Learn and practice the Two Pointers, Fast and Slow Pointers, and Modified Binary Search patterns to solve coding interview problems.

Speedrun the Apple Coding Interview: Top Problems in Python

This module groups together three of the most common patterns that may be used to solve problems where the input data is linear: Two Pointers, Fast and Slow Pointers, and Modified Binary Search. Both the Two Pointers and the Modified Binary Search patterns derive their power from their ability to efficiently reduce the size of the search space, that is, both exemplify the divide-and-conquer approach to problem-solving. The Fast and Slow Pointers pattern may be considered a variant of the Two Pointers pattern, where the two pointers move at different speeds in order to traverse the input list in a way that solves the given problem. After completing this module, we will have learned how to use this set of related patterns to solve a diverse range of problems.

Two Pointers & Co.

# Statement

Given an array of positive numbers, `nums`, such that the values lie in the range $[1, n]$, inclusive, and that there are $n+1$ numbers in the array, find and return the duplicate number present in `nums`. There is only one repeated number in `nums`, but it may appear more than once in the array.


> **Note:** You cannot modify the given array `nums`. You have to solve the problem using only constant extra space.

**Constraints:**

* $1 \leq n \leq 10^3$
* `nums.length` $= n + 1$
* $1 \leq$ `nums[i]` $\leq n$
* All the integers in `nums` are unique, except for one integer that will appear more than once.

# Examples

# Understand the problem

Let’s take a moment to make sure you’ve correctly understood the problem. The quiz below helps you check if you’re solving the correct problem:


What is the output if the following list of integers is given as input?

[1, 5, 4, 3, 2, 4, 6]

What is the output if the following list of integers is given as input?
[1, 5, 4, 3, 2, 4, 6]

What is the output if the following list of integers is given as input?

[5, 6, 1, 3, 7, 3, 2, 4, 8]

What is the output if the following list of integers is given as input?
[5, 6, 1, 3, 7, 3, 2, 4, 8]

What is the output if the following list of integers is given as input?

[2, 10, 6, 7, 11, 7, 9, 4, 3, 8, 5, 1]

What is the output if the following list of integers is given as input?
[2, 10, 6, 7, 11, 7, 9, 4, 3, 8, 5, 1]

What is the output if the following list of integers is given as input?

[9, 6, 12, 7, 15, 8, 3, 13, 2, 10, 4, 14, 1, 11, 9, 5]

What is the output if the following list of integers is given as input?
[9, 6, 12, 7, 15, 8, 3, 13, 2, 10, 4, 14, 1, 11, 9, 5]

Find The Duplicate Number

Find The Duplicate Number

# Figure it out!

We have a game for you to play. Rearrange the logical building blocks to develop a clearer understanding of how to solve this problem.

Think of the array not just as numbers, but as a trail, where each value tells you which spot to visit next. What happens if you keep following the trail forever?

Imagine two travelers walking along the same trail. One takes one step at a time, the other takes two steps. What do you expect will happen if the trail eventually loops back?

Given the two travelers meet somewhere on the trail, how could you find the exact spot where the loop begins?

# Quick Fix\nYou are Edward, a Senior Software Engineer who specializes in coding interview patterns, data structures and algorithms, and is great at debugging issues in code.\n\n- Edward, please keep in mind that you do not have to print the data of the placeholders. Also, do not mention anything about yourself.\n\nEdward, you are given the following data in the placeholders:\n- Function name: `find_duplicate`\n- Candidate's submitted solution code: USER_CODE\n- Error: ERROR_DESCRIPTION\n- Failed test case: FAILED_TEST_CASE\n- Coding language: `Python`\n\n- Edward, your task is to understand the type of error that is occurring in the coding language provided.\n- Once you've understood the error as per the error’s description, and why the test case failed, you will suggest how the candidate can improve their solution code to fix the error.\n- Edward, you will not give the corrected code, just a hint on what the error tells, and how to fix it.\n- Edward, please limit your response strictly to 100 words. No more words than the limit.

# Review Code\nEdward, your current task is to review the `find_duplicate` function(s) and the other function(s) invoked in it/them.\n\n-Take your time and review the candidate's solution code.\n- Do not review any extra/helper files or functions not invoked in the solution function `find_duplicate`.\n- Do not review the code of data structure objects instantiated like a binary tree, linked list, trie, union find, etc., in the solution functions. Just review the solution/algorithm function of the problem. \n- Also, if the solution code doesn’t use the coding pattern stated above, then please encourage the candidate to reattempt the problem using that pattern corectly.

# Review time complexity\n- Please provide a brief time complexity analysis of the function(s) `find_duplicate`. \n- While calculating time complexity, include the time complexity of built-in Python functions invoked by the code. \n- The answer should be to the point in approximately 60 words.

