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
A professional robber plans to rob some houses along a street. These houses are arranged in a circle, which means that the first and the last house are neighbors. The robber cannot rob adjacent houses because they have security alarms installed.  

Following the constraints mentioned above and given an integer array `money` representing the amount of money in each house, return the maximum amount the robber can steal without alerting the police.

**Constraints:**
* $1\leq$ `money.length` $\leq 10^3$
* $0\leq$ `money[i]` $\leq 10^3$

# 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 is given as input?

money = [2, 5, 3, 6]

What is the output if the following list is given as input?
money = [2, 5, 3, 6]

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

money = [2, 10, 14, 8, 1]

What is the output if the following list is given as input?
money = [2, 10, 14, 8, 1]

House Robber II

House Robber II

# 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.

# Try it yourself
Implement your solution in the following coding playground.

# 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: `house_robber`\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 `house_robber` 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 `house_robber`.\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) `house_robber`. \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) `house_robber`. \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
                """
        def house_robber(money):
            if len(money) == 0 or money is None:
                return 0

            if len(money) == 1:
                return money[0]

            return max(house_robber_helper(money[:-1]), house_robber_helper(money[1:]))


        def house_robber_helper(money):
            lookup_array = [0 for x in range(len(money) + 1)]
            lookup_array[0] = 0
            lookup_array[1] = money[0]
            for i in range(2, len(money)+1):
                lookup_array[i] = max(money[i-1]+lookup_array[i-2], lookup_array[i-1])

            return lookup_array[len(money)]


        # multiple outputs will be added at each index respectively for a single test_case
        expected_outputs = [] 
        expected = house_robber(self.__inputs[0])
        actual = self.__actual_outputs[0]
        expected_outputs.append(expected) 

        if expected == actual:
            self.__edu_result.store_result(expected_outputs, TestCaseResult.PASS)
        else:
            self.__edu_result.store_result(expected_outputs, TestCaseResult.FAIL)

        return self.__edu_result

def house_robber(money):

    # Replace this placeholder return statement with your code
    return -1

PrivateTestCases.yaml

testcases:
  - name: "testcase 1"
    inputs:
    - 1 : [2,3,2]
    output: 
    - 1 : 3
  - name: "testcase 2"
    inputs:
    - 1: [1,2,3,1]
    output:
    - 1 : 4
  - name: "testcase 3"
    inputs:
    - 1: [1, 5, 7, 3, 7 , 2, 3]
    output:
    - 1 : 17
  - name: "testcase 4"
    inputs:
    - 1: [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15]
    output:
    - 1 : 63
  - name: "testcase 5"
    inputs:
    - 1: [5, 5, 5, 5, 5]
    output:
    - 1: 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 the 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)

 # Inputs can be accessed using self.__inputs starting from 0 to len(self.__inputs) - 1
 if not is_valid_1d_array(self.__inputs[0]):
 self.store_result(("Invalid test case."), ValidationFunction.FAIL)
 elif len(self.__inputs[0]) < 1 or len(self.__inputs[0]) > 1000:
 self.store_result("Array values should be between 1 and 1000.", ValidationFunction.FAIL)
 elif any(x < 0 or x > 1000 for x in self.__inputs[0]):
 self.store_result("The range of numbers in array should be between 0 and 1000.", ValidationFunction.FAIL) 
 else:
 self.store_result("", ValidationFunction.PASS)

Try to solve the House Robber II problem.

Dynamic Programming

Conclusion

House Robber II

Statement

Examples

Understand the problem

Figure it out!

Try it yourself