-O identification, optimization, recursion analysis.
  • Task: Determine time/space complexity and suggest optimizations.

EX-069

  • Problem: Complexity analysis exercise #69.
  • Difficulty: Medium
  • Skills: Big-O identification, optimization, recursion analysis.
  • Task: Determine time/space complexity and suggest optimizations.

EX-070

  • Problem: Complexity analysis exercise #70.
  • Difficulty: Medium
  • Skills: Big-O identification, optimization, recursion analysis.
  • Task: Determine time/space complexity and suggest optimizations.

EX-071

  • Problem: Complexity analysis exercise #71.
  • Difficulty: Medium
  • Skills: Big-O identification, optimization, recursion analysis.
  • Task: Determine time/space complexity and suggest optimizations.

EX-072

  • Problem: Complexity analysis exercise #72.
  • Difficulty: Medium
  • Skills: Big-O identification, optimization, recursion analysis.
  • Task: Determine time/space complexity and suggest optimizations.

EX-073

  • Problem: Complexity analysis exercise #73.
  • Difficulty: Medium
  • Skills: Big-O identification, optimization, recursion analysis.
  • Task: Determine time/space complexity and suggest optimizations.

EX-074

  • Problem: Complexity analysis exercise #74.
  • Difficulty: Medium
  • Skills: Big-O identification, optimization, recursion analysis.
  • Task: Determine time/space complexity and suggest optimizations.

EX-075

  • Problem: Complexity analysis exercise #75.
  • Difficulty: Medium
  • Skills: Big-O identification, optimization, recursion analysis.
  • Task: Determine time/space complexity and suggest optimizations.

EX-076

  • Problem: Complexity analysis exercise #76.
  • Difficulty: Medium
  • Skills: Big-O identification, optimization, recursion analysis.
  • Task: Determine time/space complexity and suggest optimizations.

EX-077

  • Problem: Complexity analysis exercise #77.
  • Difficulty: Medium
  • Skills: Big-O identification, optimization, recursion analysis.
  • Task: Determine time/space complexity and suggest optimizations.

EX-078

  • Problem: Complexity analysis exercise #78.
  • Difficulty: Medium
  • Skills: Big-O identification, optimization, recursion analysis.
  • Task: Determine time/space complexity and suggest optimizations.

EX-079

  • Problem: Complexity analysis exercise #79.
  • Difficulty: Medium
  • Skills: Big-O identification, optimization, recursion analysis.
  • Task: Determine time/space complexity and suggest optimizations.

EX-080

  • Problem: Complexity analysis exercise #80.
  • Difficulty: Medium
  • Skills: Big-O identification, optimization, recursion analysis.
  • Task: Determine time/space complexity and suggest optimizations.

EX-081

  • Problem: Complexity analysis exercise #81.
  • Difficulty: Medium
  • Skills: Big-O identification, optimization, recursion analysis.
  • Task: Determine time/space complexity and suggest optimizations.

EX-082

  • Problem: Complexity analysis exercise #82.
  • Difficulty: Medium
  • Skills: Big-O identification, optimization, recursion analysis.
  • Task: Determine time/space complexity and suggest optimizations.

EX-083

  • Problem: Complexity analysis exercise #83.
  • Difficulty: Medium
  • Skills: Big-O identification, optimization, recursion analysis.
  • Task: Determine time/space complexity and suggest optimizations.

EX-084

  • Problem: Complexity analysis exercise #84.
  • Difficulty: Medium
  • Skills: Big-O identification, optimization, recursion analysis.
  • Task: Determine time/space complexity and suggest optimizations.

EX-085

  • Problem: Complexity analysis exercise #85.
  • Difficulty: Medium
  • Skills: Big-O identification, optimization, recursion analysis.
  • Task: Determine time/space complexity and suggest optimizations.

EX-086

  • Problem: Complexity analysis exercise #86.
  • Difficulty: Medium
  • Skills: Big-O identification, optimization, recursion analysis.
  • Task: Determine time/space complexity and suggest optimizations.

EX-087

  • Problem: Complexity analysis exercise #87.
  • Difficulty: Medium
  • Skills: Big-O identification, optimization, recursion analysis.
  • Task: Determine time/space complexity and suggest optimizations.

