Learn and practice the Dynamic Programming pattern to solve coding interview problems.

Speedrun the LinkedIn Coding Interview: Top Problems in Python

This module covers the most important problem-solving techniques in the optimization domain: Dynamic Programming. In computer science, we often come across problems that have a well-defined structure, where the same subproblem is encountered and solved multiple times. Dynamic Programming allows us to compute once and reuse the solutions to recurring subproblems.

Optimization Techniques

# Statement

Given an array of distinct integers, `nums`, and an integer, `target`, return a list of all unique combinations of `nums` where the chosen numbers sum up to the `target`. The combinations may be returned in any order.

An integer from `nums` may be chosen an unlimited number of times. Two combinations are unique if the 
frequency of at least one of the chosen integers is different.

**Constraints:** 
- $1 \leq$ `nums.length` $\leq 30$
- $2 \leq$ `nums[i]` $\leq 40$
- $1 \leq$ `target` $\leq 40$
- All integers of `nums` are unique.

# 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:

Given the following array and target value, what will be the answer?

nums = [3, 6, 7]

target = 10


Given the following array and target value, what will be the answer?
nums = [3, 6, 7]
target = 10

Given the following array and target value, what will be the answer?

nums = [2, 3, 5]

target = 5

Given the following array and target value, what will be the answer?
nums = [2, 3, 5]
target = 5

Given the following array and target value, what will be the answer?

nums = [5, 10, 25]

target = 15


Given the following array and target value, what will be the answer?
nums = [5, 10, 25]
target = 15

result = [[3, 3, 3, 3], [4, 4, 4], [9, 3]]

Given the following array and target value, what will be the answer?

nums = [3, 4, 9]

target = 12


Given the following array and target value, what will be the answer?
nums = [3, 4, 9]
target = 12

Combination Sum

Combination Sum

# 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: `combination_sum`\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 `combination_sum` 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 `combination_sum`.\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) `combination_sum`. \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) `combination_sum`. \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.

TwoDArray

import sys
import json

sys.path.append("../ds_v1")
from data_structure import DataStructure

# throw parsing errors for incorrect test case format
def parsingError(element_string, error_message):
    sys.stderr.write(f"Parsing Error: {element_string} {error_message}")
    exit()


# className: MyCustomDS
class TwoDArray(DataStructure):
    def __init__(self):
        # constructor
        pass

    def __str__(self):
        # override print() for your data structure
        pass

    # return value will be passed to user program
    def construct(self, value: str, type_of_arr: int) -> any:
        # parse test case in json string 'value' to your desired data structure
        return json.loads(value)

    # input param contains return value of user program
    def traverse(self, input: any, type_of_arr: int) -> str:
        # convert your data structure 'input' to a json string representing a test case output
        return json.dumps(input)


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 find_combination_sum(nums, target):
 # Initialize dp
 dp = [[] for _ in range(target + 1)]
 dp[0].append([])

 # For each value from 1 to target
 for i in range(1, target + 1):
 # Iterate over nums
 for j in range(len(nums)):
 if nums[j] <= i:
 # Checking previous results from dp
 for prev in dp[i - nums[j]]:
 temp = prev + [nums[j]]
 temp.sort()
 # If the new combination is not already in dp
 if temp not in dp[i]:
 dp[i].append(temp)
 # Return the combinations
 return dp[target]


 # multiple outputs will be added at each index respectively for a single test_case
 expected = find_combination_sum(self.__inputs[0], self.__inputs[1])
 sorted_expected = sorted([sorted(sub_array) for sub_array in expected])

 actual = self.__actual_outputs[0]
 sorted_actual = sorted([sorted(sub_array) for sub_array in actual])

 expected_outputs = []

 if sorted_expected == sorted_actual:
 expected_outputs.append(expected)
 self.__edu_result.store_result(expected_outputs, TestCaseResult.PASS)
 else:
 expected_outputs.append(expected)
 self.__edu_result.store_result(expected_outputs, TestCaseResult.FAIL)
 
 return self.__edu_result

def combination_sum(nums, target):
    
    # Replace this placeholder return statement with your code
    return []


combination_sum (3).yaml

testcases:
  - name: "testcase 1"
    inputs:
    - 1 : [2, 4, 7, 9, 11]
    - 2 : 8
    output:
    - 1 : [[3,45,5,6]]
  - name: "testcase 2"
    inputs:
    - 1: [2, 3, 9]
    - 2: 12
  - name: "testcase 3"
    inputs:
    - 1: [3, 4, 8, 11]
    - 2: 10
  - name: "testcase 4"
    inputs:
    - 1: [3]
    - 2: 3
  - name: "testcase 5"
    inputs:
    - 1: [8]
    - 2: 10

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
 """
 # inputs can be accessed using self.__inputs starting from 0 to len(self.__inputs) - 1
 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)






 nums=self.__inputs[0]
 target=self.__inputs[1]

 
 if not is_valid_1d_array(nums):
 self.store_result("Invalid input for 'nums'", ValidationFunction.FAIL)


 
 elif not (1 <= len(nums) <= 30):
 self.store_result ("Length of 'nums' should be between 1 and 30", ValidationFunction.FAIL)

 

 elif not (1 <= target <= 40):
 self.store_result ("'target' should be between 1 and 40", ValidationFunction.FAIL)

 

 elif not all( (2 <= x <= 40) for x in nums):
 self.store_result ("Integers in 'nums' should be between 2 and 40", ValidationFunction.FAIL)


 elif not sorted(nums)==sorted(list(set(nums))):
 self.store_result ("Integers in 'nums' should be unique", ValidationFunction.FAIL)


 else:
 self.store_result("", ValidationFunction.PASS)

Try to solve the Combination Sum problem.

Dynamic Programming

Conclusion

Combination Sum

Statement

Examples

Understand the problem

Figure it out!

Try it yourself