Essential Coding Patterns for Amazon L6/L7 Engineering Managers
Executive Summary
This comprehensive guide provides the essential coding patterns that L6/L7 engineering managers need to master for Amazon technical interviews. Unlike competitive programming guides, this focuses on pattern recognition, clear implementation, and strategic technical leadership communication.
Target Audience: L6/L7 engineering managers who may not code daily but need to demonstrate technical competency and leadership thinking during coding interviews.
Goal: Master 10 core patterns that cover 80% of Amazon coding interview problems, with emphasis on recognition speed, clear communication, and real-world engineering applications.
1. Essential Patterns for Managers: The Strategic Foundation
Why Patterns Matter More Than Memorization
For L6/L7 engineering managers, coding interviews aren't about algorithmic gymnastics—they're about demonstrating technical leadership through structured thinking, clear communication, and sound engineering judgment.
Key Manager Advantages of Pattern-Based Approach:
- Rapid Problem Classification: Quickly categorize problems and select appropriate solution strategies
- Technical Credibility: Demonstrate deep understanding of algorithmic foundations that inform architectural decisions
- Team Guidance: Provide effective technical direction during code reviews and design discussions
- Strategic Trade-offs: Evaluate multiple approaches and explain trade-offs clearly to stakeholders
L6 vs L7 Coding Expectations
L6 Senior Engineering Manager Expectations:
- Pattern Recognition: Identify correct pattern within 3-5 minutes
- Implementation Quality: Clean, maintainable code with basic optimization
- Communication: Explain approach clearly and handle follow-up questions
- System Connection: Relate solution to practical engineering problems
L7 Principal Engineering Manager Expectations:
- Pattern Recognition: Identify pattern within 2-3 minutes, suggest alternatives
- Implementation Quality: Optimized solution with comprehensive edge case handling
- Communication: Teach the pattern to interviewer, discuss multiple approaches
- Strategic Vision: Connect to system design, team development, and organizational impact
Time Management in Coding Rounds
The L6/L7 Manager's 45-Minute Framework:
| Text Only |
|---|
| Minutes 0-5: Problem Understanding & Pattern Recognition
- Read problem carefully, identify constraints
- Recognize which pattern(s) apply
- Clarify requirements and edge cases
Minutes 5-10: Approach Design & Communication
- Explain chosen pattern and why it fits
- Outline solution structure at high level
- Discuss time/space complexity expectations
Minutes 10-30: Implementation
- Code systematically with clear structure
- Add comments for complex logic
- Handle edge cases explicitly
Minutes 30-40: Testing & Optimization
- Test with provided examples
- Walk through edge cases
- Optimize if time permits
Minutes 40-45: Discussion & Follow-up
- Analyze final complexity
- Discuss alternative approaches
- Connect to real-world applications
|
2. Top 10 Patterns with Comprehensive Examples
Pattern 1: Two Pointers
When to Recognize This Pattern:
- Searching pairs in sorted arrays
- Palindrome problems
- Array/string optimization requiring O(n) instead of O(n²)
- Problems involving comparison from opposite ends
Template Code:
| Python |
|---|
| def two_pointers_template(arr, target):
"""
Generic two pointers template for L6/L7 managers
Focus: Clear logic, maintainable code
"""
left, right = 0, len(arr) - 1
while left < right:
current = process(arr[left], arr[right])
if current == target:
return [left, right]
elif current < target:
left += 1 # Need larger value
else:
right -= 1 # Need smaller value
return [] # No solution found
|
Amazon Interview Problems:
Problem 1: Container With Most Water (Medium)
| Python |
|---|
| def max_area(height):
"""
Amazon: Design a water container optimization system
Manager insight: Resource optimization under constraints
"""
max_water = 0
left, right = 0, len(height) - 1
while left < right:
# Calculate current area
width = right - left
current_height = min(height[left], height[right])
current_area = width * current_height
max_water = max(max_water, current_area)
# Move pointer with smaller height
if height[left] < height[right]:
left += 1
else:
right -= 1
return max_water
# Time: O(n), Space: O(1)
# Manager discussion: Similar to load balancing optimization
|
Problem 2: 3Sum (Medium)
| Python |
|---|
| def three_sum(nums):
"""
Amazon: Find all unique triplets that sum to zero
Manager insight: Duplicate detection and systematic enumeration
"""
nums.sort()
result = []
for i in range(len(nums) - 2):
# Skip duplicates for first element
if i > 0 and nums[i] == nums[i-1]:
continue
left, right = i + 1, len(nums) - 1
while left < right:
current_sum = nums[i] + nums[left] + nums[right]
if current_sum == 0:
result.append([nums[i], nums[left], nums[right]])
# Skip duplicates
while left < right and nums[left] == nums[left+1]:
left += 1
while left < right and nums[right] == nums[right-1]:
right -= 1
left += 1
right -= 1
elif current_sum < 0:
left += 1
else:
right -= 1
return result
# Time: O(n²), Space: O(1) excluding output
# Manager discussion: Systematic approach to complex constraint problems
|
Common Variations:
- Fast and slow pointers for cycle detection
- Multiple pointers for k-sum problems