# Review space complexity\n- Please provide a brief space complexity analysis of the function(s) `find_duplicate`. \n- While calculating space complexity, include the space complexity of built-in Python functions invoked by the code. \n- Do not include the space used for the input parameters and the space used for just returning an output (not used as a scratch space). \n- The answer should be to the point in approximately 60 words.

def evaluate_results(self) -> object:
        """
        self.__inputs is the list of inputs that are passed as input to function
        self.__actual_output is a list of outputs that is produced by the learner's code
        return : self.__edu__result object
        """
        # multiple outputs will be added at each index respectively for a single test_case
        expected_outputs = [] 
        # store the 1st expected output that should be displayed to the user 
        expected_outputs.append(find_duplicate(self.__inputs[0]))

        if json.dumps(find_duplicate(self.__inputs[0])) == json.dumps(self.__actual_outputs[0]):
            self.__edu_result.store_result(expected_outputs, TestCaseResult.PASS)
        else:
            self.__edu_result.store_result(expected_outputs, TestCaseResult.FAIL)

        return self.__edu_result
        
def find_duplicate(nums):
    fast = slow = nums[0]
  
    while True:
        slow = nums[slow]
        fast = nums[nums[fast]]
        if slow == fast:
            break
    
    slow = nums[0]
   
    while slow != fast:
        slow = nums[slow]
        fast = nums[fast]
    
    return fast


def find_duplicate(nums):

    # Replace this placeholder return statement with your code
    
    return 0


PrivateTestCases.yaml

testcases:
  - name: "testcase 1"
    inputs:
    - 1: [3, 4, 4, 4, 2]
    output:
    - 1: 4
  - name: "testcase 2"
    inputs:
    - 1: [1,1]
    output:
    - 1 : 1
  - name: "testcase 3"
    inputs:
    - 1: [1, 3, 4, 2, 2]
    output:
    - 1 : 2
  - name: "testcase 4"
    inputs:
    - 1: [1, 3, 6, 2, 7, 3, 5, 4]
    output:
    - 1 : 3
  - name: "testcase 5"
    inputs:
    - 1: [1, 2, 2]
    output:
    - 1 : 2

def sum(input_1, input_2):
    return input_1+input_2

def validate_inputs(self) -> None:
 """
 self.__inputs is the list of inputs that are passed as input to function
 store the result using the self.store_result(error_msg, status)
 return : void
 """
 def is_valid_1d_array(arr):
 if not isinstance(arr, list):
 return False # Not a valid 1D array if it's not a list
 
 return all(isinstance(elem, int) and not isinstance(elem, bool) for elem in arr)
 def has_only_one_repeated_element(arr):
 # Check if the length of the array is greater than 1
 if len(arr) < 2:
 return False

 # Use a set to keep track of unique elements
 unique_elements = set()

 # Use a variable to track the repeated element
 repeated_element = None

 # Iterate through the array
 for element in arr:
 # Check if the element is already in the set
 if element in unique_elements:
 # Check if this is the first repeated element
 if repeated_element is None or repeated_element == element:
 repeated_element = element
 else:
 # If there is more than one repeated element, return False
 return False
 else:
 # Add the element to the set if it's not already present
 unique_elements.add(element)

 # Check if there is exactly one repeated element
 return repeated_element is not None


 # Check if there is exactly one repeated element
 nums = self.__inputs[0]
 # inputs can be accessed using self.__inputs starting from 0 to len(self.__inputs) - 1
 if not is_valid_1d_array(nums):
 self.store_result(("Invalid test case."), ValidationFunction.FAIL)
 elif len(nums) < 1 or len(nums) > 1001:
 self.store_result("Input length should be between 1 and 10^3 + 1", ValidationFunction.FAIL)
 elif any(value < 1 or value > 10**3 for value in nums):
 self.store_result("All elements in the input set should be between 1 and n", ValidationFunction.FAIL)
 elif any(value > len(nums) for value in nums):
 self.store_result(f"Values in the input set should not be greater than n", ValidationFunction.FAIL)
 elif len(nums) != max(nums) + 1:
 self.store_result(f"Array should be in the range [1, n]", ValidationFunction.FAIL)
 elif len(nums) ==1:
 self.store_result(f"Length of array must be n+1", ValidationFunction.FAIL)
 elif not has_only_one_repeated_element(nums):
 self.store_result(f"Only one integer should be repeated in nums.", ValidationFunction.FAIL) 
 else:
 self.store_result("", ValidationFunction.PASS)

Try to solve the Find the Duplicate Number problem.

Two Pointers

Fast and Slow Pointers

Modified Binary Search

Conclusion

Find The Duplicate Number

Statement

Examples

Understand the problem

Figure it out!

Try it yourself