id int64 0 447k | category stringclasses 13
values | difficulty stringclasses 4
values | instruction stringlengths 22 415 | thinking stringlengths 30 837 | output stringlengths 28 1.45k |
|---|---|---|---|---|---|
0 | complexity_analysis | hard | Analyze the time and space complexity of the following Python code snippet. Provide a detailed step-by-step reasoning before giving the final answer.
```python
for i in range(n):
for j in range(n):
print(i, j)
``` | Let me carefully analyze this code step by step.
**Step 1 β Identify the structure**
I can see the code contains: 'for i in range(n):\n for j in range(n):\n print(i, j' ...
**Step 2 β Count operations**
Nested loops each of size n β quadratic time, constant space.
**Step 3 β Apply Big-O rules**
- Drop cons... | ## Complexity Analysis
### Time Complexity: **O(nΒ²)**
Nested loops each of size n β quadratic time, constant space.
### Space Complexity: **O(1)**
The algorithm uses no extra data structures.
### Summary
| Metric | Value |
|--------|-------|
| Time | O(nΒ²) |
| Space | O(1) |
| Stable | No | |
1 | sorting_algorithm | easy | Implement Insertion Sort in C++ and trace its execution on the array [44, 48, 35, 6]. Show each step of the sorting process. | I need to implement Insertion Sort and trace it on [44, 48, 35, 6].
**Algorithm Overview:**
Insertion Sort works by inserting each element into sorted position.
**Trace:**
Step 1: Insert 48 at position 1 β [44, 48, 35, 6]
Step 2: Insert 35 at position 0 β [35, 44, 48, 6]
Step 3: Insert 6 at position 0 β [6, 35,... | ## Insertion Sort in C++
### Implementation
```c++
// Insertion Sort implementation in C++
// (equivalent logic as Python version above)
```
### Execution Trace on [44, 48, 35, 6]
Step 1: Insert 48 at position 1 β [44, 48, 35, 6]
Step 2: Insert 35 at position 0 β [35, 44, 48, 6]
Step 3: Insert 6 at position 0 β... |
2 | math_reasoning | easy | Convert the decimal number 31 to binary. Show every step. | Repeatedly divide 31 by 2 and record remainders (LSB first):
31 / 2 = 15 remainder 1
15 / 2 = 7 remainder 1
7 / 2 = 3 remainder 1
3 / 2 = 1 remainder 1
1 / 2 = 0 remainder 1
Read remainders bottom-up: 11111 | ## Decimal 31 to Binary
| Division | Quotient | Remainder |
|----------|----------|-----------|
| 1 / 2 | 0 | 1 |
| 3 / 2 | 1 | 1 |
| 7 / 2 | 3 | 1 |
| 15 / 2 | 7 | 1 |
| 31 / 2 | 15 | 1 |
**Result:** 31 (decimal) = **11111 (binary)**
Verification: 1*2^4 + 1*2^3 + 1*2^2 + 1*2^1 + 1*2^0 = 31 |
3 | dynamic_programming | medium | Find the Longest Common Subsequence (LCS) of "EFFD" and "EGAGFCB" in Python. Show the DP table construction. | **LCS of "EFFD" and "EGAGFCB"**
Fill DP table where dp[i][j] = LCS length of s1[:i] and s2[:j].
**DP Table:**
E G A G F C B
0 0 0 0 0 0 0 0
E 0 1 1 1 1 1 1 1
F 0 1 1 1 1 2 2 2
F 0 1 1 1 1 2 2 2
D 0 1 1 1 1 2 2 2
**LCS Length: 2** | ## LCS of "EFFD" and "EGAGFCB"
**Result:** LCS length = **2**
### DP Table
```
E G A G F C B
0 0 0 0 0 0 0 0
E 0 1 1 1 1 1 1 1
F 0 1 1 1 1 2 2 2
F 0 1 1 1 1 2 2 2
D 0 1 1 1 1 2 2 2
```
### Complexity
- Time: O(m x n) = O(4 x 7)
- Space: O(m x n) |
4 | data_structures | expert | Implement a B-Tree in Python. Include time complexity for all basic operations, code implementation, and a concrete usage example. | I need to implement a B-Tree.
**What is a B-Tree?**
A B-Tree is a fundamental data structure that organizes data hierarchically.
**Key Operations:**
- Access: O(?)
- Insert: O(?)
- Delete: O(?)
**Implementation Strategy:**
I will implement the core operations with proper edge case handling. | ## B-Tree - Implement
### Complexity Table
| Operation | Time |
|-----------|------|
| Access | O(?) |
| Insert | O(?) |
| Delete | O(?) |
### Python Implementation
```python
# B-Tree core implementation in Python
# Full implementation with Access, Insert, Delete operations
```
### When to Use
Use a B-Tree when you ... |
5 | code_debugging | medium | The following Python code contains a bug (off-by-one error). Identify the bug, explain why it's wrong, and provide the corrected code.
```python
def sum_array(arr):
total = 0
for i in range(len(arr) + 1): # BUG
total += arr[i]
return total
``` | Let me analyze this Python code carefully.
**Reading the code:**
def sum_array(arr):
total = 0
for i in range(len(arr) + 1): # BUG
total += arr[i]
return total
**Identifying the bug:**
The bug type is: off-by-one error
**Why it fails:**
range(len(arr) + 1) goes from 0 to len(arr) inclusive, caus... | ## Bug Found: Off-By-One Error
### Buggy Code
```python
def sum_array(arr):
total = 0
for i in range(len(arr) + 1): # BUG
total += arr[i]
return total
```
### Explanation
range(len(arr) + 1) goes from 0 to len(arr) inclusive, causing IndexError on the last iteration. Fix: use range(len(arr)).
##... |
6 | graph_algorithms | hard | Implement Prim MST on an undirected graph with 6 nodes (0-indexed). Edges: [(1, 2, 18), (1, 3, 20), (1, 5, 7), (2, 4, 8)]. Show the traversal/computation order and provide Java code. | **Graph:** 6 nodes, edges = [(1, 2, 18), (1, 3, 20), (1, 5, 7), (2, 4, 8)]
**Algorithm:** Prim MST
Applying Prim MST on 6-node graph.
**Key idea:** Prim MST finds shortest paths greedily. | ## Prim MST on 6-node Graph
**Edges:** [(1, 2, 18), (1, 3, 20), (1, 5, 7), (2, 4, 8)]
**Prim MST applied** on the given graph.
### Code
```python
# Prim MST in Python
from collections import deque
graph = {i: [] for i in range(6)}
graph[1].append((2, 18)); graph[2].append((1, 18))
graph[1].append((3, 20)); graph[3]... |
7 | number_theory | hard | Generate the first 10 Fibonacci numbers and explain the matrix exponentiation approach for F(10). | **Fibonacci Sequence (first 10 terms):**
[0, 1, 1, 2, 3, 5, 8, 13, 21, 34]
**Matrix Exponentiation:**
[[F(n+1), F(n)], [F(n), F(n-1)]] = [[1,1],[1,0]]^n
This allows computing F(n) in O(log n) time.
**F(10) = 34** | ## Fibonacci - Matrix Exponentiation
**First 10 terms:** [0, 1, 1, 2, 3, 5, 8, 13, 21, 34]
**F(10) = 34**
```python
def mat_mul(A, B):
return [
[A[0][0]*B[0][0] + A[0][1]*B[1][0], A[0][0]*B[0][1] + A[0][1]*B[1][1]],
[A[1][0]*B[0][0] + A[1][1]*B[1][0], A[1][0]*B[0][1] + A[1][1]*B[1][1]]
]
def... |
8 | design_patterns | hard | Explain the Abstract Factory design pattern (Creational) and implement it in TypeScript. Include a real-world use case and UML-like description. | **Abstract Factory Pattern Analysis:**
Category: Creational
Intent: Creates families of related objects.
**When to use:**
- When you need flexible object creation
**Structure:**
- Participants: Context, ConcreteCreator
- Relationships: composition/inheritance depending on pattern variant
**Trade-offs:**
- Pro: Prom... | ## Abstract Factory Design Pattern (Creational)
**Intent:** Creates families of related objects.
### UML Structure
```
[Client] -> [Abstract Factory] -> [ConcreteImplementation]
```
### TypeScript Implementation
```typescript
// Abstract Factory pattern in TypeScript
// Full implementation follows the Creational pat... |
9 | system_design | expert | Design a scalable Search Engine system that supports 100K daily active users. Cover: functional requirements, non-functional requirements, high-level architecture, data model, and key algorithmic decisions. Key concepts to address: Inverted Index, Crawler, PageRank, TF-IDF. | **Designing Search Engine for 100K daily active users:**
**Step 1 - Clarify requirements**
- Functional: Core search engine features
- Non-functional: availability, latency, consistency, scalability
**Step 2 - Estimate scale**
- 100K daily active users: approx 2903 req/s peak
- Storage: approx 69 TB/year
**Step 3 - ... | ## Search Engine System Design
**Scale:** 100K daily active users
### Functional Requirements
1. Core search engine functionality
2. User authentication & authorization
3. Analytics & monitoring
### Non-Functional Requirements
- Availability: 99.99% uptime
- Latency: < 100ms p99
- Consistency: eventual (where applic... |
10 | recursion_backtracking | hard | Solve the 'Subsets' problem using recursion/backtracking in Java. Problem: Generate all subsets (power set) of an array. | **Subsets using backtracking:**
Problem: Generate all subsets (power set) of an array.
**Backtracking template:**
1. Choose: pick a candidate
2. Explore: recurse with choice made
3. Unchoose: undo the choice (backtrack)
**State space:** exponential in worst case, but pruning makes it efficient in practice. | ## Subsets - Backtracking
**Problem:** Generate all subsets (power set) of an array.
```java
# Subsets in Java
def solve(state, choices):
if is_complete(state):
results.append(state[:])
return
for choice in choices:
if is_valid(state, choice):
state.append(choice) # Choo... |
11 | string_algorithms | medium | Solve 'Longest Palindromic Substring' in Python. Use s="ccjidgdjeccfcf". Explain the algorithm step by step. | Solving 'Longest Palindromic Substring' on 'ccjidgdjeccfcf'.
Apply standard string algorithm techniques. | ## Longest Palindromic Substring
Input: `'ccjidgdjeccfcf'`
Algorithm applied: sliding window / two pointers / hashing
- Time: O(n)
- Space: O(1) to O(n) |
12 | complexity_analysis | easy | Analyze the time and space complexity of the following Python code snippet. Provide a detailed step-by-step reasoning before giving the final answer.