- Sliding window as dynamic two pointers
Manager-Level Discussion Points:
- How this pattern optimizes brute force O(n²) to O(n)
- Applications in database query optimization
- Load balancing and resource allocation algorithms
- Connection to binary search in optimization problems
Pattern 2: Sliding Window
When to Recognize This Pattern:
- Subarray/substring problems with size constraints
- Problems asking for "maximum/minimum in window"
- String matching with character frequency
- Any problem involving "consecutive elements"
Template Code:
| Python |
|---|
| def sliding_window_template(arr, k):
"""
Generic sliding window for fixed and variable sizes
L6/L7 focus: Real-time data processing understanding
"""
# Fixed window size
window_sum = sum(arr[:k])
max_sum = window_sum
for i in range(k, len(arr)):
# Slide window: remove left, add right
window_sum = window_sum - arr[i-k] + arr[i]
max_sum = max(max_sum, window_sum)
return max_sum
def variable_sliding_window(s, condition):
"""
Variable window template for constraint-based problems
"""
left = 0
best_result = 0
for right in range(len(s)):
# Expand window
add_to_window(s[right])
# Contract window while condition violated
while window_violates_condition():
remove_from_window(s[left])
left += 1
# Update result if current window is better
best_result = max(best_result, right - left + 1)
return best_result
|
Amazon Interview Problems:
Problem 1: Longest Substring Without Repeating Characters (Medium)
| Python |
|---|
| def length_of_longest_substring(s):
"""
Amazon: Design a cache optimization system
Manager insight: Understanding LRU cache behavior
"""
char_index = {}
left = 0
max_length = 0
for right in range(len(s)):
# If character seen before and within current window
if s[right] in char_index and char_index[s[right]] >= left:
left = char_index[s[right]] + 1
char_index[s[right]] = right
max_length = max(max_length, right - left + 1)
return max_length
# Time: O(n), Space: O(min(m,n)) where m is charset size
# Manager discussion: Cache eviction policies and memory management
|
Problem 2: Minimum Window Substring (Hard)
| Python |
|---|
| def min_window(s, t):
"""
Amazon: Find minimum data window containing all required elements
Manager insight: Resource allocation with constraints
"""
from collections import Counter, defaultdict
if not s or not t:
return ""
# Count required characters
required = Counter(t)
required_length = len(required)
# Window tracking
window_counts = defaultdict(int)
formed = 0 # Number of unique chars in window with required frequency
left = 0
min_len = float('inf')
min_left = 0
for right in range(len(s)):
# Expand window
char = s[right]
window_counts[char] += 1
if char in required and window_counts[char] == required[char]:
formed += 1
# Contract window
while formed == required_length and left <= right:
# Update minimum window if smaller
if right - left + 1 < min_len:
min_len = right - left + 1
min_left = left
# Remove leftmost character
char = s[left]
window_counts[char] -= 1
if char in required and window_counts[char] < required[char]:
formed -= 1
left += 1
return s[min_left:min_left + min_len] if min_len != float('inf') else ""
# Time: O(|s| + |t|), Space: O(|s| + |t|)
# Manager discussion: Minimum resource allocation for SLA compliance
|
Manager-Level Discussion Points:
- Real-time monitoring and alerting systems
- Rate limiting and sliding window counters
- Database connection pooling optimization
- Stream processing and windowed aggregations
Pattern 3: Fast & Slow Pointers (Floyd's Cycle Detection)
When to Recognize This Pattern:
- Cycle detection in linked lists
- Finding middle element in one pass
- Determining if number is "happy"
- Any problem requiring O(1) space for traversal
Template Code:
| Python |
|---|
| def floyd_cycle_detection(head):
"""
Generic cycle detection template
L6/L7 insight: Distributed system health checking
"""
if not head or not head.next:
return False
slow = fast = head
# Phase 1: Detect cycle
while fast and fast.next:
slow = slow.next
fast = fast.next.next
if slow == fast:
break
else:
return False # No cycle found
# Phase 2: Find cycle start (if needed)
slow = head
while slow != fast:
slow = slow.next
fast = fast.next
return slow # Cycle start node
|
Amazon Interview Problems:
Problem 1: Linked List Cycle (Easy)
| Python |
|---|
| def has_cycle(head):
"""
Amazon: Detect circular dependencies in service mesh
Manager insight: System dependency validation
"""
if not head or not head.next:
return False
slow = fast = head
while fast and fast.next:
slow = slow.next
fast = fast.next.next
if slow == fast:
return True
return False
# Time: O(n), Space: O(1)
# Manager discussion: Dependency cycle detection in microservices
|
Problem 2: Find the Duplicate Number (Medium)
| Python |
|---|
| def find_duplicate(nums):
"""
Amazon: Find duplicate resource allocation
Manager insight: Resource leak detection
"""
# Treat array as linked list where nums[i] points to nums[nums[i]]
slow = fast = nums[0]
# Phase 1: Find intersection point
while True:
slow = nums[slow]
fast = nums[nums[fast]]
if slow == fast:
break
# Phase 2: Find entrance to cycle (duplicate number)
slow = nums[0]
while slow != fast:
slow = nums[slow]
fast = nums[fast]
return slow
# Time: O(n), Space: O(1)
# Manager discussion: Memory leak detection and resource management
|
Manager-Level Discussion Points:
- Distributed system health monitoring