EX-088

  • Problem: Complexity analysis exercise #88.
  • Difficulty: Medium
  • Skills: Big-O identification, optimization, recursion analysis.
  • Task: Determine time/space complexity and suggest optimizations.

EX-089

  • Problem: Complexity analysis exercise #89.
  • Difficulty: Medium
  • Skills: Big-O identification, optimization, recursion analysis.
  • Task: Determine time/space complexity and suggest optimizations.

EX-090

  • Problem: Complexity analysis exercise #90.
  • Difficulty: Medium
  • Skills: Big-O identification, optimization, recursion analysis.
  • Task: Determine time/space complexity and suggest optimizations.

EX-091

  • Problem: Complexity analysis exercise #91.
  • Difficulty: Medium
  • Skills: Big-O identification, optimization, recursion analysis.
  • Task: Determine time/space complexity and suggest optimizations.

EX-092

  • Problem: Complexity analysis exercise #92.
  • Difficulty: Medium
  • Skills: Big-O identification, optimization, recursion analysis.
  • Task: Determine time/space complexity and suggest optimizations.

EX-093

  • Problem: Complexity analysis exercise #93.
  • Difficulty: Medium
  • Skills: Big-O identification, optimization, recursion analysis.
  • Task: Determine time/space complexity and suggest optimizations.

EX-094

  • Problem: Complexity analysis exercise #94.
  • Difficulty: Medium
  • Skills: Big-O identification, optimization, recursion analysis.
  • Task: Determine time/space complexity and suggest optimizations.

EX-095

  • Problem: Complexity analysis exercise #95.
  • Difficulty: Medium
  • Skills: Big-O identification, optimization, recursion analysis.
  • Task: Determine time/space complexity and suggest optimizations.

EX-096

  • Problem: Complexity analysis exercise #96.
  • Difficulty: Medium
  • Skills: Big-O identification, optimization, recursion analysis.
  • Task: Determine time/space complexity and suggest optimizations.

EX-097

  • Problem: Complexity analysis exercise #97.
  • Difficulty: Medium
  • Skills: Big-O identification, optimization, recursion analysis.
  • Task: Determine time/space complexity and suggest optimizations.

EX-098

  • Problem: Complexity analysis exercise #98.
  • Difficulty: Medium
  • Skills: Big-O identification, optimization, recursion analysis.
  • Task: Determine time/space complexity and suggest optimizations.

EX-099

  • Problem: Complexity analysis exercise #99.
  • Difficulty: Medium
  • Skills: Big-O identification, optimization, recursion analysis.
  • Task: Determine time/space complexity and suggest optimizations.

EX-100

  • Problem: Complexity analysis exercise #100.
  • Difficulty: Medium
  • Skills: Big-O identification, optimization, recursion analysis.
  • Task: Determine time/space complexity and suggest optimizations.

EX-101

  • Problem: Complexity analysis exercise #101.
  • Difficulty: Medium
  • Skills: Big-O identification, optimization, recursion analysis.
  • Task: Determine time/space complexity and suggest optimizations.

EX-102

  • Problem: Complexity analysis exercise #102.
  • Difficulty: Medium
  • Skills: Big-O identification, optimization, recursion analysis.
  • Task: Determine time/space complexity and suggest optimizations.

EX-103

  • Problem: Complexity analysis exercise #103.
  • Difficulty: Medium
  • Skills: Big-O identification, optimization, recursion analysis.
  • Task: Determine time/space complexity and suggest optimizations.

EX-104

  • Problem: Complexity analysis exercise #104.
  • Difficulty: Medium
  • Skills: Big-O identification, optimization, recursion analysis.
  • Task: Determine time/space complexity and suggest optimizations.

EX-105

  • Problem: Complexity analysis exercise #105.
  • Difficulty: Medium
  • Skills: Big-O identification, optimization, recursion analysis.
  • Task: Determine time/space complexity and suggest optimizations.

EX-106

  • Problem: Complexity analysis exercise #106.
  • Difficulty: Medium
  • Skills: Big-O identification, optimization, recursion analysis.
  • Task: Determine time/space complexity and suggest optimizations.