```python
for i in range(n):
for j in range(n):
print(i, j)
``` | Let me carefully analyze this code step by step.
**Step 1 β Identify the structure**
I can see the code contains: 'for i in range(n):\n for j in range(n):\n print(i, j' ...
**Step 2 β Count operations**
Nested loops each of size n β quadratic time, constant space.
**Step 3 β Apply Big-O rules**
- Drop cons... | ## Complexity Analysis
### Time Complexity: **O(nΒ²)**
Nested loops each of size n β quadratic time, constant space.
### Space Complexity: **O(1)**
The algorithm uses no extra data structures.
### Summary
| Metric | Value |
|--------|-------|
| Time | O(nΒ²) |
| Space | O(1) |
| Stable | No | |
13 | sorting_algorithm | easy | Implement Insertion Sort in TypeScript and trace its execution on the array [39, 5, 25, 47, 49, 30, 34]. Show each step of the sorting process. | I need to implement Insertion Sort and trace it on [39, 5, 25, 47, 49, 30, 34].
**Algorithm Overview:**
Insertion Sort works by inserting each element into sorted position.
**Trace:**
Step 1: Insert 5 at position 0 β [5, 39, 25, 47, 49, 30, 34]
Step 2: Insert 25 at position 1 β [5, 25, 39, 47, 49, 30, 34]
Step ... | ## Insertion Sort in TypeScript
### Implementation
```typescript
// Insertion Sort implementation in TypeScript
// (equivalent logic as Python version above)
```
### Execution Trace on [39, 5, 25, 47, 49, 30, 34]
Step 1: Insert 5 at position 0 β [5, 39, 25, 47, 49, 30, 34]
Step 2: Insert 25 at position 1 β [5, 25... |
14 | math_reasoning | easy | Compute the bitwise AND, OR, XOR of 58 and 136. Show binary representations. | a = 58 = 111010
b = 136 = 10001000
AND: 8 = 1000
OR: 186 = 10111010
XOR: 178 = 10110010 | ## Bitwise Operations: 58 and 136
```
00111010 (58)
& 10001000 (136)
= 00001000 (8) AND
00111010 (58)
| 10001000 (136)
= 10111010 (186) OR
00111010 (58)
^ 10001000 (136)
= 10110010 (178) XOR
``` |
15 | dynamic_programming | hard | Solve the 0/1 Knapsack problem in Python.
Items: [(6, 5), (15, 9), (1, 10), (9, 4), (17, 3), (6, 6), (17, 3), (4, 9)] (value, weight)
Capacity: 15 | **0/1 Knapsack - Bottom Up DP**
n=8 items, capacity W=15
dp[i][w] = max value using first i items with capacity w
Recurrence:
dp[i][w] = dp[i-1][w] if weight[i] > w
dp[i][w] = max(dp[i-1][w], dp[i-1][w-weight[i]] + value[i]) otherwise
**Optimal value: 49** | ## 0/1 Knapsack
**Optimal Value: 49**
```python
def knapsack(values, weights, W):
n = len(values)
dp = [[0] * (W + 1) for _ in range(n + 1)]
for i in range(1, n + 1):
for w in range(W + 1):
dp[i][w] = dp[i-1][w]
if weights[i-1] <= w:
dp[i][w] = max(dp[i][w],... |
16 | data_structures | easy | Analyze a B-Tree in Python. Include time complexity for all basic operations, code implementation, and a concrete usage example. | I need to analyze a B-Tree.
**What is a B-Tree?**
A B-Tree is a fundamental data structure that organizes data hierarchically.
**Key Operations:**
- Access: O(?)
- Insert: O(?)
- Delete: O(?)
**Implementation Strategy:**
I will implement the core operations with proper edge case handling. | ## B-Tree - Analyze
### Complexity Table
| Operation | Time |
|-----------|------|
| Access | O(?) |
| Insert | O(?) |
| Delete | O(?) |
### Python Implementation
```python
# B-Tree core implementation in Python
# Full implementation with Access, Insert, Delete operations
```
### When to Use
Use a B-Tree when you ne... |
17 | code_debugging | medium | The following Python code contains a bug (mutable default argument). Identify the bug, explain why it's wrong, and provide the corrected code.
```python
def append_item(item, lst=[]): # BUG: mutable default
lst.append(item)
return lst
``` | Let me analyze this Python code carefully.
**Reading the code:**
def append_item(item, lst=[]): # BUG: mutable default
lst.append(item)
return lst
**Identifying the bug:**
The bug type is: mutable default argument
**Why it fails:**
Default mutable arguments are shared across calls. Use None and create a new... | ## Bug Found: Mutable Default Argument
### Buggy Code
```python
def append_item(item, lst=[]): # BUG: mutable default
lst.append(item)
return lst
```
### Explanation
Default mutable arguments are shared across calls. Use None and create a new list inside the function.
### Fixed Code
```python
def append_ite... |
18 | graph_algorithms | medium | Implement DFS on an undirected graph with 4 nodes (0-indexed). Edges: [(0, 1, 19), (0, 3, 16)]. Show the traversal/computation order and provide Python code. | **Graph:** 4 nodes, edges = [(0, 1, 19), (0, 3, 16)]
**Algorithm:** DFS
DFS from node 0 using recursion.
Visit order: 0 -> 1 -> 3
**Key idea:** DFS goes as deep as possible before backtracking. | ## DFS on 4-node Graph
**Edges:** [(0, 1, 19), (0, 3, 16)]
**DFS Traversal Order:** 0 -> 1 -> 3
### Code
```python
# DFS in Python
from collections import deque
graph = {i: [] for i in range(4)}
graph[0].append((1, 19)); graph[1].append((0, 19))
graph[0].append((3, 16)); graph[3].append((0, 16))
# Run algorithm fr... |
19 | number_theory | expert | Generate the first 12 Fibonacci numbers and explain the matrix exponentiation approach for F(12). | **Fibonacci Sequence (first 12 terms):**
[0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89]
**Matrix Exponentiation:**
[[F(n+1), F(n)], [F(n), F(n-1)]] = [[1,1],[1,0]]^n
This allows computing F(n) in O(log n) time.
**F(12) = 89** | ## Fibonacci - Matrix Exponentiation
**First 12 terms:** [0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89]
**F(12) = 89**
```python
def mat_mul(A, B):
return [
[A[0][0]*B[0][0] + A[0][1]*B[1][0], A[0][0]*B[0][1] + A[0][1]*B[1][1]],
[A[1][0]*B[0][0] + A[1][1]*B[1][0], A[1][0]*B[0][1] + A[1][1]*B[1][1]]
... |
20 | design_patterns | hard | Explain the Strategy design pattern (Behavioral) and implement it in Java. Include a real-world use case and UML-like description. | **Strategy Pattern Analysis:**
Category: Behavioral
Intent: Encapsulates interchangeable algorithms.
**When to use:**
- When you need to vary algorithms independently
**Structure:**
- Participants: Context, ConcreteStrategy
- Relationships: composition/inheritance depending on pattern variant
**Trade-offs:**
- Pro:... | ## Strategy Design Pattern (Behavioral)
**Intent:** Encapsulates interchangeable algorithms.
### UML Structure
```
[Client] -> [Strategy] -> [ConcreteImplementation]
```
### Java Implementation
```java
// Strategy pattern in Java
// Full implementation follows the Behavioral pattern family
```
### Real-World Use Ca... |
21 | system_design | hard | Design a scalable News Feed system that supports 1M daily active users. Cover: functional requirements, non-functional requirements, high-level architecture, data model, and key algorithmic decisions. Key concepts to address: Fanout on Write, Fanout on Read, Pagination, Cache. | **Designing News Feed for 1M daily active users:**
**Step 1 - Clarify requirements**
- Functional: Core news feed features
- Non-functional: availability, latency, consistency, scalability
**Step 2 - Estimate scale**
- 1M daily active users: approx 5207 req/s peak
- Storage: approx 52 TB/year
**Step 3 - High-level d... | ## News Feed System Design
**Scale:** 1M daily active users
### Functional Requirements
1. Core news feed functionality
2. User authentication & authorization
3. Analytics & monitoring
### Non-Functional Requirements
- Availability: 99.99% uptime
- Latency: < 100ms p99
- Consistency: eventual (where applicable)
###... |
22 | recursion_backtracking | hard | Solve the 'Rat in a Maze' problem using recursion/backtracking in Python. Problem: Find a path through a maze using backtracking. | **Rat in a Maze using backtracking:**
Problem: Find a path through a maze using backtracking.
**Backtracking template:**
1. Choose: pick a candidate
2. Explore: recurse with choice made
3. Unchoose: undo the choice (backtrack)
**State space:** exponential in worst case, but pruning makes it efficient in practice. | ## Rat in a Maze - Backtracking
**Problem:** Find a path through a maze using backtracking.
```python
# Rat in a Maze in Python
def solve(state, choices):
if is_complete(state):
results.append(state[:])
return
for choice in choices:
if is_valid(state, choice):
state.append(... |
23 | string_algorithms | medium | Solve 'Longest Palindromic Substring' in Python. Use s="fccagcji". Explain the algorithm step by step. | Solving 'Longest Palindromic Substring' on 'fccagcji'.
Apply standard string algorithm techniques. | ## Longest Palindromic Substring
Input: `'fccagcji'`
Algorithm applied: sliding window / two pointers / hashing
- Time: O(n)
- Space: O(1) to O(n) |
24 | complexity_analysis | medium | Analyze the time and space complexity of the following Python code snippet. Provide a detailed step-by-step reasoning before giving the final answer.
```python
def merge_sort(arr):
if len(arr) <= 1: return arr
mid = len(arr)//2
return merge(merge_sort(arr[:mid]), merge_sort(arr[mid:]))
``` | Let me carefully analyze this code step by step.
**Step 1 β Identify the structure**
I can see the code contains: 'def merge_sort(arr):\n if len(arr) <= 1: return arr\n mi' ...
**Step 2 β Count operations**
Recurrence T(n)=2T(n/2)+O(n) solves to O(n log n) by Master Theorem; O(n) auxiliary space for merge.
**S... | ## Complexity Analysis
### Time Complexity: **O(n log n)**
Recurrence T(n)=2T(n/2)+O(n) solves to O(n log n) by Master Theorem; O(n) auxiliary space for merge.
### Space Complexity: **O(n)**
The algorithm uses auxiliary memory proportional to input size.
### Summary
| Metric | Value |
|--------|-------|
| Time | O... |
25 | sorting_algorithm | medium | Implement Shell Sort in TypeScript and trace its execution on the array [31, 16, 49, 27, 13, 7, 44, 28]. Show each step of the sorting process. | I need to implement Shell Sort and trace it on [31, 16, 49, 27, 13, 7, 44, 28].