- Deadlock detection in resource allocation
- Performance monitoring with minimal overhead
- Graceful degradation and circuit breaker patterns
Pattern 4: Tree/Graph Traversal (BFS/DFS)
When to Recognize This Pattern:
- Hierarchical data processing
- Level-by-level operations
- Shortest path problems
- Tree/graph validation
Template Code:
| Python |
|---|
| # DFS Template
def dfs_template(root):
"""
Generic DFS for tree problems
L6/L7 focus: Organizational hierarchy processing
"""
if not root:
return
# Process current node
process(root)
# Recursive DFS
dfs_template(root.left)
dfs_template(root.right)
# BFS Template
def bfs_template(root):
"""
Generic BFS for level-order processing
L6/L7 focus: System rollout and dependency management
"""
if not root:
return []
from collections import deque
queue = deque([root])
result = []
while queue:
level_size = len(queue)
level_nodes = []
for _ in range(level_size):
node = queue.popleft()
level_nodes.append(node.val)
if node.left:
queue.append(node.left)
if node.right:
queue.append(node.right)
result.append(level_nodes)
return result
|
Amazon Interview Problems:
Problem 1: Binary Tree Level Order Traversal (Medium)
| Python |
|---|
| def level_order(root):
"""
Amazon: Process organizational hierarchy by levels
Manager insight: Rollout planning and dependency management
"""
if not root:
return []
from collections import deque
queue = deque([root])
result = []
while queue:
level_size = len(queue)
current_level = []
for _ in range(level_size):
node = queue.popleft()
current_level.append(node.val)
if node.left:
queue.append(node.left)
if node.right:
queue.append(node.right)
result.append(current_level)
return result
# Time: O(n), Space: O(w) where w is maximum width
# Manager discussion: Parallel processing and dependency resolution
|
Problem 2: Validate Binary Search Tree (Medium)
| Python |
|---|
| def is_valid_bst(root):
"""
Amazon: Validate system invariants and constraints
Manager insight: System validation and constraint checking
"""
def validate(node, min_val, max_val):
if not node:
return True
# Check BST property
if node.val <= min_val or node.val >= max_val:
return False
# Recursively validate subtrees with updated bounds
return (validate(node.left, min_val, node.val) and
validate(node.right, node.val, max_val))
return validate(root, float('-inf'), float('inf'))
# Time: O(n), Space: O(h) where h is height
# Manager discussion: System invariant validation and constraint enforcement
|
Manager-Level Discussion Points:
- Microservice dependency resolution
- Organizational hierarchy processing
- System rollout planning and phases
- Configuration management and validation
Pattern 5: Binary Search Variations
When to Recognize This Pattern:
- Searching in sorted/rotated arrays
- Finding optimal value with constraints
- Peak finding problems
- Time-based optimization
Template Code:
| Python |
|---|
| def binary_search_template(arr, target):
"""
Generic binary search with manager insights
L6/L7 focus: Optimization and decision boundaries
"""
left, right = 0, len(arr) - 1
while left <= right:
mid = left + (right - left) // 2 # Prevent overflow
if arr[mid] == target:
return mid
elif arr[mid] < target:
left = mid + 1
else:
right = mid - 1
return -1 # Not found
def binary_search_optimization(condition_function):
"""
Binary search for optimization problems
Finding optimal threshold or boundary
"""
left, right = min_value, max_value
while left < right:
mid = left + (right - left) // 2
if condition_function(mid):
right = mid # Solution might be mid or lower
else:
left = mid + 1 # Solution must be higher
return left
|
Amazon Interview Problems:
Problem 1: Search in Rotated Sorted Array (Medium)
| Python |
|---|
| def search_rotated_array(nums, target):
"""
Amazon: Search in distributed system with failover rotation
Manager insight: System resilience and adaptive search
"""
left, right = 0, len(nums) - 1
while left <= right:
mid = left + (right - left) // 2
if nums[mid] == target:
return mid
# Determine which half is sorted
if nums[left] <= nums[mid]: # Left half is sorted
if nums[left] <= target < nums[mid]:
right = mid - 1
else:
left = mid + 1
else: # Right half is sorted
if nums[mid] < target <= nums[right]:
left = mid + 1
else:
right = mid - 1
return -1
# Time: O(log n), Space: O(1)
# Manager discussion: Handling system rotation and failover scenarios
|
Problem 2: Find Minimum in Rotated Sorted Array (Medium)
| Python |
|---|
| def find_min_rotated(nums):
"""
Amazon: Find optimal configuration after system rotation
Manager insight: Finding optimal state after disruption
"""
left, right = 0, len(nums) - 1
while left < right:
mid = left + (right - left) // 2
if nums[mid] > nums[right]:
# Minimum is in right half
left = mid + 1
else:
# Minimum is in left half (including mid)
right = mid
return nums[left]
# Time: O(log n), Space: O(1)
# Manager discussion: Finding optimal state after system disruption
|
Manager-Level Discussion Points:
- Capacity planning and threshold optimization
- Performance tuning and configuration search
- A/B testing and optimal parameter finding
- System recovery and optimal restart points
Pattern 6: Dynamic Programming Basics
When to Recognize This Pattern:
- Optimization problems with overlapping subproblems
- "Maximum/minimum" with choices at each step
- Counting number of ways to achieve something
- Problems with recursive structure
Template Code:
| Python |
|---|
| def dp_template_1d(n):
"""
1D DP template for sequence problems
L6/L7 focus: Strategic optimization over time
"""
# Initialize DP array
dp = [0] * (n + 1)
dp[0] = base_case
# Build solution bottom-up
for i in range(1, n + 1):
dp[i] = optimal_choice(dp[i-1], other_options)
return dp[n]
def dp_template_2d(m, n):
"""
2D DP template for grid/matrix problems
L6/L7 focus: Resource allocation across dimensions
"""
# Initialize DP table
dp = [[0] * n for _ in range(m)]
# Set base cases
for i in range(m):
dp[i][0] = base_case_col
for j in range(n):
dp[0][j] = base_case_row
# Fill table
for i in range(1, m):
for j in range(1, n):
dp[i][j] = optimal_choice(dp[i-1][j], dp[i][j-1])
return dp[m-1][n-1]
|
Amazon Interview Problems:
Problem 1: Climbing Stairs (Easy)
| Python |
|---|
| def climb_stairs(n):
"""
Amazon: Optimize deployment rollout strategies
Manager insight: Strategic planning with multiple paths
"""
if n <= 2:
return n
# DP approach: ways[i] = ways to reach step i
prev_prev, prev = 1, 2
for i in range(3, n + 1):
current = prev + prev_prev
prev_prev, prev = prev, current
return prev
# Time: O(n), Space: O(1)
# Manager discussion: Strategic planning with multiple viable paths
|
Problem 2: House Robber (Medium)
| Python |
|---|
| def rob(nums):
"""
Amazon: Optimize resource allocation with constraints
Manager insight: Strategic trade-offs and constraint optimization
"""
if not nums:
return 0
if len(nums) == 1:
return nums[0]
# DP: max money robbed up to house i
prev_prev = nums[0]
prev = max(nums[0], nums[1])
for i in range(2, len(nums)):
current = max(prev, prev_prev + nums[i])
prev_prev, prev = prev, current
return prev
# Time: O(n), Space: O(1)
# Manager discussion: Resource optimization with mutual exclusion constraints
|
Manager-Level Discussion Points:
- Strategic planning and optimization over time
- Budget allocation with constraints
- Feature prioritization and trade-offs
- Capacity planning and growth optimization
Pattern 7: Backtracking
When to Recognize This Pattern:
- Generate all possible solutions
- Problems with constraints and choices
- Permutations, combinations, subsets
- Puzzle solving with valid/invalid states
Template Code:
| Python |
|---|
| def backtrack_template(candidates, path, result):
"""
Generic backtracking template
L6/L7 focus: Systematic exploration of solution space
"""
# Base case: found valid solution
if is_valid_solution(path):
result.append(path[:]) # Make copy
return
# Try each candidate
for candidate in candidates:
if is_valid_choice(candidate, path):
# Make choice
path.append(candidate)
# Recurse with updated state
backtrack_template(get_next_candidates(candidates, candidate),
path, result)
# Backtrack (undo choice)
path.pop()
|
Amazon Interview Problems:
Problem 1: Generate Parentheses (Medium)
| Python |
|---|
| def generate_parentheses(n):
"""
Amazon: Generate all valid system configurations
Manager insight: Systematic configuration exploration
"""
result = []
def backtrack(current, open_count, close_count):
# Base case: complete valid configuration
if len(current) == 2 * n:
result.append(current)
return
# Add opening parenthesis if possible
if open_count < n:
backtrack(current + "(", open_count + 1, close_count)
# Add closing parenthesis if valid
if close_count < open_count:
backtrack(current + ")", open_count, close_count + 1)
backtrack("", 0, 0)
return result
# Time: O(4^n / √n), Space: O(4^n / √n)
# Manager discussion: Systematic generation of valid configurations
|
Problem 2: Word Search (Medium)
| Python |
|---|
| def word_search(board, word):
"""
Amazon: Search through distributed system topology
Manager insight: Systematic path finding with constraints
"""
if not board or not board[0]:
return False
rows, cols = len(board), len(board[0])
def backtrack(row, col, index):
# Base case: found complete word
if index == len(word):
return True
# Boundary and character checks
if (row < 0 or row >= rows or col < 0 or col >= cols or
board[row][col] != word[index]):
return False
# Mark as visited
temp = board[row][col]
board[row][col] = '#'
# Explore all directions
found = (backtrack(row + 1, col, index + 1) or
backtrack(row - 1, col, index + 1) or
backtrack(row, col + 1, index + 1) or
backtrack(row, col - 1, index + 1))
# Restore state
board[row][col] = temp
return found
# Try starting from each cell
for i in range(rows):
for j in range(cols):
if backtrack(i, j, 0):
return True
return False
# Time: O(N * 4^L) where N is cells, L is word length
# Manager discussion: Systematic search with state management
|
Manager-Level Discussion Points:
- Configuration space exploration
- Decision tree analysis and optimization
- Systematic testing and validation strategies
- Resource allocation and scheduling optimization
Pattern 8: Heap/Priority Queue
When to Recognize This Pattern:
- Finding k largest/smallest elements
- Merge operations maintaining order
- Scheduling and priority-based problems
- Streaming data with top-k queries
Template Code:
| Python |
|---|
| import heapq
def heap_template_max_k(nums, k):
"""
Find k largest elements using min heap
L6/L7 focus: Priority-based resource management
"""
min_heap = []
for num in nums:
heapq.heappush(min_heap, num)
# Maintain heap size of k
if len(min_heap) > k:
heapq.heappop(min_heap)
return sorted(min_heap, reverse=True)
def heap_template_streaming():
"""
Streaming median using two heaps
L6/L7 focus: Real-time data processing
