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 Go

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.

Given `nums = [-3, -3, 6, 1, 2, -3]`, how many unique triplets sum to zero?

Given <code>nums = [-3, -3, 6, 1, 2, -3]</code>, how many unique triplets sum to zero?

[[0, 0, 0], [0, 0, 0], [0, 0, 0], [0, 0, 0]]

Given `nums = [0, 0, 0, 0]`, what is the output?

Given <code>nums = [0, 0, 0, 0]</code>, what is the output?

Given `nums = [1, -1, 2, -2, 3, -3, 0]`, how many unique triplets sum to zero?

Given <code>nums = [1, -1, 2, -2, 3, -3, 0]</code>, how many unique triplets sum to zero?

[[-100000, 50000, 50000], [-100000, 0, 50000]]

Given `nums = [-100000, 50000, 50000, 0]`, what is the output?

Given <code>nums = [-100000, 50000, 50000, 0]</code>, what is the output?

Given `nums = [4, -2, -2, -5, 5, 0, 1, -1, 3]`, which of the following is a valid triplet in the output?

Given <code>nums = [4, -2, -2, -5, 5, 0, 1, -1, 3]</code>, which of the following is a valid triplet in the output?

3Sum

3Sum

Can we reduce the problem to something simpler?

We’re looking for three numbers—say `x`, `y`, and `z`—such that `x + y + z = 0`. What if we fix one number, say `x`, and then search for two numbers that sum to `-x`? That turns the problem into a familiar Two Sum!

In the **Two Sum** problem, once you fix one number (say `x`), you must look for another number (`y`) such that `y = target - x`. Typically, you'd have to scan the entire array to find `y`. Can we sort or transform the array to allow us to search more efficiently?

Duplicates can lead to repeated triplets!

After sorting, how can we skip over duplicate values to ensure each triplet is unique? Maybe we should skip the same number if it reappears after a match.

vector<vector<int>> ThreeSum(vector<int>& nums)
{
 // Replace this placeholder return statement with your code
 return {{}};
}

package main

func threeSum(nums []int) [][]int {
    
    // Replace this placeholder return statement with your code
    return [][]int{}
}

# 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: `threeSum`\n- Candidate's submitted solution code: USER_CODE\n- Error: ERROR_DESCRIPTION\n- Failed test case: FAILED_TEST_CASE\n- Coding language: `Go`\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 `threeSum` 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 `threeSum`.\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) `threeSum`. \n- While calculating time complexity, include the time complexity of built-in Go 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) `threeSum`. \n- While calculating space complexity, include the space complexity of built-in Go 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.

TwoDArray

package main

import (
    "fmt"
    "os"
    "encoding/json"
)

type TwoDArray struct {
    // class attributes
    parsedData [][]int
}

func (ds *TwoDArray) generateError(data string) {
    fmt.Fprintln(os.Stderr, "Parsing Error: ", data, " in MyCustomDS is not parsable")
    os.Exit(-1)
}

func (ds *TwoDArray) String() string {
    // override print() for your data structure
    return ""
}

// return value will be passed to user program
func (ds *TwoDArray) Construct(value string, type_of_arr int) any {
    // parse test case in json string 'value' to your desired data structure
    json.Unmarshal([]byte(value), &ds.parsedData)
    return *ds
}

// input param contains return value of user program
func (ds *TwoDArray) Traverse(input any, type_of_arr int) string {
    // convert your data structure 'input' to a json string representing a test case output
    cast, ok := input.(TwoDArray)
    if !ok {
    }
    st, _ := json.Marshal(cast.parsedData)
    return string(st)
}

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
 """
 def three_sum(nums):
 res = []
 nums.sort()
 for i in range(len(nums)):
 if nums[i] > 0:
 break
 if i == 0 or nums[i - 1] != nums[i]:
 twoSumII(nums, i, res)
 return res
 
 def twoSumII(nums, i, res):
 lo, hi = i + 1, len(nums) - 1
 while lo < hi:
 sum = nums[i] + nums[lo] + nums[hi]
 if sum < 0:
 lo += 1
 elif sum > 0:
 hi -= 1
 else:
 res.append([nums[i], nums[lo], nums[hi]])
 lo += 1
 hi -= 1
 while lo < hi and nums[lo] == nums[lo - 1]:
 lo += 1
 
 def sort_2d_array(arr):
 if arr is None:
 return [] # Return an empty list instead of raising an error
 
 # Sort each inner list
 sorted_inner_lists = [sorted(inner) for inner in arr]
 
 # Sort the 2D list based on the elements of each inner list
 return sorted(sorted_inner_lists, key=lambda x: tuple(x + [float('inf')] * (3 - len(x))))

 

 expected_outputs = [] 
 expected = three_sum(self.__inputs[0])
 expected_outputs.append(expected)

 actual_output = self.__actual_outputs[0]
 if sort_2d_array(actual_output) == sort_2d_array(expected):
 self.__edu_result.store_result(expected_outputs, TestCaseResult.PASS)
 else:
 self.__edu_result.store_result(expected_outputs, TestCaseResult.FAIL)
 return self.__edu_result

package main

func mainFun(nums [] int) TwoDArray {
    var ds TwoDArray
    ds.parsedData = threeSum(nums)
    return ds
}

3sum_cip_gen_testcases.yaml

testcases:
  - name: "Test Case 1 (EC1 - mixed values, multiple triplets)"
    inputs:
      - 1: [-3, -1, 0, 1, 2, 3, -2, 4]
    output:
      - 1: [[-3, -1, 4], [-3, 0, 3], [-3, 1, 2], [-2, -1, 3], [-2, 0, 2], [-1, 0, 1]]

  - name: "Test Case 2 (EC6 - minimum size, sums to zero)"
    inputs:
      - 1: [1, -2, 1]
    output:
      - 1: [[-2, 1, 1]]

  - name: "Test Case 3 (EC4 - all positive, no triplet)"
    inputs:
      - 1: [1, 2, 3, 4, 5]
    output:
      - 1: []

  - name: "Test Case 4 (EC8 - zeros and other values)"
    inputs:
      - 1: [0, 0, 0, -1, 1, 2, -2]
    output:
      - 1: [[-2, 0, 2], [-1, 0, 1], [0, 0, 0]]

  - name: "Test Case 5 (EC3 - heavy duplicates)"
    inputs:
      - 1: [-1, -1, -1, 0, 1, 1, 1, 2, 2]
    output:
      - 1: [[-1, -1, 2], [-1, 0, 1]]

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_integer_array(arr):
 return all(isinstance(item, int) for item in arr)
 
 def is_within_range(arr, min_value=-100000, max_value=100000):
 return all(min_value <= item <= max_value for item in arr)
 
 arrr = self.__inputs[0]
 if not is_integer_array(arrr) :
 self.store_result ("input array should contain integer values", ValidationFunction.FAIL)
 elif not 3 <= len(arrr) <= 3000:
 self.store_result("input length should be within range [3, 500]", ValidationFunction.FAIL)
 elif not is_within_range(arrr):
 self.store_result("Each element of the input array should be within range [-1000, 1000]", ValidationFunction.FAIL)
 else:
 self.store_result("", ValidationFunction.PASS)

Sum of Three Values

Statement

Examples

Understand the problem

Figure it out!

Try it yourself