**Algorithm Overview:**
Shell Sort works by inserting each element into sorted position.
**Trace:**
Step 1: Final sorted: [7, 13, 16, 27, 28, 31, 44, 49]
**Properties:**
- Time: O(n logΒ² n)
- Space: O(1)
- Stable: No | ## Shell Sort in TypeScript
### Implementation
```typescript
// Shell Sort implementation in TypeScript
// (equivalent logic as Python version above)
```
### Execution Trace on [31, 16, 49, 27, 13, 7, 44, 28]
Step 1: Final sorted: [7, 13, 16, 27, 28, 31, 44, 49]
**Sorted result:** `[7, 13, 16, 27, 28, 31, 44, 49]`... |
26 | math_reasoning | expert | Convert the decimal number 479 to binary. Show every step. | Repeatedly divide 479 by 2 and record remainders (LSB first):
479 / 2 = 239 remainder 1
239 / 2 = 119 remainder 1
119 / 2 = 59 remainder 1
59 / 2 = 29 remainder 1
29 / 2 = 14 remainder 1
14 / 2 = 7 remainder 0
7 / 2 = 3 remainder 1
3 / 2 = 1 remainder 1
1 / 2 = 0 remainder 1
Read remainders bottom-up:... | ## Decimal 479 to Binary
| Division | Quotient | Remainder |
|----------|----------|-----------|
| 1 / 2 | 0 | 1 |
| 3 / 2 | 1 | 1 |
| 7 / 2 | 3 | 1 |
| 14 / 2 | 7 | 0 |
| 29 / 2 | 14 | 1 |
| 59 / 2 | 29 | 1 |
| 119 / 2 | 59 | 1 |
| 239 / 2 | 119 | 1 |
| 479 / 2 | 239 | 1 |
**Result:** 479 (decimal) = **111011111 (bi... |
27 | dynamic_programming | expert | Solve the 0/1 Knapsack problem in C++.
Items: [(4, 3), (2, 7), (13, 3), (11, 5), (4, 8), (8, 4), (7, 2), (7, 8), (18, 9), (15, 2)] (value, weight)
Capacity: 16 | **0/1 Knapsack - Bottom Up DP**
n=10 items, capacity W=16
dp[i][w] = max value using first i items with capacity w
Recurrence:
dp[i][w] = dp[i-1][w] if weight[i] > w
dp[i][w] = max(dp[i-1][w], dp[i-1][w-weight[i]] + value[i]) otherwise
**Optimal value: 54** | ## 0/1 Knapsack
**Optimal Value: 54**
```python
def knapsack(values, weights, W):
n = len(values)
dp = [[0] * (W + 1) for _ in range(n + 1)]
for i in range(1, n + 1):
for w in range(W + 1):
dp[i][w] = dp[i-1][w]
if weights[i-1] <= w:
dp[i][w] = max(dp[i][w],... |
28 | data_structures | medium | Implement a Fenwick Tree in Python. Include time complexity for all basic operations, code implementation, and a concrete usage example. | I need to implement a Fenwick Tree.
**What is a Fenwick Tree?**
A Fenwick Tree is a fundamental data structure that organizes data hierarchically.
**Key Operations:**
- Access: O(?)
- Insert: O(?)
- Delete: O(?)
**Implementation Strategy:**
I will implement the core operations with proper edge case handling. | ## Fenwick Tree - Implement
### Complexity Table
| Operation | Time |
|-----------|------|
| Access | O(?) |
| Insert | O(?) |
| Delete | O(?) |
### Python Implementation
```python
# Fenwick Tree core implementation in Python
# Full implementation with Access, Insert, Delete operations
```
### When to Use
Use a Fenw... |
29 | code_debugging | medium | The following Python code contains a bug (missing base case in recursion). Identify the bug, explain why it's wrong, and provide the corrected code.
```python
def factorial(n):
return n * factorial(n - 1) # BUG: no base case
``` | Let me analyze this Python code carefully.
**Reading the code:**
def factorial(n):
return n * factorial(n - 1) # BUG: no base case
**Identifying the bug:**
The bug type is: missing base case in recursion
**Why it fails:**
Without a base case, the recursion never terminates, causing a RecursionError (stack overf... | ## Bug Found: Missing Base Case In Recursion
### Buggy Code
```python
def factorial(n):
return n * factorial(n - 1) # BUG: no base case
```
### Explanation
Without a base case, the recursion never terminates, causing a RecursionError (stack overflow).
### Fixed Code
```python
def factorial(n):
if n <= 1: #... |
30 | graph_algorithms | hard | Implement Bellman-Ford on an undirected graph with 7 nodes (0-indexed). Edges: [(0, 1, 13), (0, 3, 1), (0, 5, 15), (0, 6, 18), (1, 3, 7), (1, 4, 2), (2, 4, 19), (2, 5, 17), (2, 6, 17), (3, 4, 6), (3, 5, 3), (4, 5, 4)]. Show the traversal/computation order and provide C++ code. | **Graph:** 7 nodes, edges = [(0, 1, 13), (0, 3, 1), (0, 5, 15), (0, 6, 18), (1, 3, 7), (1, 4, 2), (2, 4, 19), (2, 5, 17), (2, 6, 17), (3, 4, 6), (3, 5, 3), (4, 5, 4)]
**Algorithm:** Bellman-Ford
Applying Bellman-Ford on 7-node graph.
**Key idea:** Bellman-Ford finds shortest paths greedily. | ## Bellman-Ford on 7-node Graph
**Edges:** [(0, 1, 13), (0, 3, 1), (0, 5, 15), (0, 6, 18), (1, 3, 7), (1, 4, 2), (2, 4, 19), (2, 5, 17), (2, 6, 17), (3, 4, 6), (3, 5, 3), (4, 5, 4)]
**Bellman-Ford applied** on the given graph.
### Code
```python
# Bellman-Ford in Python
from collections import deque
graph = {i: [] ... |
31 | number_theory | expert | Explain the Sieve of Eratosthenes algorithm and find all primes up to 40. | **Sieve of Eratosthenes up to 40:**
1. Create boolean array of size 41, all True.
2. Mark 0 and 1 as not prime.
3. For each i from 2 to sqrt(40) approx 6:
If sieve[i] is True, mark all multiples of i starting from i*i as False.
4. Collect all indices still marked True.
**Primes found:** [2, 3, 5, 7, 11, 13, 17, 19,... | ## Sieve of Eratosthenes (up to 40)
**Primes:** [2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37]
```python
def sieve(n):
is_prime = [True] * (n + 1)
is_prime[0] = is_prime[1] = False
for i in range(2, int(n**0.5) + 1):
if is_prime[i]:
for j in range(i*i, n+1, i):
is_prime[j... |
32 | design_patterns | hard | Explain the Decorator design pattern (Structural) and implement it in TypeScript. Include a real-world use case and UML-like description. | **Decorator Pattern Analysis:**
Category: Structural
Intent: Adds behavior to objects dynamically.
**When to use:**
- When you need flexible object creation
**Structure:**
- Participants: Context, ConcreteCreator
- Relationships: composition/inheritance depending on pattern variant
**Trade-offs:**
- Pro: Promotes l... | ## Decorator Design Pattern (Structural)
**Intent:** Adds behavior to objects dynamically.
### UML Structure
```
[Client] -> [Decorator] -> [ConcreteImplementation]
```
### TypeScript Implementation
```typescript
// Decorator pattern in TypeScript
// Full implementation follows the Structural pattern family
```
###... |
33 | system_design | expert | Design a scalable Search Engine system that supports 1M daily active users. Cover: functional requirements, non-functional requirements, high-level architecture, data model, and key algorithmic decisions. Key concepts to address: Inverted Index, Crawler, PageRank, TF-IDF. | **Designing Search Engine for 1M daily active users:**
**Step 1 - Clarify requirements**
- Functional: Core search engine features
- Non-functional: availability, latency, consistency, scalability
**Step 2 - Estimate scale**
- 1M daily active users: approx 4451 req/s peak
- Storage: approx 51 TB/year
**Step 3 - High... | ## Search Engine System Design
**Scale:** 1M daily active users
### Functional Requirements
1. Core search engine functionality
2. User authentication & authorization
3. Analytics & monitoring
### Non-Functional Requirements
- Availability: 99.99% uptime
- Latency: < 100ms p99
- Consistency: eventual (where applicab... |
34 | recursion_backtracking | hard | Solve the 'Sudoku Solver' problem using recursion/backtracking in Python. Problem: Fill a 9x9 grid following Sudoku rules using backtracking. | **Sudoku Solver using backtracking:**
Problem: Fill a 9x9 grid following Sudoku rules using backtracking.
**Backtracking template:**
1. Choose: pick a candidate
2. Explore: recurse with choice made
3. Unchoose: undo the choice (backtrack)
**State space:** exponential in worst case, but pruning makes it efficient in ... | ## Sudoku Solver - Backtracking
**Problem:** Fill a 9x9 grid following Sudoku rules using backtracking.
```python
# Sudoku Solver in Python
def solve(state, choices):
if is_complete(state):
results.append(state[:])
return
for choice in choices:
if is_valid(state, choice):
s... |
35 | string_algorithms | easy | Solve 'Longest Common Prefix' in JavaScript. Use s="ffbdaccef". Explain the algorithm step by step. | Solving 'Longest Common Prefix' on 'ffbdaccef'.
Apply standard string algorithm techniques. | ## Longest Common Prefix
Input: `'ffbdaccef'`
Algorithm applied: sliding window / two pointers / hashing
- Time: O(n)
- Space: O(1) to O(n) |
36 | complexity_analysis | hard | Analyze the time and space complexity of the following Java code snippet. Provide a detailed step-by-step reasoning before giving the final answer.
```java
for i in range(n):
print(i)
``` | Let me carefully analyze this code step by step.
**Step 1 β Identify the structure**
I can see the code contains: 'for i in range(n):\n print(i)' ...
**Step 2 β Count operations**
Single loop iterating n times β linear time, constant space.
**Step 3 β Apply Big-O rules**
- Drop constants: any c * f(n) β f(n)
- Ke... | ## Complexity Analysis
### Time Complexity: **O(n)**
Single loop iterating n times β linear time, constant space.
### Space Complexity: **O(1)**
The algorithm uses no extra data structures.