"""
max_heap = [] # For smaller half (negate values)
min_heap = [] # For larger half
def add_number(num):
# Add to appropriate heap
if not max_heap or num <= -max_heap[0]:
heapq.heappush(max_heap, -num)
else:
heapq.heappush(min_heap, num)
# Balance heaps
if len(max_heap) > len(min_heap) + 1:
heapq.heappush(min_heap, -heapq.heappop(max_heap))
elif len(min_heap) > len(max_heap) + 1:
heapq.heappush(max_heap, -heapq.heappop(min_heap))
def get_median():
if len(max_heap) == len(min_heap):
return (-max_heap[0] + min_heap[0]) / 2.0
elif len(max_heap) > len(min_heap):
return -max_heap[0]
else:
return min_heap[0]
|
Amazon Interview Problems:
Problem 1: Top K Frequent Elements (Medium)
| Python |
|---|
| def top_k_frequent(nums, k):
"""
Amazon: Find most active users/resources
Manager insight: Priority-based monitoring and alerting
"""
from collections import Counter
import heapq
# Count frequencies
count = Counter(nums)
# Use min heap to find k most frequent
heap = []
for num, freq in count.items():
heapq.heappush(heap, (freq, num))
if len(heap) > k:
heapq.heappop(heap)
# Extract results (most frequent first)
result = []
while heap:
freq, num = heapq.heappop(heap)
result.append(num)
return result[::-1]
# Time: O(n log k), Space: O(n + k)
# Manager discussion: Real-time analytics and alerting systems
|
Problem 2: Merge k Sorted Lists (Hard)
| Python |
|---|
| def merge_k_lists(lists):
"""
Amazon: Merge multiple data streams efficiently
Manager insight: Distributed data aggregation
"""
import heapq
# Handle edge cases
if not lists:
return None
# Initialize heap with first node from each list
heap = []
for i, lst in enumerate(lists):
if lst:
heapq.heappush(heap, (lst.val, i, lst))
# Create dummy head for result
dummy = ListNode(0)
current = dummy
while heap:
val, list_idx, node = heapq.heappop(heap)
# Add node to result
current.next = node
current = current.next
# Add next node from same list if exists
if node.next:
heapq.heappush(heap, (node.next.val, list_idx, node.next))
return dummy.next
# Time: O(n log k), Space: O(k) where n is total nodes, k is number of lists
# Manager discussion: Distributed system data aggregation strategies
|
Manager-Level Discussion Points:
- Priority-based resource allocation
- Real-time monitoring and alerting
- Load balancing and traffic management
- Distributed system coordination
Pattern 9: Intervals
When to Recognize This Pattern:
- Meeting/scheduling problems
- Overlapping ranges or time periods
- Merging or inserting intervals
- Calendar and resource booking systems
Template Code:
| Python |
|---|
| def intervals_template(intervals):
"""
Generic interval processing template
L6/L7 focus: Resource scheduling and conflict resolution
"""
if not intervals:
return []
# Sort intervals by start time
intervals.sort(key=lambda x: x[0])
merged = [intervals[0]]
for current in intervals[1:]:
last = merged[-1]
# Check for overlap
if current[0] <= last[1]:
# Merge intervals
last[1] = max(last[1], current[1])
else:
# No overlap, add new interval
merged.append(current)
return merged
|
Amazon Interview Problems:
Problem 1: Merge Intervals (Medium)
| Python |
|---|
| def merge_intervals(intervals):
"""
Amazon: Optimize resource allocation windows
Manager insight: Capacity planning and resource optimization
"""
if not intervals:
return []
# Sort by start time
intervals.sort(key=lambda x: x[0])
merged = [intervals[0]]
for current in intervals[1:]:
last_merged = merged[-1]
# Check if intervals overlap
if current[0] <= last_merged[1]:
# Merge overlapping intervals
last_merged[1] = max(last_merged[1], current[1])
else:
# No overlap, add as new interval
merged.append(current)
return merged
# Time: O(n log n), Space: O(1) excluding output
# Manager discussion: Resource consolidation and optimization
|
Problem 2: Meeting Rooms II (Medium)
| Python |
|---|
| def min_meeting_rooms(intervals):
"""
Amazon: Optimize conference room allocation
Manager insight: Resource capacity planning
"""
if not intervals:
return 0
import heapq
# Sort meetings by start time
intervals.sort(key=lambda x: x[0])
# Min heap to track meeting end times
heap = []
for meeting in intervals:
start, end = meeting[0], meeting[1]
# If there's a room that's free (earliest end time <= current start)
if heap and heap[0] <= start:
heapq.heappop(heap)
# Add current meeting's end time
heapq.heappush(heap, end)
# Number of rooms needed is heap size
return len(heap)
# Time: O(n log n), Space: O(n)
# Manager discussion: Resource capacity planning and allocation
|
Manager-Level Discussion Points:
- Resource scheduling and capacity planning
- Calendar optimization and conflict resolution
- System maintenance windows and coordination
- Cost optimization through resource sharing
Pattern 10: Topological Sort
When to Recognize This Pattern:
- Dependency resolution problems
- Prerequisites and ordering
- Build systems and task scheduling
- Course scheduling and planning
Template Code:
| Python |
|---|
| def topological_sort_dfs(graph):
"""
DFS-based topological sort
L6/L7 focus: Dependency management and rollout planning
"""
visited = set()
rec_stack = set()
result = []
def dfs(node):
if node in rec_stack:
return False # Cycle detected
if node in visited:
return True
visited.add(node)
rec_stack.add(node)
# Visit all dependencies
for neighbor in graph.get(node, []):
if not dfs(neighbor):
return False
rec_stack.remove(node)
result.append(node)
