Learn and practice the Greedy Techniques and Dynamic Programming patterns to solve coding interview problems.

Speedrun the Microsoft Coding Interview: Top Problems in C++

This module teaches you two of the most important problem-solving techniques in the optimization domain: Greedy Techniques and Dynamic Programming. Not all problems require an exhaustive search through the solution space. Rather, consistently choosing the locally optimal solution can be proven to yield the globally optimal solution. In such situations, Greedy Techniques result in simple, highly efficient solutions. Other problems have a well-defined structure, where the same subproblem is encountered and solved multiple times. Dynamic Programming techniques allow us to compute once and reuse the solutions to recurring subproblems.

Optimization Techniques

# Statement

There are $n$ gas stations along a circular route, where the amount of gas at the $i^{th}$ station is `gas[i]`.


We have a car with an unlimited gas tank, and it costs `cost[i]` of gas to travel from the $i^{th}$ station to the next $(i+1)^{th}$ station. We begin the journey with an empty tank at one of the gas stations.


Find the index of the gas station in the integer array `gas` such that if we start from that index we may return to the same index by traversing through all the elements, collecting `gas[i]` and consuming `cost[i]`.

* If it is not possible, return -1.


* If there exists such index, it is guaranteed to be unique.

**Constraints:**

- `gas.length` $==$ `cost.length`
- 1 $\leq$ `gas.length`, `cost.length` $\leq 10^3$ 
- 0 $\leq$ `gas[i]`, `cost[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 will the output be if the following gas and cost arrays are provided as input?

gas = [3, 1, 1]

cost = [1, 2, 2]

What will the output be if the following gas and cost arrays are provided as input?
gas = [3, 1, 1]
cost = [1, 2, 2]

What will the output be if the following gas and cost arrays are provided as input?

gas = [6, 0, 1, 3, 2]

cost = [4, 5, 2, 5, 5]

What will the output be if the following gas and cost arrays are provided as input?
gas = [6, 0, 1, 3, 2]
cost = [4, 5, 2, 5, 5]

What will the output be if the following gas and cost arrays are provided as input?

gas = [5, 1, 2, 3, 4]

cost = [4, 4, 1, 5, 1]

What will the output be if the following gas and cost arrays are provided as input?
gas = [5, 1, 2, 3, 4]
cost = [4, 4, 1, 5, 1]

Gas Stations

Gas Stations

## 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 `main.cpp` 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: `GasStationJourney`\n- Candidate's submitted solution code: USER_CODE\n- Error: ERROR_DESCRIPTION\n- Failed test case: FAILED_TEST_CASE\n- Coding language: `C++`\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 `GasStationJourney` 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 `GasStationJourney`.\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) `GasStationJourney`. \n- While calculating time complexity, include the time complexity of built-in C++ 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) `GasStationJourney`. \n- While calculating space complexity, include the space complexity of built-in C++ 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 gas_station_journey(gas, cost):
 
 if sum(cost) > sum(gas): 
 return -1 

 current_gas, starting_index = 0, 0

 for i in range(len(gas)): 
 
 current_gas = current_gas + (gas[i] - cost[i])
 
 if current_gas < 0:
 current_gas = 0
 starting_index = i + 1

 return starting_index

 # multiple outputs will be added at each index respectively for a single test_case
 expected_outputs = []
 input1 = self.__inputs[0]
 input2 = self.__inputs[1]
 expected = gas_station_journey(input1, input2)
 # store the 1st expected output that should be displayed to the user 
 expected_outputs.append(expected)
 actual = self.__actual_outputs[0]
 
 if json.dumps(expected) == json.dumps(actual):
 self.__edu_result.store_result(expected_outputs, TestCaseResult.PASS)
 else:
 self.__edu_result.store_result(expected_outputs, TestCaseResult.FAIL)

 return self.__edu_result

#include <iostream>
#include <vector>

int GasStationJourney(vector<int> gas, vector<int> cost)
{
 // Replace this placeholder return statement with your code
 return -1;
}

gas_stations.yaml

testcases:
  - name: "testcase 1"
    inputs:
    - 1 : [1, 2, 3, 4, 5]
    - 2 : [3, 4, 5, 1, 2]
    output: 
    - 1 : 3
  - name: "testcase 2"
    inputs:
    - 1: [2, 3, 4]
    - 2: [3, 4, 3]
    output:
    - 1 : -1
  - name: "testcase 3"
    inputs:
    - 1 : [1, 1, 1, 1, 10]
    - 2 : [2, 2, 1, 3, 1]
    output: 
    - 1 : 4
  - name: "testcase 4"
    inputs:
    - 1: [1, 1, 1, 1, 1]
    - 2: [1, 2, 3, 4, 5]
    output:
    - 1 : -1
  - name: "testcase 5"
    inputs:
    - 1: [1]
    - 2: [1]
    output:
    - 1 : 0

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 check_multiple_start_indexes(gas, cost):
 n = len(gas)

 valid_start_count = 0

 for start in range(n):
 fuel = 0
 can_travel = True

 for i in range(start, start + n):
 index = i % n
 fuel += gas[index] - cost[index]

 if fuel < 0:
 can_travel = False
 break

 if can_travel:
 valid_start_count += 1

 return valid_start_count > 1
 
 
 def gas_station_journey(gas, cost):
 
 if sum(cost) > sum(gas): 
 return -1 

 current_gas, starting_index = 0, 0

 for i in range(len(gas)): 
 
 current_gas = current_gas + (gas[i] - cost[i])
 
 if current_gas < 0:
 current_gas = 0
 starting_index = i + 1

 return starting_index

 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
 gas_array = self.__inputs[0]
 cost_array = self.__inputs[1]

 if not is_valid_1d_array(gas_array):
 self.store_result(("Not a Valid 1D Integer 'gas' Array."), ValidationFunction.FAIL)
 elif not is_valid_1d_array(cost_array):
 self.store_result(("Not a Valid 1D Integer 'cost' Array."), ValidationFunction.FAIL)
 elif not (len(gas_array) == len(cost_array)):
 self.store_result ("'gas' and 'cost' must have same length", ValidationFunction.FAIL)
 elif not (1 <= len(gas_array) <= 1000 and 1 <= len(cost_array) <= 1000):
 self.store_result ("'gas' and 'cost' to have 1 <= size <= 1000", ValidationFunction.FAIL)
 elif not all(0 <= num <= 1000 for num in gas_array):
 self.store_result ("'gas' must consist of values from 0 to 1000 only", ValidationFunction.FAIL)
 elif not all(0 <= num <= 1000 for num in cost_array):
 self.store_result ("'cost' must consist of values from 0 to 1000 only", ValidationFunction.FAIL)
 elif ((gas_station_journey(gas_array, cost_array) != -1) and (check_multiple_start_indexes(gas_array, cost_array))):
 self.store_result ("There should be unique solution", ValidationFunction.FAIL)
 else:
 self.store_result("", ValidationFunction.PASS)

Greedy Techniques

Dynamic Programming

Conclusion

Gas Stations

Statement

Examples

Understand the problem

Figure it out!

Try it yourself