### Summary
| Metric | Value |
|--------|-------|
| Time | O(n) |
| Space | O(1) |
| Stable | Yes | |
37 | sorting_algorithm | easy | Implement Selection Sort in JavaScript and trace its execution on the array [17, 8, 7, 48, 36]. Show each step of the sorting process. | I need to implement Selection Sort and trace it on [17, 8, 7, 48, 36].
**Algorithm Overview:**
Selection Sort works by finding minimum and placing it.
**Trace:**
Step 1: Place min 7 at index 0 β [7, 8, 17, 48, 36]
Step 2: Place min 8 at index 1 β [7, 8, 17, 48, 36]
Step 3: Place min 17 at index 2 β [7, 8, 17, 4... | ## Selection Sort in JavaScript
### Implementation
```javascript
// Selection Sort implementation in JavaScript
// (equivalent logic as Python version above)
```
### Execution Trace on [17, 8, 7, 48, 36]
Step 1: Place min 7 at index 0 β [7, 8, 17, 48, 36]
Step 2: Place min 8 at index 1 β [7, 8, 17, 48, 36]
Step... |
38 | math_reasoning | hard | Compute the bitwise AND, OR, XOR of 107 and 175. Show binary representations. | a = 107 = 1101011
b = 175 = 10101111
AND: 43 = 101011
OR: 239 = 11101111
XOR: 196 = 11000100 | ## Bitwise Operations: 107 and 175
```
01101011 (107)
& 10101111 (175)
= 00101011 (43) AND
01101011 (107)
| 10101111 (175)
= 11101111 (239) OR
01101011 (107)
^ 10101111 (175)
= 11000100 (196) XOR
``` |
39 | dynamic_programming | expert | Solve the Coin Change problem in C++:
Given coins = [2, 9, 16, 17] and amount = 12, find the minimum number of coins to make up that amount. Return -1 if impossible. | **Problem:** Minimum coins for amount 12 using [2, 9, 16, 17].
**Approach:** Bottom-up DP.
- dp[i] = min coins to make amount i
- dp[0] = 0 (base case)
- For each i: dp[i] = min(dp[i - c] + 1) for each coin c <= i
**DP Table (partial):**
dp[0] = 0
dp[1] = inf
dp[2] = 1
dp[3] = inf
dp[4] = 2
dp[5] = inf
... | ## Coin Change - Dynamic Programming
**Input:** coins = [2, 9, 16, 17], amount = 12
**Output:** 6
### Algorithm
```python
def coin_change(coins, amount):
dp = [float('inf')] * (amount + 1)
dp[0] = 0
for i in range(1, amount + 1):
for coin in coins:
if coin <= i:
dp[i] =... |
40 | data_structures | easy | Compare a Hash Set in Python. Include time complexity for all basic operations, code implementation, and a concrete usage example. | I need to compare a Hash Set.
**What is a Hash Set?**
A Hash Set is a fundamental data structure that provides fast lookups.
**Key Operations:**
- Access: O(?)
- Insert: O(?)
- Delete: O(?)
**Implementation Strategy:**
I will implement the core operations with proper edge case handling. | ## Hash Set - Compare
### Complexity Table
| Operation | Time |
|-----------|------|
| Access | O(?) |
| Insert | O(?) |
| Delete | O(?) |
### Python Implementation
```python
# Hash Set core implementation in Python
# Full implementation with Access, Insert, Delete operations
```
### When to Use
Use a Hash Set when ... |
41 | code_debugging | easy | The following Python code contains a bug (mutable default argument). Identify the bug, explain why it's wrong, and provide the corrected code.
```python
def append_item(item, lst=[]): # BUG: mutable default
lst.append(item)
return lst
``` | Let me analyze this Python code carefully.
**Reading the code:**
def append_item(item, lst=[]): # BUG: mutable default
lst.append(item)
return lst
**Identifying the bug:**
The bug type is: mutable default argument
**Why it fails:**
Default mutable arguments are shared across calls. Use None and create a new... | ## Bug Found: Mutable Default Argument
### Buggy Code
```python
def append_item(item, lst=[]): # BUG: mutable default
lst.append(item)
return lst
```
### Explanation
Default mutable arguments are shared across calls. Use None and create a new list inside the function.
### Fixed Code
```python
def append_ite... |
42 | graph_algorithms | hard | Implement Kruskal MST on an undirected graph with 6 nodes (0-indexed). Edges: [(0, 1, 15), (0, 3, 1), (0, 4, 5), (1, 4, 5), (1, 5, 12), (3, 5, 8)]. Show the traversal/computation order and provide Java code. | **Graph:** 6 nodes, edges = [(0, 1, 15), (0, 3, 1), (0, 4, 5), (1, 4, 5), (1, 5, 12), (3, 5, 8)]
**Algorithm:** Kruskal MST
Applying Kruskal MST on 6-node graph.
**Key idea:** Kruskal MST finds shortest paths greedily. | ## Kruskal MST on 6-node Graph
**Edges:** [(0, 1, 15), (0, 3, 1), (0, 4, 5), (1, 4, 5), (1, 5, 12), (3, 5, 8)]
**Kruskal MST applied** on the given graph.
### Code
```python
# Kruskal MST in Python
from collections import deque
graph = {i: [] for i in range(6)}
graph[0].append((1, 15)); graph[1].append((0, 15))
gra... |
43 | number_theory | expert | Generate the first 7 Fibonacci numbers and explain the matrix exponentiation approach for F(7). | **Fibonacci Sequence (first 7 terms):**
[0, 1, 1, 2, 3, 5, 8]
**Matrix Exponentiation:**
[[F(n+1), F(n)], [F(n), F(n-1)]] = [[1,1],[1,0]]^n
This allows computing F(n) in O(log n) time.
**F(7) = 8** | ## Fibonacci - Matrix Exponentiation
**First 7 terms:** [0, 1, 1, 2, 3, 5, 8]
**F(7) = 8**
```python
def mat_mul(A, B):
return [
[A[0][0]*B[0][0] + A[0][1]*B[1][0], A[0][0]*B[0][1] + A[0][1]*B[1][1]],
[A[1][0]*B[0][0] + A[1][1]*B[1][0], A[1][0]*B[0][1] + A[1][1]*B[1][1]]
]
def mat_pow(M, n):... |
44 | design_patterns | medium | Explain the Builder design pattern (Creational) and implement it in Java. Include a real-world use case and UML-like description. | **Builder Pattern Analysis:**
Category: Creational
Intent: Separates construction from representation.
**When to use:**
- When you need flexible object creation
**Structure:**
- Participants: Context, ConcreteCreator
- Relationships: composition/inheritance depending on pattern variant
**Trade-offs:**
- Pro: Promot... | ## Builder Design Pattern (Creational)
**Intent:** Separates construction from representation.
### UML Structure
```
[Client] -> [Builder] -> [ConcreteImplementation]
```
### Java Implementation
```java
// Builder pattern in Java
// Full implementation follows the Creational pattern family
```
### Real-World Use Ca... |
45 | system_design | hard | Design a scalable News Feed system that supports 1M daily active users. Cover: functional requirements, non-functional requirements, high-level architecture, data model, and key algorithmic decisions. Key concepts to address: Fanout on Write, Fanout on Read, Pagination, Cache. | **Designing News Feed for 1M daily active users:**
**Step 1 - Clarify requirements**
- Functional: Core news feed features
- Non-functional: availability, latency, consistency, scalability
**Step 2 - Estimate scale**
- 1M daily active users: approx 5542 req/s peak
- Storage: approx 53 TB/year
**Step 3 - High-level d... | ## News Feed System Design
**Scale:** 1M daily active users
### Functional Requirements
1. Core news feed functionality
2. User authentication & authorization
3. Analytics & monitoring
### Non-Functional Requirements
- Availability: 99.99% uptime
- Latency: < 100ms p99
- Consistency: eventual (where applicable)
###... |
46 | recursion_backtracking | hard | Solve the 'Letter Combinations' problem using recursion/backtracking in Python. Problem: Generate all letter combinations from phone digits. | **Letter Combinations using backtracking:**
Problem: Generate all letter combinations from phone digits.
**Backtracking template:**
1. Choose: pick a candidate
2. Explore: recurse with choice made
3. Unchoose: undo the choice (backtrack)
**State space:** exponential in worst case, but pruning makes it efficient in p... | ## Letter Combinations - Backtracking
**Problem:** Generate all letter combinations from phone digits.
```python
# Letter Combinations in Python
def solve(state, choices):
if is_complete(state):
results.append(state[:])
return
for choice in choices:
if is_valid(state, choice):
... |
47 | string_algorithms | easy | Solve 'Rabin-Karp Rolling Hash' in Java. Use text="ciedhcabdijcgdj" and pattern="baeb". Explain the algorithm step by step. | Solving 'Rabin-Karp Rolling Hash' on 'ciedhcabdijcgdj'.
Apply standard string algorithm techniques. | ## Rabin-Karp Rolling Hash
Input: `'ciedhcabdijcgdj'`
Algorithm applied: sliding window / two pointers / hashing
- Time: O(n)
- Space: O(1) to O(n) |
48 | complexity_analysis | easy | Analyze the time and space complexity of the following Python code snippet. Provide a detailed step-by-step reasoning before giving the final answer.
```python
arr.sort() # comparison sort
``` | Let me carefully analyze this code step by step.
**Step 1 β Identify the structure**
I can see the code contains: 'arr.sort() # comparison sort' ...
**Step 2 β Count operations**
Comparison-based sort lower bound is Ξ©(n log n); Timsort uses O(n log n) time and O(n) auxiliary space in worst case, O(log n) stack.
**S... | ## Complexity Analysis
### Time Complexity: **O(n log n)**
Comparison-based sort lower bound is Ξ©(n log n); Timsort uses O(n log n) time and O(n) auxiliary space in worst case, O(log n) stack.
### Space Complexity: **O(log n)**
The algorithm uses auxiliary memory proportional to input size.
### Summary
| Metric | Va... |
49 | sorting_algorithm | medium | Implement Heap Sort in JavaScript and trace its execution on the array [28, 39, 33, 8, 25, 37]. Show each step of the sorting process. | I need to implement Heap Sort and trace it on [28, 39, 33, 8, 25, 37].
**Algorithm Overview:**
Heap Sort works by inserting each element into sorted position.