return True
# Process all nodes
for node in graph:
if node not in visited:
if not dfs(node):
return [] # Cycle detected
return result[::-1] # Reverse for correct order
def topological_sort_kahn(graph, in_degree):
"""
Kahn's algorithm (BFS-based)
L6/L7 focus: Parallel execution planning
"""
from collections import deque
# Find nodes with no incoming edges
queue = deque([node for node in in_degree if in_degree[node] == 0])
result = []
while queue:
node = queue.popleft()
result.append(node)
# Remove edges from this node
for neighbor in graph.get(node, []):
in_degree[neighbor] -= 1
if in_degree[neighbor] == 0:
queue.append(neighbor)
# Check for cycles
if len(result) != len(in_degree):
return [] # Cycle detected
return result
|
Amazon Interview Problems:
Problem 1: Course Schedule (Medium)
| Python |
|---|
| def can_finish(num_courses, prerequisites):
"""
Amazon: Validate training program dependencies
Manager insight: Dependency validation and cycle detection
"""
from collections import defaultdict, deque
# Build graph and in-degree count
graph = defaultdict(list)
in_degree = [0] * num_courses
for course, prereq in prerequisites:
graph[prereq].append(course)
in_degree[course] += 1
# Find courses with no prerequisites
queue = deque([i for i in range(num_courses) if in_degree[i] == 0])
completed = 0
while queue:
course = queue.popleft()
completed += 1
# "Complete" prerequisite, update dependent courses
for next_course in graph[course]:
in_degree[next_course] -= 1
if in_degree[next_course] == 0:
queue.append(next_course)
return completed == num_courses
# Time: O(V + E), Space: O(V + E)
# Manager discussion: Dependency validation and planning
|
Problem 2: Alien Dictionary (Hard)
| Python |
|---|
| def alien_order(words):
"""
Amazon: Determine system component ordering from partial information
Manager insight: Dependency inference and system ordering
"""
from collections import defaultdict, deque
# Build character set
chars = set()
for word in words:
chars.update(word)
# Build graph from word comparisons
graph = defaultdict(set)
in_degree = {c: 0 for c in chars}
# Compare adjacent words
for i in range(len(words) - 1):
word1, word2 = words[i], words[i + 1]
min_len = min(len(word1), len(word2))
# Check for invalid ordering (longer word is prefix of shorter)
if len(word1) > len(word2) and word1[:min_len] == word2:
return ""
# Find first different character
for j in range(min_len):
if word1[j] != word2[j]:
if word2[j] not in graph[word1[j]]:
graph[word1[j]].add(word2[j])
in_degree[word2[j]] += 1
break
# Topological sort using Kahn's algorithm
queue = deque([c for c in chars if in_degree[c] == 0])
result = []
while queue:
char = queue.popleft()
result.append(char)
for next_char in graph[char]:
in_degree[next_char] -= 1
if in_degree[next_char] == 0:
queue.append(next_char)
# Check if all characters are processed (no cycles)
return ''.join(result) if len(result) == len(chars) else ""
# Time: O(C) where C is total length of all words, Space: O(1) for alphabet
# Manager discussion: Dependency inference from partial information
|
Manager-Level Discussion Points:
- System deployment and rollout planning
- Dependency management and resolution
- Build system optimization
- Team coordination and task scheduling
3. Pattern Recognition Framework
The Manager's Pattern Decision Tree
| Text Only |
|---|
| 1. PROBLEM ANALYSIS (30 seconds)
├── Array/String with two elements → Two Pointers
├── Subarray/substring optimization → Sliding Window
├── Linked list with cycle/middle → Fast & Slow Pointers
├── Hierarchical data → Tree/Graph Traversal
├── Sorted array search → Binary Search
├── Optimization with choices → Dynamic Programming
├── Generate all solutions → Backtracking
├── Top-k or priority → Heap/Priority Queue
├── Time ranges/scheduling → Intervals
└── Dependencies/ordering → Topological Sort
2. CONSTRAINT ANALYSIS (1 minute)
├── Time: O(1) space required → Two Pointers/Fast & Slow
├── Time: Real-time processing → Sliding Window/Heap
├── Time: Sorted input → Binary Search
├── Space: Overlapping subproblems → Dynamic Programming
└── Space: Generate all possibilities → Backtracking
3. PATTERN CONFIRMATION (30 seconds)
├── Keywords: "pair", "two elements" → Two Pointers
├── Keywords: "subarray", "window" → Sliding Window
├── Keywords: "cycle", "middle" → Fast & Slow Pointers
├── Keywords: "level", "layer" → BFS/DFS
├── Keywords: "maximum", "minimum" → DP/Binary Search
├── Keywords: "all possible", "generate" → Backtracking
├── Keywords: "k largest", "priority" → Heap
├── Keywords: "intervals", "meetings" → Intervals
└── Keywords: "order", "dependencies" → Topological Sort
|
Pattern Selection Confidence Matrix
| Pattern |
Recognition Speed |
Implementation Complexity |
Amazon Frequency |
| Two Pointers |
High |
Low |
High |
| Sliding Window |
High |
Medium |
High |
| Fast & Slow Pointers |
Medium |
Low |
Medium |
| Tree/Graph Traversal |
High |
Medium |
High |
| Binary Search |
High |
Medium |
High |
| Dynamic Programming |
Medium |
High |
High |
| Backtracking |
Medium |
High |
Medium |
| Heap/Priority Queue |
Medium |
Medium |
Medium |
| Intervals |
High |
Low |
Medium |
| Topological Sort |
Low |
Medium |
Low |
4. Manager-Specific Coding Strategies
Communicating While Coding
The L6/L7 Communication Framework:
-
Pattern Declaration (30 seconds)
| Text Only |
|---|
| "This looks like a [PATTERN] problem because [REASON].