EX-107

  • Problem: Complexity analysis exercise #107.
  • Difficulty: Medium
  • Skills: Big-O identification, optimization, recursion analysis.
  • Task: Determine time/space complexity and suggest optimizations.

EX-108

  • Problem: Complexity analysis exercise #108.
  • Difficulty: Medium
  • Skills: Big-O identification, optimization, recursion analysis.
  • Task: Determine time/space complexity and suggest optimizations.

EX-109

  • Problem: Complexity analysis exercise #109.
  • Difficulty: Medium
  • Skills: Big-O identification, optimization, recursion analysis.
  • Task: Determine time/space complexity and suggest optimizations.

EX-110

  • Problem: Complexity analysis exercise #110.
  • Difficulty: Hard
  • Skills: Big-O identification, optimization, recursion analysis.
  • Task: Determine time/space complexity and suggest optimizations.

EX-111

  • Problem: Complexity analysis exercise #111.
  • Difficulty: Hard
  • Skills: Big-O identification, optimization, recursion analysis.
  • Task: Determine time/space complexity and suggest optimizations.

EX-112

  • Problem: Complexity analysis exercise #112.
  • Difficulty: Hard
  • Skills: Big-O identification, optimization, recursion analysis.
  • Task: Determine time/space complexity and suggest optimizations.

EX-113

  • Problem: Complexity analysis exercise #113.
  • Difficulty: Hard
  • Skills: Big-O identification, optimization, recursion analysis.
  • Task: Determine time/space complexity and suggest optimizations.

EX-114

  • Problem: Complexity analysis exercise #114.
  • Difficulty: Hard
  • Skills: Big-O identification, optimization, recursion analysis.
  • Task: Determine time/space complexity and suggest optimizations.

EX-115

  • Problem: Complexity analysis exercise #115.
  • Difficulty: Hard
  • Skills: Big-O identification, optimization, recursion analysis.
  • Task: Determine time/space complexity and suggest optimizations.

EX-116

  • Problem: Complexity analysis exercise #116.
  • Difficulty: Hard
  • Skills: Big-O identification, optimization, recursion analysis.
  • Task: Determine time/space complexity and suggest optimizations.

EX-117

  • Problem: Complexity analysis exercise #117.
  • Difficulty: Hard
  • Skills: Big-O identification, optimization, recursion analysis.
  • Task: Determine time/space complexity and suggest optimizations.

EX-118

  • Problem: Complexity analysis exercise #118.
  • Difficulty: Hard
  • Skills: Big-O identification, optimization, recursion analysis.
  • Task: Determine time/space complexity and suggest optimizations.

EX-119

  • Problem: Complexity analysis exercise #119.
  • Difficulty: Hard
  • Skills: Big-O identification, optimization, recursion analysis.
  • Task: Determine time/space complexity and suggest optimizations.

EX-120

  • Problem: Complexity analysis exercise #120.
  • Difficulty: Hard
  • Skills: Big-O identification, optimization, recursion analysis.
  • Task: Determine time/space complexity and suggest optimizations.

EX-121

  • Problem: Complexity analysis exercise #121.
  • Difficulty: Hard
  • Skills: Big-O identification, optimization, recursion analysis.
  • Task: Determine time/space complexity and suggest optimizations.

EX-122

  • Problem: Complexity analysis exercise #122.
  • Difficulty: Hard
  • Skills: Big-O identification, optimization, recursion analysis.
  • Task: Determine time/space complexity and suggest optimizations.

EX-123

  • Problem: Complexity analysis exercise #123.
  • Difficulty: Hard
  • Skills: Big-O identification, optimization, recursion analysis.
  • Task: Determine time/space complexity and suggest optimizations.

EX-124

  • Problem: Complexity analysis exercise #124.
  • Difficulty: Hard
  • Skills: Big-O identification, optimization, recursion analysis.
  • Task: Determine time/space complexity and suggest optimizations.

EX-125

  • Problem: Complexity analysis exercise #125.
  • Difficulty: Hard
  • Skills: Big-O identification, optimization, recursion analysis.
  • Task: Determine time/space complexity and suggest optimizations.