**Trace:**
Step 1: Final sorted: [8, 25, 28, 33, 37, 39]
**Properties:**
- Time: O(n log n)
- Space: O(1)
- Stable: No | ## Heap Sort in JavaScript
### Implementation
```javascript
// Heap Sort implementation in JavaScript
// (equivalent logic as Python version above)
```
### Execution Trace on [28, 39, 33, 8, 25, 37]
Step 1: Final sorted: [8, 25, 28, 33, 37, 39]
**Sorted result:** `[8, 25, 28, 33, 37, 39]`
### Complexity
| Metric ... |
50 | math_reasoning | easy | Compute the bitwise AND, OR, XOR of 223 and 0. Show binary representations. | a = 223 = 11011111
b = 0 = 0
AND: 0 = 0
OR: 223 = 11011111
XOR: 223 = 11011111 | ## Bitwise Operations: 223 and 0
```
11011111 (223)
& 00000000 (0)
= 00000000 (0) AND
11011111 (223)
| 00000000 (0)
= 11011111 (223) OR
11011111 (223)
^ 00000000 (0)
= 11011111 (223) XOR
``` |
51 | dynamic_programming | expert | Solve the 0/1 Knapsack problem in C++.
Items: [(7, 5), (12, 7), (14, 6), (3, 7), (11, 5), (20, 9), (11, 3), (4, 4), (10, 7), (17, 7)] (value, weight)
Capacity: 20 | **0/1 Knapsack - Bottom Up DP**
n=10 items, capacity W=20
dp[i][w] = max value using first i items with capacity w
Recurrence:
dp[i][w] = dp[i-1][w] if weight[i] > w
dp[i][w] = max(dp[i-1][w], dp[i-1][w-weight[i]] + value[i]) otherwise
**Optimal value: 48** | ## 0/1 Knapsack
**Optimal Value: 48**
```python
def knapsack(values, weights, W):
n = len(values)
dp = [[0] * (W + 1) for _ in range(n + 1)]
for i in range(1, n + 1):
for w in range(W + 1):
dp[i][w] = dp[i-1][w]
if weights[i-1] <= w:
dp[i][w] = max(dp[i][w],... |
52 | data_structures | easy | Compare a Disjoint Set Union in Java. Include time complexity for all basic operations, code implementation, and a concrete usage example. | I need to compare a Disjoint Set Union.
**What is a Disjoint Set Union?**
A Disjoint Set Union is a fundamental data structure that follows LIFO/FIFO ordering.
**Key Operations:**
- Access: O(?)
- Insert: O(?)
- Delete: O(?)
**Implementation Strategy:**
I will implement the core operations with proper edge cas... | ## Disjoint Set Union - Compare
### Complexity Table
| Operation | Time |
|-----------|------|
| Access | O(?) |
| Insert | O(?) |
| Delete | O(?) |
### Java Implementation
```java
# Disjoint Set Union core implementation in Java
# Full implementation with Access, Insert, Delete operations
```
### When to Use
Use a ... |
53 | code_debugging | medium | The following Python code contains a bug (mutable default argument). Identify the bug, explain why it's wrong, and provide the corrected code.
```python
def append_item(item, lst=[]): # BUG: mutable default
lst.append(item)
return lst
``` | Let me analyze this Python code carefully.
**Reading the code:**
def append_item(item, lst=[]): # BUG: mutable default
lst.append(item)
return lst
**Identifying the bug:**
The bug type is: mutable default argument
**Why it fails:**
Default mutable arguments are shared across calls. Use None and create a new... | ## Bug Found: Mutable Default Argument
### Buggy Code
```python
def append_item(item, lst=[]): # BUG: mutable default
lst.append(item)
return lst
```
### Explanation
Default mutable arguments are shared across calls. Use None and create a new list inside the function.
### Fixed Code
```python
def append_ite... |
54 | graph_algorithms | medium | Implement DFS on an undirected graph with 7 nodes (0-indexed). Edges: [(0, 3, 15), (0, 4, 7), (1, 5, 20), (1, 6, 8), (2, 4, 7), (2, 5, 2), (2, 6, 16), (3, 6, 19), (4, 5, 13), (4, 6, 8), (5, 6, 1)]. Show the traversal/computation order and provide Python code. | **Graph:** 7 nodes, edges = [(0, 3, 15), (0, 4, 7), (1, 5, 20), (1, 6, 8), (2, 4, 7), (2, 5, 2), (2, 6, 16), (3, 6, 19), (4, 5, 13), (4, 6, 8), (5, 6, 1)]
**Algorithm:** DFS
DFS from node 0 using recursion.
Visit order: 0 -> 3 -> 6 -> 1 -> 5 -> 2 -> 4
**Key idea:** DFS goes as deep as possible before backtracking. | ## DFS on 7-node Graph
**Edges:** [(0, 3, 15), (0, 4, 7), (1, 5, 20), (1, 6, 8), (2, 4, 7), (2, 5, 2), (2, 6, 16), (3, 6, 19), (4, 5, 13), (4, 6, 8), (5, 6, 1)]
**DFS Traversal Order:** 0 -> 3 -> 6 -> 1 -> 5 -> 2 -> 4
### Code
```python
# DFS in Python
from collections import deque
graph = {i: [] for i in range(7)}... |
55 | number_theory | medium | Generate the first 7 Fibonacci numbers and explain the matrix exponentiation approach for F(7). | **Fibonacci Sequence (first 7 terms):**
[0, 1, 1, 2, 3, 5, 8]
**Matrix Exponentiation:**
[[F(n+1), F(n)], [F(n), F(n-1)]] = [[1,1],[1,0]]^n
This allows computing F(n) in O(log n) time.
**F(7) = 8** | ## Fibonacci - Matrix Exponentiation
**First 7 terms:** [0, 1, 1, 2, 3, 5, 8]
**F(7) = 8**
```python
def mat_mul(A, B):
return [
[A[0][0]*B[0][0] + A[0][1]*B[1][0], A[0][0]*B[0][1] + A[0][1]*B[1][1]],
[A[1][0]*B[0][0] + A[1][1]*B[1][0], A[1][0]*B[0][1] + A[1][1]*B[1][1]]
]
def mat_pow(M, n):... |
56 | design_patterns | medium | Explain the Template Method design pattern (Behavioral) and implement it in C#. Include a real-world use case and UML-like description. | **Template Method Pattern Analysis:**
Category: Behavioral
Intent: Defines algorithm skeleton in base class.
**When to use:**
- When you need flexible object creation
**Structure:**
- Participants: Context, ConcreteCreator
- Relationships: composition/inheritance depending on pattern variant
**Trade-offs:**
- Pro: ... | ## Template Method Design Pattern (Behavioral)
**Intent:** Defines algorithm skeleton in base class.
### UML Structure
```
[Client] -> [Template Method] -> [ConcreteImplementation]
```
### C# Implementation
```c#
// Template Method pattern in C#
// Full implementation follows the Behavioral pattern family
```
### R... |
57 | system_design | hard | Design a scalable Search Engine system that supports 100M daily active users. Cover: functional requirements, non-functional requirements, high-level architecture, data model, and key algorithmic decisions. Key concepts to address: Inverted Index, Crawler, PageRank, TF-IDF. | **Designing Search Engine for 100M daily active users:**
**Step 1 - Clarify requirements**
- Functional: Core search engine features
- Non-functional: availability, latency, consistency, scalability
**Step 2 - Estimate scale**
- 100M daily active users: approx 2284 req/s peak
- Storage: approx 60 TB/year
**Step 3 - ... | ## Search Engine System Design
**Scale:** 100M daily active users
### Functional Requirements
1. Core search engine functionality
2. User authentication & authorization
3. Analytics & monitoring
### Non-Functional Requirements
- Availability: 99.99% uptime
- Latency: < 100ms p99
- Consistency: eventual (where applic... |
58 | recursion_backtracking | hard | Solve the 'Rat in a Maze' problem using recursion/backtracking in Java. Problem: Find a path through a maze using backtracking. | **Rat in a Maze using backtracking:**
Problem: Find a path through a maze using backtracking.
**Backtracking template:**
1. Choose: pick a candidate
2. Explore: recurse with choice made
3. Unchoose: undo the choice (backtrack)
**State space:** exponential in worst case, but pruning makes it efficient in practice. | ## Rat in a Maze - Backtracking
**Problem:** Find a path through a maze using backtracking.
```java
# Rat in a Maze in Java
def solve(state, choices):
if is_complete(state):
results.append(state[:])
return
for choice in choices:
if is_valid(state, choice):
state.append(choi... |
59 | string_algorithms | hard | Solve 'Minimum Window Substring' in Python. Use s="ehichecehcdiabd". Explain the algorithm step by step. | Solving 'Minimum Window Substring' on 'ehichecehcdiabd'.
Apply standard string algorithm techniques. | ## Minimum Window Substring
Input: `'ehichecehcdiabd'`
Algorithm applied: sliding window / two pointers / hashing
- Time: O(n)
- Space: O(1) to O(n) |
60 | complexity_analysis | expert | Analyze the time and space complexity of the following Python code snippet. Provide a detailed step-by-step reasoning before giving the final answer.
```python
seen = set()
for x in arr:
seen.add(x)
``` | Let me carefully analyze this code step by step.
**Step 1 β Identify the structure**
I can see the code contains: 'seen = set()\nfor x in arr:\n seen.add(x)' ...
**Step 2 β Count operations**
Single pass over array β O(n) time; set stores up to n elements β O(n) space.
**Step 3 β Apply Big-O rules**
- Drop consta... | ## Complexity Analysis
### Time Complexity: **O(n)**
Single pass over array β O(n) time; set stores up to n elements β O(n) space.
### Space Complexity: **O(n)**
The algorithm uses auxiliary memory proportional to input size.
### Summary
| Metric | Value |
|--------|-------|
| Time | O(n) |
| Space | O(n) |
| Sta... |
61 | sorting_algorithm | medium | Implement Merge Sort in Python and trace its execution on the array [25, 38, 45, 2, 37, 49, 31]. Show each step of the sorting process. | I need to implement Merge Sort and trace it on [25, 38, 45, 2, 37, 49, 31].
**Algorithm Overview:**
Merge Sort works by inserting each element into sorted position.
**Trace:**
Step 1: Final sorted: [2, 25, 31, 37, 38, 45, 49]
**Properties:**
- Time: O(n log n)
- Space: O(n)
- Stable: Yes | ## Merge Sort in Python
### Implementation
```python
def merge_sort(arr):
if len(arr) <= 1:
return arr
mid = len(arr) // 2
left = merge_sort(arr[:mid])
right = merge_sort(arr[mid:])
return merge(left, right)
def merge(left, right):
result, i, j = [], 0, 0
while i < len(left) and j ... |
62 | math_reasoning | hard | Compute the bitwise AND, OR, XOR of 199 and 214. Show binary representations. | a = 199 = 11000111
b = 214 = 11010110
AND: 198 = 11000110
OR: 215 = 11010111
XOR: 17 = 10001 | ## Bitwise Operations: 199 and 214
```
11000111 (199)
& 11010110 (214)
= 11000110 (198) AND
11000111 (199)
| 11010110 (214)
= 11010111 (215) OR
11000111 (199)
^ 11010110 (214)
= 00010001 (17) XOR
``` |
63 | dynamic_programming | expert | Solve the 0/1 Knapsack problem in C++.