I'm going to use [APPROACH] which will give us [COMPLEXITY]."
|
-
Structure Explanation (1 minute)
| Text Only |
|---|
| "My approach will be:
1. [HIGH-LEVEL STEP 1]
2. [HIGH-LEVEL STEP 2]
3. [HIGH-LEVEL STEP 3]
This maps to our [REAL-WORLD ANALOGY]."
|
-
Implementation Narration (During coding)
| Text Only |
|---|
| "Now I'm implementing [SPECIFIC PART] which handles [PURPOSE].
This edge case matters because [REASON]."
|
-
Optimization Discussion (End)
| Text Only |
|---|
| "Alternative approaches include [OPTION 1] and [OPTION 2].
I chose this because [TRADE-OFF REASONING].
In production, we'd also consider [OPERATIONAL CONCERNS]."
|
Balancing Correctness vs Optimization
The Manager's Priority Framework:
- Correctness First (60% of time)
- Get working solution with clear logic
- Handle basic edge cases
-
Demonstrate systematic thinking
-
Communication Second (25% of time)
- Explain approach clearly
- Connect to real-world problems
-
Show strategic understanding
-
Optimization Third (15% of time)
- Improve time/space complexity if time permits
- Discuss alternative approaches
- Consider production implications
When to Ask for Hints
Strategic Hint Timing for L6/L7:
- After 3 minutes: If you can't identify the pattern
- After 8 minutes: If you can't design the approach
- After 20 minutes: If implementation is significantly stuck
- Never: Ask for hints on basic syntax or simple edge cases
How to Ask for Hints (maintains technical credibility):
| Text Only |
|---|
| "I'm deciding between approach A and approach B.
Approach A would use [PATTERN] with [COMPLEXITY],
while approach B would use [PATTERN] with [COMPLEXITY].
Could you confirm if I'm on the right track with approach A?"
|
Architectural Implications Discussion
Connecting Patterns to System Design:
- Two Pointers → Load balancing and resource optimization
- Sliding Window → Real-time monitoring and rate limiting
- Fast & Slow Pointers → Health checks and cycle detection
- Tree/Graph Traversal → Dependency resolution and rollout planning
- Binary Search → Configuration optimization and threshold tuning
- Dynamic Programming → Cost optimization and strategic planning
- Backtracking → Configuration space exploration
- Heap/Priority Queue → Resource scheduling and priority management
- Intervals → Capacity planning and resource allocation
- Topological Sort → Build systems and deployment orchestration
5. Practice Problems Mapped to Patterns
Two Pointers Practice Progression
Beginner (15 minutes each):
1. Two Sum II - Input array is sorted
2. Valid Palindrome
3. Remove Duplicates from Sorted Array
4. Move Zeroes
5. Reverse String
Intermediate (20 minutes each):
1. Container With Most Water
2. 3Sum
3. Sort Colors
4. Trapping Rain Water
5. Longest Palindromic Substring
Advanced (30 minutes each):
1. 3Sum Closest
2. 4Sum
3. Minimum Window Substring
4. Palindrome Pairs
5. Shortest Unsorted Continuous Subarray
Sliding Window Practice Progression
Beginner (15 minutes each):
1. Maximum Average Subarray I
2. Longest Substring Without Repeating Characters
3. Minimum Size Subarray Sum
4. Find All Anagrams in a String
5. Permutation in String
Intermediate (20 minutes each):
1. Minimum Window Substring
2. Longest Repeating Character Replacement
3. Max Consecutive Ones III
4. Fruit Into Baskets
5. Subarrays with K Different Integers
Advanced (30 minutes each):
1. Sliding Window Maximum
2. Minimum Number of K Consecutive Bit Flips
3. Get Equal Substrings Within Budget
4. Number of Substrings Containing All Three Characters
5. Longest Substring with At Most K Distinct Characters
Fast & Slow Pointers Practice Progression
Beginner (15 minutes each):
1. Linked List Cycle
2. Find the Middle of the Linked List
3. Remove Nth Node From End of List
4. Happy Number
5. Palindrome Linked List
Intermediate (20 minutes each):
1. Linked List Cycle II
2. Find the Duplicate Number
3. Circular Array Loop
4. Rotate List
5. Reorder List
Advanced (30 minutes each):
1. Intersection of Two Linked Lists
2. Remove Duplicates from Sorted List II
3. Sort List
4. Copy List with Random Pointer
5. Flatten a Multilevel Doubly Linked List
Tree/Graph Traversal Practice Progression
Beginner (15 minutes each):
1. Binary Tree Inorder Traversal
2. Binary Tree Level Order Traversal
3. Maximum Depth of Binary Tree
4. Same Tree
5. Invert Binary Tree
Intermediate (20 minutes each):
1. Validate Binary Search Tree
2. Path Sum
3. Lowest Common Ancestor of a Binary Tree
4. Binary Tree Right Side View