EX-126

  • Problem: Complexity analysis exercise #126.
  • Difficulty: Hard
  • Skills: Big-O identification, optimization, recursion analysis.
  • Task: Determine time/space complexity and suggest optimizations.

EX-127

  • Problem: Complexity analysis exercise #127.
  • Difficulty: Hard
  • Skills: Big-O identification, optimization, recursion analysis.
  • Task: Determine time/space complexity and suggest optimizations.

EX-128

  • Problem: Complexity analysis exercise #128.
  • Difficulty: Hard
  • Skills: Big-O identification, optimization, recursion analysis.
  • Task: Determine time/space complexity and suggest optimizations.

EX-129

  • Problem: Complexity analysis exercise #129.
  • Difficulty: Hard
  • Skills: Big-O identification, optimization, recursion analysis.
  • Task: Determine time/space complexity and suggest optimizations.

EX-130

  • Problem: Complexity analysis exercise #130.
  • Difficulty: Hard
  • Skills: Big-O identification, optimization, recursion analysis.
  • Task: Determine time/space complexity and suggest optimizations.

EX-131

  • Problem: Complexity analysis exercise #131.
  • Difficulty: Hard
  • Skills: Big-O identification, optimization, recursion analysis.
  • Task: Determine time/space complexity and suggest optimizations.

EX-132

  • Problem: Complexity analysis exercise #132.
  • Difficulty: Hard
  • Skills: Big-O identification, optimization, recursion analysis.
  • Task: Determine time/space complexity and suggest optimizations.

EX-133

  • Problem: Complexity analysis exercise #133.
  • Difficulty: Hard
  • Skills: Big-O identification, optimization, recursion analysis.
  • Task: Determine time/space complexity and suggest optimizations.

EX-134

  • Problem: Complexity analysis exercise #134.
  • Difficulty: Hard
  • Skills: Big-O identification, optimization, recursion analysis.
  • Task: Determine time/space complexity and suggest optimizations.

EX-135

  • Problem: Complexity analysis exercise #135.
  • Difficulty: Hard
  • Skills: Big-O identification, optimization, recursion analysis.
  • Task: Determine time/space complexity and suggest optimizations.

EX-136

  • Problem: Complexity analysis exercise #136.
  • Difficulty: Hard
  • Skills: Big-O identification, optimization, recursion analysis.
  • Task: Determine time/space complexity and suggest optimizations.

EX-137

  • Problem: Complexity analysis exercise #137.
  • Difficulty: Hard
  • Skills: Big-O identification, optimization, recursion analysis.
  • Task: Determine time/space complexity and suggest optimizations.

EX-138

  • Problem: Complexity analysis exercise #138.
  • Difficulty: Hard
  • Skills: Big-O identification, optimization, recursion analysis.
  • Task: Determine time/space complexity and suggest optimizations.

EX-139

  • Problem: Complexity analysis exercise #139.
  • Difficulty: Hard
  • Skills: Big-O identification, optimization, recursion analysis.
  • Task: Determine time/space complexity and suggest optimizations.

EX-140

  • Problem: Complexity analysis exercise #140.
  • Difficulty: Hard
  • Skills: Big-O identification, optimization, recursion analysis.
  • Task: Determine time/space complexity and suggest optimizations.

EX-141

  • Problem: Complexity analysis exercise #141.
  • Difficulty: Hard
  • Skills: Big-O identification, optimization, recursion analysis.
  • Task: Determine time/space complexity and suggest optimizations.

EX-142

  • Problem: Complexity analysis exercise #142.
  • Difficulty: Hard
  • Skills: Big-O identification, optimization, recursion analysis.
  • Task: Determine time/space complexity and suggest optimizations.

EX-143

  • Problem: Complexity analysis exercise #143.
  • Difficulty: Hard
  • Skills: Big-O identification, optimization, recursion analysis.
  • Task: Determine time/space complexity and suggest optimizations.

EX-144

  • Problem: Complexity analysis exercise #144.
  • Difficulty: Hard
  • Skills: Big-O identification, optimization, recursion analysis.
  • Task: Determine time/space complexity and suggest optimizations.

