Is that solution correct ? Complete Circuit

PHP
1

Hi

I have this question:

You have a circular route with n gas stations. Each station is defined by the amount of gas[i] available, and the cost of fuel[i] to get from that station to the next. You start the journey at any station but with an empty tank.

The goal of this challenge: Your inputs are two integer arrays, gas and cost. You are asked to determine the index of the station where you can start the journey, such that you can go around the route once in a clockwise direction without running out of fuel. If you do not find any station that allows you to complete the loop, you must return (-1)

I found the solution like this

function canCompleteCircuit($gas, $cost) {
    $n = count($gas); // Number of stations
    $totalGas = 0; // Total gas available
    $totalCost = 0; // Total cost required
    $start = 0; // Starting station index
    $tank = 0; // Current tank fuel

    for ($i = 0; $i < $n; $i++) {
        $totalGas += $gas[$i];
        $totalCost += $cost[$i];
        $tank += $gas[$i] - $cost[$i];

        // If the tank is negative, we can't start the journey from the current start
        if ($tank < 0) {
            $start = $i + 1; // Update start to the next station
            $tank = 0; // Reset the tank
        }
    }

    // Check if total gas is sufficient to cover total cost
    return $totalGas >= $totalCost ? $start : -1;
}

What I dont understand that in the line $start = $i + 1; $i get increased but the second iteration of the for loop $i = 2 not 1 so how can this be the solution ?

PS The test platform accepted this solution.

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2

It’s difficult to see whether that’s a good solution without seeing the calling code. Presumably you are calling this function multiple times based on the return from it, but as the function will always start at position zero, I can only presume that the calling code is manipulating the arrays prior to calling the function again.

3

It is one of the test questions

4

The Travelling Salesman Problem. Or at least, a modification thereof.

The challenge fails to dictate how to translate “clockwise” in terms of the arrays, so a point off from your teacher for that. Arrays are not clocks, and the stations would be spatially located on a plane, which would give them a “clockwise”, which could match any combination of array keys. I shall assume, for the sake of the teacher, that “clockwise” is meant to be “in ascending order of index, with modulo wrapping”.

Right, rant over.

So… those two sentences together tell me the response is “You didnt find the solution, ChatGPT did.”, because you just told me you wrote code that you dont understand. Most teachers will catch on to that if you tell them. Just a word of warning.

Also, your code doesnt do what the question asked. There’s that. ChatGPT has led you down a false positive, and the test platform has failed to catch your error.

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5

I think that the part that’s throwing my brain off (the logic is… not the way any human brain thinks about solving the problem, imo…) is that it assumes that there will be exactly 1 station for which the condition holds true, but there can be many; [5,5,5] , [5,5,5] - all 3 stations are valid answers to the question at that point.

It’s trying to work on the principle that if the total amount of gas available on the circuit isnt enough to complete the circuit, that no matter what, you’ll never get an answer. Which is true, but could be a shortcircuit to the function on line 1 (if sum(gas) < sum(cost) return -1).

If that condition is passed, there exists at least one answer where it is true, but there may be many. (Trivial case, gas[i] = cost[i] for all i; all stations are valid answers.)

The code as written doesnt technically check to see if the entire loop is completable from a given point (it just checks to the end of the array without looping), but considers that good enough to make a conclusion.

6

There is no teacher I am trying to study these questions by myself which all already answered

7

I think I found the reason of $start = $i + 1; because $i start at 0 while I should return a number starting from 1 or else return -1

8

no, you’d be returning the index of the array. Which could be 0.

9

That’s why I wondered if the array is re-arranged by the calling code, and the function called again, if the starting point used is not suitable. That, and the fact that it always starts at element zero - if the array isn’t rearranged, how would it ever check from a different starting point? Unless I’m missing something obvious, which is entirely possible.

10

It seems to be crutching itself on the idea that, given that there is at least one valid path in the set (which there should be if available >= cost), if you skip any problematic short chain spot, whatevers left must be the answer. Which… might work? but its not immediately clear that theory holds true…and if it does, it would still find an answer rather than all answers

12

Your solution is correct and efficient. It checks if the total gas is sufficient (totalGas >= totalCost) and uses the tank variable to track feasibility. If the tank goes negative, the start station is updated. This ensures an O(n)O(n)O(n) time complexity by avoiding redundant checks. Well done!

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