Day 25: Review Common Patterns in Problems.

Here are detailed notes for Day 25: Review Common Patterns in Problems. This day focuses on identifying and revisiting key problem-solving patterns that frequently appear in coding interviews, which will help you recognize and apply them during actual interview scenarios.

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1. Importance of Recognizing Patterns

Recognizing common patterns in coding problems can simplify the problem-solving process and lead to more efficient solutions. Understanding these patterns allows you to:

• Quickly identify the best approach to a problem.

• Reduce the time spent on new problems by applying known techniques.

• Improve your confidence and performance in interviews.

2. Common Patterns in Coding Problems

Here are several common patterns with brief explanations and examples:

2.1 Sliding Window

• Concept: This pattern involves creating a window that can either expand or contract to solve problems related to arrays or strings.

• Typical Problems:

  • Longest substring with at most k distinct characters.

  • Minimum size subarray sum.

• Example:

  def min_sub_array_len(target, nums):
      left, total, min_length = 0, 0, float('inf')
      for right in range(len(nums)):
          total += nums[right]
          while total >= target:
              min_length = min(min_length, right - left + 1)
              total -= nums[left]
              left += 1
      return min_length if min_length != float('inf') else 0

2.2 Two Pointers

• Concept: Use two pointers to solve problems involving arrays or linked lists, typically to find pairs or subarrays.

• Typical Problems:

  • Valid palindrome.

  • 3Sum problem.

• Example:

  def three_sum(nums):
      nums.sort()
      result = []
      for i in range(len(nums) - 2):
          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:
                  left += 1
              elif current_sum > 0:
                  right -= 1
              else:
                  result.append([nums[i], nums[left], nums[right]])
                  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
      return result

2.3 Fast and Slow Pointers

• Concept: This technique uses two pointers moving at different speeds to detect cycles or find middle points in linked lists.

• Typical Problems:

  • Detecting a cycle in a linked list (Floyd’s Tortoise and Hare).

  • Finding the middle of a linked list.

• Example:

  def has_cycle(head):
      slow, fast = head, head
      while fast and fast.next:
          slow = slow.next
          fast = fast.next.next
          if slow == fast:
              return True
      return False

2.4 Backtracking

• Concept: This is a depth-first search technique used for solving problems that require exploring all potential solutions.

• Typical Problems:

  • N-Queens problem.

  • Permutations and combinations.

• Example:

  def permute(nums):
      result = []
      def backtrack(first=0):
          if first == len(nums):
              result.append(nums[:])
          for i in range(first, len(nums)):
              nums[first], nums[i] = nums[i], nums[first]  # swap
              backtrack(first + 1)
              nums[first], nums[i] = nums[i], nums[first]  # backtrack
      backtrack()
      return result

2.5 Dynamic Programming

• Concept: This approach involves breaking down problems into simpler subproblems and storing the results to avoid redundant computations.

• Typical Problems:

  • Fibonacci sequence.

  • Coin change problem.

• Example:

  def fib(n):
      if n <= 1:
          return n
      dp = [0] * (n + 1)
      dp[1] = 1
      for i in range(2, n + 1):
          dp[i] = dp[i - 1] + dp[i - 2]
      return dp[n]

2.6 Binary Search

• Concept: This technique is used for searching in a sorted array or finding optimal solutions.

• Typical Problems:

  • Search in rotated sorted array.

  • Find the square root of a number.

• Example:

  def binary_search(arr, target):
      left, right = 0, len(arr) - 1
      while left <= right:
          mid = left + (right - left) // 2
          if arr[mid] == target:
              return mid
          elif arr[mid] < target:
              left = mid + 1
          else:
              right = mid - 1
      return -1

3. Practice Exercises

• Review and practice problems that fit these patterns. Here are some recommended exercises:

  • Sliding Window: Maximum sum of a subarray of size k.

  • Two Pointers: Container with most water.

  • Backtracking: Subset sum problem.

  • Dynamic Programming: Longest common subsequence.

  • Binary Search: Find peak element.

4. Reflection on Patterns

• After practicing, reflect on how identifying these patterns helped you solve problems more efficiently.

• Document key takeaways and any variations in how the patterns were applied.

5. Conclusion

Understanding and practicing common problem-solving patterns is crucial for success in coding interviews, especially at Google. Recognizing these patterns during an interview can help you devise a solution more quickly and efficiently. Continue practicing problems across these patterns to build confidence and proficiency, which will ultimately lead to better performance in interviews.