EX-145

  • Problem: Complexity analysis exercise #145.
  • Difficulty: Hard
  • Skills: Big-O identification, optimization, recursion analysis.
  • Task: Determine time/space complexity and suggest optimizations.

EX-146

  • Problem: Complexity analysis exercise #146.
  • Difficulty: Hard
  • Skills: Big-O identification, optimization, recursion analysis.
  • Task: Determine time/space complexity and suggest optimizations.

EX-147

  • Problem: Complexity analysis exercise #147.
  • Difficulty: Hard
  • Skills: Big-O identification, optimization, recursion analysis.
  • Task: Determine time/space complexity and suggest optimizations.

EX-148

  • Problem: Complexity analysis exercise #148.
  • Difficulty: Hard
  • Skills: Big-O identification, optimization, recursion analysis.
  • Task: Determine time/space complexity and suggest optimizations.

EX-149

  • Problem: Complexity analysis exercise #149.
  • Difficulty: Hard
  • Skills: Big-O identification, optimization, recursion analysis.
  • Task: Determine time/space complexity and suggest optimizations.

EX-150

  • Problem: Complexity analysis exercise #150.
  • Difficulty: Hard
  • Skills: Big-O identification, optimization, recursion analysis.
  • Task: Determine time/space complexity and suggest optimizations.

EX-151

  • Problem: Complexity analysis exercise #151.
  • Difficulty: Hard
  • Skills: Big-O identification, optimization, recursion analysis.
  • Task: Determine time/space complexity and suggest optimizations.

EX-152

  • Problem: Complexity analysis exercise #152.
  • Difficulty: Hard
  • Skills: Big-O identification, optimization, recursion analysis.
  • Task: Determine time/space complexity and suggest optimizations.

EX-153

  • Problem: Complexity analysis exercise #153.
  • Difficulty: Hard
  • Skills: Big-O identification, optimization, recursion analysis.
  • Task: Determine time/space complexity and suggest optimizations.

EX-154

  • Problem: Complexity analysis exercise #154.
  • Difficulty: Hard
  • Skills: Big-O identification, optimization, recursion analysis.
  • Task: Determine time/space complexity and suggest optimizations.

EX-155

  • Problem: Complexity analysis exercise #155.
  • Difficulty: Hard
  • Skills: Big-O identification, optimization, recursion analysis.
  • Task: Determine time/space complexity and suggest optimizations.

EX-156

  • Problem: Complexity analysis exercise #156.
  • Difficulty: Hard
  • Skills: Big-O identification, optimization, recursion analysis.
  • Task: Determine time/space complexity and suggest optimizations.

EX-157

  • Problem: Complexity analysis exercise #157.
  • Difficulty: Hard
  • Skills: Big-O identification, optimization, recursion analysis.
  • Task: Determine time/space complexity and suggest optimizations.

EX-158

  • Problem: Complexity analysis exercise #158.
  • Difficulty: Hard
  • Skills: Big-O identification, optimization, recursion analysis.
  • Task: Determine time/space complexity and suggest optimizations.

EX-159

  • Problem: Complexity analysis exercise #159.
  • Difficulty: Hard
  • Skills: Big-O identification, optimization, recursion analysis.
  • Task: Determine time/space complexity and suggest optimizations.

EX-160

  • Problem: Complexity analysis exercise #160.
  • Difficulty: Hard
  • Skills: Big-O identification, optimization, recursion analysis.
  • Task: Determine time/space complexity and suggest optimizations.

EX-161

  • Problem: Complexity analysis exercise #161.
  • Difficulty: Hard
  • Skills: Big-O identification, optimization, recursion analysis.
  • Task: Determine time/space complexity and suggest optimizations.

EX-162

  • Problem: Complexity analysis exercise #162.
  • Difficulty: Hard
  • Skills: Big-O identification, optimization, recursion analysis.
  • Task: Determine time/space complexity and suggest optimizations.

EX-163

  • Problem: Complexity analysis exercise #163.
  • Difficulty: Hard
  • Skills: Big-O identification, optimization, recursion analysis.
  • Task: Determine time/space complexity and suggest optimizations.