5. Count Complete Tree Nodes
Advanced (30 minutes each):
1. Serialize and Deserialize Binary Tree
2. Binary Tree Maximum Path Sum
3. Recover Binary Search Tree
4. House Robber III
5. Vertical Order Traversal of a Binary Tree
Binary Search Practice Progression
Beginner (15 minutes each):
1. Binary Search
2. First Bad Version
3. Search Insert Position
4. Peak Index in a Mountain Array
5. Valid Perfect Square
Intermediate (20 minutes each):
1. Search in Rotated Sorted Array
2. Find Minimum in Rotated Sorted Array
3. Search a 2D Matrix
4. Find Peak Element
5. Search for a Range
Advanced (30 minutes each):
1. Median of Two Sorted Arrays
2. Koko Eating Bananas
3. Capacity To Ship Packages Within D Days
4. Split Array Largest Sum
5. Minimize Max Distance to Gas Station
Quick Reference Guide
Pattern Recognition Cheat Sheet
| Problem Keywords |
Likely Pattern |
Time Complexity |
| "two sum", "pair", "palindrome" |
Two Pointers |
O(n) |
| "subarray", "window", "consecutive" |
Sliding Window |
O(n) |
| "cycle", "middle", "duplicate" |
Fast & Slow Pointers |
O(n) |
| "tree", "graph", "level", "path" |
BFS/DFS |
O(V + E) |
| "sorted", "rotated", "peak" |
Binary Search |
O(log n) |
| "maximum", "minimum", "count ways" |
Dynamic Programming |
O(n²) |
| "all possible", "generate", "permutation" |
Backtracking |
O(2ⁿ) |
| "k largest", "top k", "priority" |
Heap |
O(n log k) |
| "intervals", "meetings", "merge" |
Intervals |
O(n log n) |
| "dependencies", "order", "schedule" |
Topological Sort |
O(V + E) |
Complexity Quick Reference
| Pattern |
Best Time |
Average Time |
Space |
Notes |
| Two Pointers |
O(n) |
O(n) |
O(1) |
Linear scan |
| Sliding Window |
O(n) |
O(n) |
O(k) |
Window size |
| Fast & Slow Pointers |
O(n) |
O(n) |
O(1) |
Cycle detection |
| Tree Traversal |
O(n) |
O(n) |
O(h) |
Height dependent |
| Binary Search |
O(log n) |
O(log n) |
O(1) |
Sorted input |
| Dynamic Programming |
O(n) |
O(n²) |
O(n) |
Problem dependent |
| Backtracking |
O(k^n) |
O(2^n) |
O(n) |
Exponential |
| Heap Operations |
O(log n) |
O(n log k) |
O(k) |
Priority queue |
| Intervals |
O(n log n) |
O(n log n) |
O(1) |
Sort required |
| Topological Sort |
O(V + E) |
O(V + E) |
O(V) |
Graph algorithms |
Manager Interview Success Framework
Pre-Interview (5 minutes):
- Review pattern keywords and recognition cues
- Practice explaining approaches at high level
- Prepare real-world engineering analogies
During Interview:
1. Listen actively (30 seconds) - Identify pattern signals
2. Clarify requirements (1 minute) - Confirm understanding
3. Declare approach (1 minute) - State pattern and reasoning
4. Implement systematically (25 minutes) - Code with clear structure
5. Test and optimize (10 minutes) - Validate and discuss alternatives
6. Connect to systems (3 minutes) - Relate to production engineering
Post-Interview:
- Reflect on pattern recognition speed
- Note communication clarity
- Identify areas for improvement
Conclusion
Mastering these 10 coding patterns provides L6/L7 engineering managers with the foundation needed for Amazon technical interviews. Success comes not from memorizing solutions, but from developing pattern recognition skills, clear communication, and the ability to connect algorithmic thinking to real-world engineering challenges.
Key Takeaways for L6/L7 Success:
- Focus on Recognition Speed: Practice identifying patterns within 2-3 minutes
- Emphasize Clear Communication: Explain your thinking throughout the process
- Connect to Real Systems: Relate every pattern to production engineering problems
- Balance Correctness and Optimization: Get working solutions first, optimize second
- Demonstrate Leadership: Show how you'd guide teams and make architectural decisions
Next Steps:
1. Practice one pattern per day using the progression outlined
2. Time yourself on pattern recognition (aim for under 3 minutes)
3. Record yourself explaining solutions to improve communication
4. Connect each pattern to your current engineering responsibilities
5. Schedule mock interviews focusing on pattern-based problems
Remember: Your goal as an L6/L7 manager isn't to be the fastest coder—it's to demonstrate the technical judgment, systematic thinking, and communication skills needed to lead engineering teams effectively.
This guide represents the culmination of pattern-based preparation specifically designed for L6/L7 engineering managers. Focus on understanding over memorization, communication over speed, and strategic thinking over algorithmic optimization.