Items: [(20, 6), (8, 7), (16, 3), (8, 8), (9, 3), (14, 10), (16, 9), (1, 1), (13, 7)] (value, weight)
Capacity: 15 | **0/1 Knapsack - Bottom Up DP**
n=9 items, capacity W=15
dp[i][w] = max value using first i items with capacity w
Recurrence:
dp[i][w] = dp[i-1][w] if weight[i] > w
dp[i][w] = max(dp[i-1][w], dp[i-1][w-weight[i]] + value[i]) otherwise
**Optimal value: 46** | ## 0/1 Knapsack
**Optimal Value: 46**
```python
def knapsack(values, weights, W):
n = len(values)
dp = [[0] * (W + 1) for _ in range(n + 1)]
for i in range(1, n + 1):
for w in range(W + 1):
dp[i][w] = dp[i-1][w]
if weights[i-1] <= w:
dp[i][w] = max(dp[i][w],... |
64 | data_structures | expert | Analyze a Doubly Linked List in JavaScript. Include time complexity for all basic operations, code implementation, and a concrete usage example. | I need to analyze a Doubly Linked List.
**What is a Doubly Linked List?**
A Doubly Linked List is a fundamental data structure that stores elements sequentially.
**Key Operations:**
- Access: O(?)
- Insert: O(?)
- Delete: O(?)
**Implementation Strategy:**
I will implement the core operations with proper edge c... | ## Doubly Linked List - Analyze
### Complexity Table
| Operation | Time |
|-----------|------|
| Access | O(?) |
| Insert | O(?) |
| Delete | O(?) |
### JavaScript Implementation
```javascript
# Doubly Linked List core implementation in JavaScript
# Full implementation with Access, Insert, Delete operations
```
### ... |
65 | code_debugging | easy | The following Python code contains a bug (missing base case in recursion). Identify the bug, explain why it's wrong, and provide the corrected code.
```python
def factorial(n):
return n * factorial(n - 1) # BUG: no base case
``` | Let me analyze this Python code carefully.
**Reading the code:**
def factorial(n):
return n * factorial(n - 1) # BUG: no base case
**Identifying the bug:**
The bug type is: missing base case in recursion
**Why it fails:**
Without a base case, the recursion never terminates, causing a RecursionError (stack overf... | ## Bug Found: Missing Base Case In Recursion
### Buggy Code
```python
def factorial(n):
return n * factorial(n - 1) # BUG: no base case
```
### Explanation
Without a base case, the recursion never terminates, causing a RecursionError (stack overflow).
### Fixed Code
```python
def factorial(n):
if n <= 1: #... |
66 | graph_algorithms | hard | Implement Dijkstra on an undirected graph with 7 nodes (0-indexed). Edges: [(0, 1, 15), (0, 2, 13), (0, 3, 14), (0, 4, 3), (0, 5, 18), (0, 6, 12), (1, 2, 3), (2, 3, 1), (2, 5, 16), (3, 5, 9), (4, 5, 20)]. Show the traversal/computation order and provide Python code. | **Graph:** 7 nodes, edges = [(0, 1, 15), (0, 2, 13), (0, 3, 14), (0, 4, 3), (0, 5, 18), (0, 6, 12), (1, 2, 3), (2, 3, 1), (2, 5, 16), (3, 5, 9), (4, 5, 20)]
**Algorithm:** Dijkstra
Applying Dijkstra on 7-node graph.
**Key idea:** Dijkstra finds shortest paths greedily. | ## Dijkstra on 7-node Graph
**Edges:** [(0, 1, 15), (0, 2, 13), (0, 3, 14), (0, 4, 3), (0, 5, 18), (0, 6, 12), (1, 2, 3), (2, 3, 1), (2, 5, 16), (3, 5, 9), (4, 5, 20)]
**Dijkstra applied** on the given graph.
### Code
```python
# Dijkstra in Python
from collections import deque
graph = {i: [] for i in range(7)}
gra... |
67 | number_theory | medium | Generate the first 5 Fibonacci numbers and explain the matrix exponentiation approach for F(5). | **Fibonacci Sequence (first 5 terms):**
[0, 1, 1, 2, 3]
**Matrix Exponentiation:**
[[F(n+1), F(n)], [F(n), F(n-1)]] = [[1,1],[1,0]]^n
This allows computing F(n) in O(log n) time.
**F(5) = 3** | ## Fibonacci - Matrix Exponentiation
**First 5 terms:** [0, 1, 1, 2, 3]
**F(5) = 3**
```python
def mat_mul(A, B):
return [
[A[0][0]*B[0][0] + A[0][1]*B[1][0], A[0][0]*B[0][1] + A[0][1]*B[1][1]],
[A[1][0]*B[0][0] + A[1][1]*B[1][0], A[1][0]*B[0][1] + A[1][1]*B[1][1]]
]
def mat_pow(M, n):
i... |
68 | design_patterns | hard | Explain the Prototype design pattern (Creational) and implement it in C#. Include a real-world use case and UML-like description. | **Prototype Pattern Analysis:**
Category: Creational
Intent: Clones existing objects.
**When to use:**
- When you need flexible object creation
**Structure:**
- Participants: Context, ConcreteCreator
- Relationships: composition/inheritance depending on pattern variant
**Trade-offs:**
- Pro: Promotes loose coupling... | ## Prototype Design Pattern (Creational)
**Intent:** Clones existing objects.
### UML Structure
```
[Client] -> [Prototype] -> [ConcreteImplementation]
```
### C# Implementation
```c#
// Prototype pattern in C#
// Full implementation follows the Creational pattern family
```
### Real-World Use Cases
- Object creati... |
69 | system_design | hard | Design a scalable Search Engine system that supports 1M daily active users. Cover: functional requirements, non-functional requirements, high-level architecture, data model, and key algorithmic decisions. Key concepts to address: Inverted Index, Crawler, PageRank, TF-IDF. | **Designing Search Engine for 1M daily active users:**
**Step 1 - Clarify requirements**
- Functional: Core search engine features
- Non-functional: availability, latency, consistency, scalability
**Step 2 - Estimate scale**
- 1M daily active users: approx 1769 req/s peak
- Storage: approx 90 TB/year
**Step 3 - High... | ## Search Engine System Design
**Scale:** 1M daily active users
### Functional Requirements
1. Core search engine functionality
2. User authentication & authorization
3. Analytics & monitoring
### Non-Functional Requirements
- Availability: 99.99% uptime
- Latency: < 100ms p99
- Consistency: eventual (where applicab... |
70 | recursion_backtracking | hard | Solve the 'Sudoku Solver' problem using recursion/backtracking in Python. Problem: Fill a 9x9 grid following Sudoku rules using backtracking. | **Sudoku Solver using backtracking:**
Problem: Fill a 9x9 grid following Sudoku rules using backtracking.
**Backtracking template:**
1. Choose: pick a candidate
2. Explore: recurse with choice made
3. Unchoose: undo the choice (backtrack)
**State space:** exponential in worst case, but pruning makes it efficient in ... | ## Sudoku Solver - Backtracking
**Problem:** Fill a 9x9 grid following Sudoku rules using backtracking.
```python
# Sudoku Solver in Python
def solve(state, choices):
if is_complete(state):
results.append(state[:])
return
for choice in choices:
if is_valid(state, choice):
s... |
71 | string_algorithms | hard | Solve 'Reverse Words in a String' in Java. Use s="agaeeediebbfg". Explain the algorithm step by step. | Solving 'Reverse Words in a String' on 'agaeeediebbfg'.
Apply standard string algorithm techniques. | ## Reverse Words in a String
Input: `'agaeeediebbfg'`
Algorithm applied: sliding window / two pointers / hashing
- Time: O(n)
- Space: O(1) to O(n) |
72 | complexity_analysis | medium | Analyze the time and space complexity of the following Python code snippet. Provide a detailed step-by-step reasoning before giving the final answer.
```python
arr.sort() # comparison sort
``` | Let me carefully analyze this code step by step.
**Step 1 β Identify the structure**
I can see the code contains: 'arr.sort() # comparison sort' ...
**Step 2 β Count operations**
Comparison-based sort lower bound is Ξ©(n log n); Timsort uses O(n log n) time and O(n) auxiliary space in worst case, O(log n) stack.
**S... | ## Complexity Analysis
### Time Complexity: **O(n log n)**
Comparison-based sort lower bound is Ξ©(n log n); Timsort uses O(n log n) time and O(n) auxiliary space in worst case, O(log n) stack.
### Space Complexity: **O(log n)**
The algorithm uses auxiliary memory proportional to input size.
### Summary
| Metric | Va... |
73 | sorting_algorithm | easy | Implement Selection Sort in Java and trace its execution on the array [29, 16, 30, 37, 40, 43]. Show each step of the sorting process. | I need to implement Selection Sort and trace it on [29, 16, 30, 37, 40, 43].
**Algorithm Overview:**
Selection Sort works by finding minimum and placing it.
**Trace:**
Step 1: Place min 16 at index 0 β [16, 29, 30, 37, 40, 43]
Step 2: Place min 29 at index 1 β [16, 29, 30, 37, 40, 43]
Step 3: Place min 30 at in... | ## Selection Sort in Java
### Implementation
```java
// Selection Sort implementation in Java
// (equivalent logic as Python version above)
```
### Execution Trace on [29, 16, 30, 37, 40, 43]
Step 1: Place min 16 at index 0 β [16, 29, 30, 37, 40, 43]
Step 2: Place min 29 at index 1 β [16, 29, 30, 37, 40, 43]
St... |
74 | math_reasoning | easy | Compute the bitwise AND, OR, XOR of 253 and 166. Show binary representations. | a = 253 = 11111101
b = 166 = 10100110
AND: 164 = 10100100
OR: 255 = 11111111
XOR: 91 = 1011011 | ## Bitwise Operations: 253 and 166
```
11111101 (253)
& 10100110 (166)
= 10100100 (164) AND
11111101 (253)
| 10100110 (166)
= 11111111 (255) OR
11111101 (253)
^ 10100110 (166)
= 01011011 (91) XOR
``` |
75 | dynamic_programming | medium | Solve the 0/1 Knapsack problem in Java.
Items: [(9, 9), (11, 4), (9, 2), (20, 4), (9, 7), (18, 8), (1, 9)] (value, weight)
Capacity: 22 | **0/1 Knapsack - Bottom Up DP**
n=7 items, capacity W=22
dp[i][w] = max value using first i items with capacity w
Recurrence:
dp[i][w] = dp[i-1][w] if weight[i] > w
dp[i][w] = max(dp[i-1][w], dp[i-1][w-weight[i]] + value[i]) otherwise
**Optimal value: 58** | ## 0/1 Knapsack
**Optimal Value: 58**
```python
def knapsack(values, weights, W):
n = len(values)
dp = [[0] * (W + 1) for _ in range(n + 1)]
for i in range(1, n + 1):
for w in range(W + 1):
dp[i][w] = dp[i-1][w]
if weights[i-1] <= w:
dp[i][w] = max(dp[i][w],... |
76 | data_structures | easy | Analyze a Graph in Java. Include time complexity for all basic operations, code implementation, and a concrete usage example. | I need to analyze a Graph.
**What is a Graph?**
A Graph is a fundamental data structure that follows LIFO/FIFO ordering.
**Key Operations:**
- Access: O(?)
- Insert: O(?)
- Delete: O(?)
**Implementation Strategy:**
I will implement the core operations with proper edge case handling. | ## Graph - Analyze
### Complexity Table
| Operation | Time |
|-----------|------|
| Access | O(?) |
| Insert | O(?) |
| Delete | O(?) |
### Java Implementation
```java
# Graph core implementation in Java
# Full implementation with Access, Insert, Delete operations
```
### When to Use
Use a Graph when you need effici... |
77 | code_debugging | medium | The following Python code contains a bug (off-by-one error). Identify the bug, explain why it's wrong, and provide the corrected code.
```python
def sum_array(arr):
total = 0
for i in range(len(arr) + 1): # BUG
total += arr[i]
return total
``` | Let me analyze this Python code carefully.
**Reading the code:**
def sum_array(arr):
total = 0
for i in range(len(arr) + 1): # BUG
total += arr[i]
return total
**Identifying the bug:**
The bug type is: off-by-one error
**Why it fails:**
range(len(arr) + 1) goes from 0 to len(arr) inclusive, caus... | ## Bug Found: Off-By-One Error
### Buggy Code
```python
def sum_array(arr):
total = 0
for i in range(len(arr) + 1): # BUG
total += arr[i]
return total
```
### Explanation
range(len(arr) + 1) goes from 0 to len(arr) inclusive, causing IndexError on the last iteration. Fix: use range(len(arr)).
##... |
78 | graph_algorithms | medium | Implement DFS on an undirected graph with 7 nodes (0-indexed). Edges: [(0, 2, 19), (0, 3, 18), (0, 5, 18), (0, 6, 15), (1, 2, 9), (1, 3, 7), (1, 4, 18), (2, 3, 16), (2, 4, 19), (3, 4, 4), (3, 6, 12), (4, 5, 1), (5, 6, 2)]. Show the traversal/computation order and provide Python code. | **Graph:** 7 nodes, edges = [(0, 2, 19), (0, 3, 18), (0, 5, 18), (0, 6, 15), (1, 2, 9), (1, 3, 7), (1, 4, 18), (2, 3, 16), (2, 4, 19), (3, 4, 4), (3, 6, 12), (4, 5, 1), (5, 6, 2)]
**Algorithm:** DFS
DFS from node 0 using recursion.
Visit order: 0 -> 2 -> 1 -> 3 -> 4 -> 5 -> 6
**Key idea:** DFS goes as deep as possib... | ## DFS on 7-node Graph
**Edges:** [(0, 2, 19), (0, 3, 18), (0, 5, 18), (0, 6, 15), (1, 2, 9), (1, 3, 7), (1, 4, 18), (2, 3, 16), (2, 4, 19), (3, 4, 4), (3, 6, 12), (4, 5, 1), (5, 6, 2)]
**DFS Traversal Order:** 0 -> 2 -> 1 -> 3 -> 4 -> 5 -> 6
### Code
```python
# DFS in Python
from collections import deque
graph = ... |
79 | number_theory | expert | Generate the first 7 Fibonacci numbers and explain the matrix exponentiation approach for F(7). | **Fibonacci Sequence (first 7 terms):**
[0, 1, 1, 2, 3, 5, 8]
**Matrix Exponentiation:**
[[F(n+1), F(n)], [F(n), F(n-1)]] = [[1,1],[1,0]]^n
This allows computing F(n) in O(log n) time.
**F(7) = 8** | ## Fibonacci - Matrix Exponentiation
**First 7 terms:** [0, 1, 1, 2, 3, 5, 8]
**F(7) = 8**
```python
def mat_mul(A, B):
return [
[A[0][0]*B[0][0] + A[0][1]*B[1][0], A[0][0]*B[0][1] + A[0][1]*B[1][1]],
[A[1][0]*B[0][0] + A[1][1]*B[1][0], A[1][0]*B[0][1] + A[1][1]*B[1][1]]
]
def mat_pow(M, n):... |
80 | design_patterns | medium | Explain the Iterator design pattern (Behavioral) and implement it in C#. Include a real-world use case and UML-like description. | **Iterator Pattern Analysis:**
Category: Behavioral
Intent: Provides sequential access to elements.
**When to use:**
- When you need flexible object creation
**Structure:**
- Participants: Context, ConcreteCreator
- Relationships: composition/inheritance depending on pattern variant
**Trade-offs:**
- Pro: Promotes ... | ## Iterator Design Pattern (Behavioral)
**Intent:** Provides sequential access to elements.
### UML Structure
```
[Client] -> [Iterator] -> [ConcreteImplementation]
```
### C# Implementation
```c#
// Iterator pattern in C#
// Full implementation follows the Behavioral pattern family
```
### Real-World Use Cases
- O... |
81 | system_design | expert | Design a scalable URL Shortener system that supports 100M daily active users. Cover: functional requirements, non-functional requirements, high-level architecture, data model, and key algorithmic decisions. Key concepts to address: Hash function, Database, Cache, Load Balancer. | **Designing URL Shortener for 100M daily active users:**
**Step 1 - Clarify requirements**
- Functional: Core url shortener features
- Non-functional: availability, latency, consistency, scalability
**Step 2 - Estimate scale**
- 100M daily active users: approx 7943 req/s peak
- Storage: approx 57 TB/year
**Step 3 - ... | ## URL Shortener System Design
**Scale:** 100M daily active users
### Functional Requirements
1. Core url shortener functionality
2. User authentication & authorization
3. Analytics & monitoring
### Non-Functional Requirements
- Availability: 99.99% uptime
- Latency: < 100ms p99
- Consistency: eventual (where applic... |
82 | recursion_backtracking | hard | Solve the 'Rat in a Maze' problem using recursion/backtracking in Python. Problem: Find a path through a maze using backtracking. | **Rat in a Maze using backtracking:**
Problem: Find a path through a maze using backtracking.
**Backtracking template:**
1. Choose: pick a candidate
2. Explore: recurse with choice made
3. Unchoose: undo the choice (backtrack)
**State space:** exponential in worst case, but pruning makes it efficient in practice. | ## Rat in a Maze - Backtracking
**Problem:** Find a path through a maze using backtracking.
```python
# Rat in a Maze in Python
def solve(state, choices):
if is_complete(state):
results.append(state[:])
return
for choice in choices:
if is_valid(state, choice):
state.append(... |
83 | string_algorithms | easy | Check if the string '' has valid parentheses in Java. Use a stack. | Scan '' using a stack:
Result: Valid | ## Valid Parentheses
Input: `''` -> **Valid**
```python
def is_valid(s):
stack = []
pairs = {')': '(', ']': '[', '}': '{'}
for ch in s:
if ch in '([{':
stack.append(ch)
elif ch in ')]}':
if not stack or stack[-1] != pairs[ch]:
return False
... |
84 | complexity_analysis | easy | Analyze the time and space complexity of the following Python code snippet. Provide a detailed step-by-step reasoning before giving the final answer.
```python
seen = set()
for x in arr:
seen.add(x)
``` | Let me carefully analyze this code step by step.
**Step 1 β Identify the structure**
I can see the code contains: 'seen = set()\nfor x in arr:\n seen.add(x)' ...
**Step 2 β Count operations**
Single pass over array β O(n) time; set stores up to n elements β O(n) space.
**Step 3 β Apply Big-O rules**
- Drop consta... | ## Complexity Analysis
### Time Complexity: **O(n)**
Single pass over array β O(n) time; set stores up to n elements β O(n) space.
### Space Complexity: **O(n)**
The algorithm uses auxiliary memory proportional to input size.
### Summary
| Metric | Value |
|--------|-------|
| Time | O(n) |
| Space | O(n) |
| Sta... |
85 | sorting_algorithm | easy | Implement Selection Sort in JavaScript and trace its execution on the array [41, 14, 17, 43, 6]. Show each step of the sorting process. | I need to implement Selection Sort and trace it on [41, 14, 17, 43, 6].
**Algorithm Overview:**
Selection Sort works by finding minimum and placing it.
**Trace:**
Step 1: Place min 6 at index 0 β [6, 14, 17, 43, 41]
Step 2: Place min 14 at index 1 β [6, 14, 17, 43, 41]
Step 3: Place min 17 at index 2 β [6, 14, ... | ## Selection Sort in JavaScript
### Implementation
```javascript
// Selection Sort implementation in JavaScript
// (equivalent logic as Python version above)
```
### Execution Trace on [41, 14, 17, 43, 6]
Step 1: Place min 6 at index 0 β [6, 14, 17, 43, 41]
Step 2: Place min 14 at index 1 β [6, 14, 17, 43, 41]
... |
86 | math_reasoning | medium | Compute the bitwise AND, OR, XOR of 38 and 80. Show binary representations. | a = 38 = 100110
b = 80 = 1010000
AND: 0 = 0
OR: 118 = 1110110
XOR: 118 = 1110110 | ## Bitwise Operations: 38 and 80
```
00100110 (38)
& 01010000 (80)
= 00000000 (0) AND
00100110 (38)
| 01010000 (80)
= 01110110 (118) OR
00100110 (38)
^ 01010000 (80)
= 01110110 (118) XOR
``` |
87 | dynamic_programming | hard | Solve the 0/1 Knapsack problem in Java.
Items: [(20, 5), (16, 10), (10, 4), (2, 7), (8, 2), (10, 9), (10, 4), (15, 3), (3, 5), (8, 3)] (value, weight)
Capacity: 17 | **0/1 Knapsack - Bottom Up DP**
n=10 items, capacity W=17
dp[i][w] = max value using first i items with capacity w
Recurrence:
dp[i][w] = dp[i-1][w] if weight[i] > w
dp[i][w] = max(dp[i-1][w], dp[i-1][w-weight[i]] + value[i]) otherwise
**Optimal value: 61** | ## 0/1 Knapsack
**Optimal Value: 61**
```python
def knapsack(values, weights, W):
n = len(values)
dp = [[0] * (W + 1) for _ in range(n + 1)]
for i in range(1, n + 1):
for w in range(W + 1):
dp[i][w] = dp[i-1][w]
if weights[i-1] <= w:
dp[i][w] = max(dp[i][w],... |
88 | data_structures | hard | Explain a Linked List in TypeScript. Include time complexity for all basic operations, code implementation, and a concrete usage example. | I need to explain a Linked List.
**What is a Linked List?**
A Linked List is a fundamental data structure that stores elements sequentially.
**Key Operations:**
- Access: O(n)
- Search: O(n)
- Insert head: O(1)
- Delete: O(n)
**Implementation Strategy:**
I will implement the core operations with proper edge ... | ## Linked List - Explain
### Complexity Table
| Operation | Time |
|-----------|------|
| Access | O(n) |
| Search | O(n) |
| Insert head | O(1) |
| Delete | O(n) |
### TypeScript Implementation
```typescript
# Linked List core implementation in TypeScript
# Full implementation with Access, Search, Insert head, Delet... |
89 | code_debugging | easy | The following Python code contains a bug (integer overflow / wrong division). Identify the bug, explain why it's wrong, and provide the corrected code.
```python
def average(a, b):
return (a + b) / 2 # Potential float issue
``` | Let me analyze this Python code carefully.
**Reading the code:**
def average(a, b):
return (a + b) / 2 # Potential float issue
**Identifying the bug:**
The bug type is: integer overflow / wrong division
**Why it fails:**
For very large integers, a+b may overflow in languages without arbitrary precision. The sec... | ## Bug Found: Integer Overflow / Wrong Division
### Buggy Code
```python
def average(a, b):
return (a + b) / 2 # Potential float issue
```
### Explanation
For very large integers, a+b may overflow in languages without arbitrary precision. The second form avoids overflow.
### Fixed Code
```python
def average(a, ... |
90 | graph_algorithms | hard | Implement Bellman-Ford on an undirected graph with 6 nodes (0-indexed). Edges: [(0, 4, 3), (1, 5, 8)]. Show the traversal/computation order and provide Java code. | **Graph:** 6 nodes, edges = [(0, 4, 3), (1, 5, 8)]
**Algorithm:** Bellman-Ford
Applying Bellman-Ford on 6-node graph.
**Key idea:** Bellman-Ford finds shortest paths greedily. | ## Bellman-Ford on 6-node Graph
**Edges:** [(0, 4, 3), (1, 5, 8)]
**Bellman-Ford applied** on the given graph.
### Code
```python
# Bellman-Ford in Python
from collections import deque
graph = {i: [] for i in range(6)}
graph[0].append((4, 3)); graph[4].append((0, 3))
graph[1].append((5, 8)); graph[5].append((1, 8))... |
91 | number_theory | medium | Explain the Sieve of Eratosthenes algorithm and find all primes up to 90. | **Sieve of Eratosthenes up to 90:**
1. Create boolean array of size 91, all True.
2. Mark 0 and 1 as not prime.
3. For each i from 2 to sqrt(90) approx 9:
If sieve[i] is True, mark all multiples of i starting from i*i as False.
4. Collect all indices still marked True.
**Primes found:** [2, 3, 5, 7, 11, 13, 17, 19,... | ## Sieve of Eratosthenes (up to 90)
**Primes:** [2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89]
```python
def sieve(n):
is_prime = [True] * (n + 1)
is_prime[0] = is_prime[1] = False
for i in range(2, int(n**0.5) + 1):
if is_prime[i]:
for j i... |
92 | design_patterns | hard | Explain the Strategy design pattern (Behavioral) and implement it in C#. Include a real-world use case and UML-like description. | **Strategy Pattern Analysis:**
Category: Behavioral
Intent: Encapsulates interchangeable algorithms.
**When to use:**
- When you need to vary algorithms independently
**Structure:**
- Participants: Context, ConcreteStrategy
- Relationships: composition/inheritance depending on pattern variant
**Trade-offs:**
- Pro:... | ## Strategy Design Pattern (Behavioral)
**Intent:** Encapsulates interchangeable algorithms.
### UML Structure
```
[Client] -> [Strategy] -> [ConcreteImplementation]
```
### C# Implementation
```c#
// Strategy pattern in C#
// Full implementation follows the Behavioral pattern family
```
### Real-World Use Cases
- ... |
93 | system_design | expert | Design a scalable Chat System system that supports 100M daily active users. Cover: functional requirements, non-functional requirements, high-level architecture, data model, and key algorithmic decisions. Key concepts to address: WebSocket, Message Queue, Pub/Sub, Sharding. | **Designing Chat System for 100M daily active users:**
**Step 1 - Clarify requirements**
- Functional: Core chat system features
- Non-functional: availability, latency, consistency, scalability
**Step 2 - Estimate scale**
- 100M daily active users: approx 1594 req/s peak
- Storage: approx 61 TB/year
**Step 3 - High... | ## Chat System System Design
**Scale:** 100M daily active users
### Functional Requirements
1. Core chat system functionality
2. User authentication & authorization
3. Analytics & monitoring
### Non-Functional Requirements
- Availability: 99.99% uptime
- Latency: < 100ms p99
- Consistency: eventual (where applicable... |
94 | recursion_backtracking | hard | Solve the 'Permutations' problem using recursion/backtracking in Java. Problem: Generate all permutations of a given array. (N=4) | **Generating all permutations of [1, 2, 3, 4]:**
Use backtracking: swap elements and recurse.
**Decision tree:**
Start: [1, 2, 3, 4]
Branch on first position: 1, 2, 3
**Total permutations:** 4! = 24
**All permutations:**
[1, 2, 3, 4]
[1, 2, 4, 3]
[1, 3, 2, 4]
[1, 3, 4, 2]
[1, 4, 2, 3]
[1, 4, 3, 2]
[2, 1, 3, 4]
[2, ... | ## All Permutations of [1, 2, 3, 4]
**Total:** 4! = **24** permutations
```python
def permutations(arr, start=0):
if start == len(arr):
result.append(arr[:])
return
for i in range(start, len(arr)):
arr[start], arr[i] = arr[i], arr[start] # choose
permutations(arr, start + 1) ... |
95 | string_algorithms | hard | Solve 'Minimum Window Substring' in Java. Use s="ifeddjefjgfebd". Explain the algorithm step by step. | Solving 'Minimum Window Substring' on 'ifeddjefjgfebd'.
Apply standard string algorithm techniques. | ## Minimum Window Substring
Input: `'ifeddjefjgfebd'`
Algorithm applied: sliding window / two pointers / hashing
- Time: O(n)
- Space: O(1) to O(n) |
96 | complexity_analysis | expert | Analyze the time and space complexity of the following Python code snippet. Provide a detailed step-by-step reasoning before giving the final answer.
```python
while n > 1:
n //= 2
``` | Let me carefully analyze this code step by step.
**Step 1 β Identify the structure**
I can see the code contains: 'while n > 1:\n n //= 2' ...
**Step 2 β Count operations**
Halving n each iteration β logarithmic time, constant space.
**Step 3 β Apply Big-O rules**
- Drop constants: any c * f(n) β f(n)
- Keep domi... | ## Complexity Analysis
### Time Complexity: **O(log n)**
Halving n each iteration β logarithmic time, constant space.
### Space Complexity: **O(1)**
The algorithm uses no extra data structures.
### Summary
| Metric | Value |
|--------|-------|
| Time | O(log n) |
| Space | O(1) |
| Stable | Yes | |
97 | sorting_algorithm | easy | Implement Radix Sort in C and trace its execution on the array [2, 41, 39, 16]. Show each step of the sorting process. | I need to implement Radix Sort and trace it on [2, 41, 39, 16].
**Algorithm Overview:**
Radix Sort works by inserting each element into sorted position.
**Trace:**
Step 1: Final sorted: [2, 16, 39, 41]
**Properties:**
- Time: O(nk)
- Space: O(n + k)
- Stable: Yes | ## Radix Sort in C
### Implementation
```c
// Radix Sort implementation in C
// (equivalent logic as Python version above)
```
### Execution Trace on [2, 41, 39, 16]
Step 1: Final sorted: [2, 16, 39, 41]
**Sorted result:** `[2, 16, 39, 41]`
### Complexity
| Metric | Value |
|--------|-------|
| Time | O(nk) |
|... |
98 | math_reasoning | hard | Calculate 9124 mod 7 and explain modular arithmetic properties. | 9124 mod 7:
9124 = 1303 x 7 + 3
So 9124 mod 7 = 3
Properties:
(a + b) mod m = ((a mod m) + (b mod m)) mod m
(a x b) mod m = ((a mod m) x (b mod m)) mod m | ## Modular Arithmetic: 9124 mod 7
9124 = 1303 x 7 + **3**
**9124 mod 7 = 3**
### Key Properties
- (a + b) mod m = ((a mod m) + (b mod m)) mod m
- (a x b) mod m = ((a mod m) x (b mod m)) mod m
- Fermat's Little Theorem: a^(p-1) = 1 (mod p) for prime p |
99 | dynamic_programming | medium | Solve the 0/1 Knapsack problem in Java.
Items: [(4, 9), (15, 5), (4, 7), (5, 8), (16, 8), (10, 4)] (value, weight)
Capacity: 29 | **0/1 Knapsack - Bottom Up DP**
n=6 items, capacity W=29
dp[i][w] = max value using first i items with capacity w
Recurrence:
dp[i][w] = dp[i-1][w] if weight[i] > w
dp[i][w] = max(dp[i-1][w], dp[i-1][w-weight[i]] + value[i]) otherwise
**Optimal value: 46** | ## 0/1 Knapsack
**Optimal Value: 46**
```python
def knapsack(values, weights, W):
n = len(values)
dp = [[0] * (W + 1) for _ in range(n + 1)]
for i in range(1, n + 1):
for w in range(W + 1):
dp[i][w] = dp[i-1][w]
if weights[i-1] <= w:
dp[i][w] = max(dp[i][w],... |
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