Algorithm for truck moving around a circle of gas stations

Question

You have a truck moving around a circular track with gas stations spaced out around the circle. Each station has a finite amount of gas. The gas tank on the truck is infinit

Answer 1

This is basically the maximum subarray sum problem. On the other hand, we can look at it from somewhat different POV. Let us find out where will we have the most deficiency in the fuel if we start the journey from the very first gas station. Since we know that reaching this point shall take the most of the fuel, we can conclude that the truck has to start at this point to minimize the negative fuell balance. Below is the solution with the driver program with O(N) time and O(1) space complexity and there is no need for any DP, since everything is done in a single pass and using only two integers to store the start point index and its value (though this is needed only for printing purposes).

#include 
#include 
#include 
#include 
#include 

using namespace std;

int gasoline[] = {8, 6, 30, 9, 15, 21, 2, 18};
int stations[] = {15, 8, 2, 6, 18, 9, 21, 30};

int rnd_num(const int& low, const int& high)
{
    int rndnum = (int) (((double) rand() / (double) RAND_MAX) * (high - low + 1) + low);
    return rndnum;
}

void swap(int data[], const int& idxlow, const int& idxhigh)
{
    int tmp = data[idxlow];
    data[idxlow] = data[idxhigh];
    data[idxhigh] = tmp;
}

void print_array(const char* label, int data[], int size)
{
    printf("%-10s: ", label);
    for (int i = 0; i < size; ++i){
        printf("%-3d ", data[i]);
    }
    printf("\n");
}

void print_vector(const char* label, const vector& data)
{
    printf("%-10s: ", label);
    for (vector::size_type i = 0; i < data.size(); ++i){
        printf("%-3d ", data[i]);
    }
    printf("\n");
}

void shuffle(int data[], int size)
{
    for (int i = 0; i < size - 1; ++i){
        int idx = rnd_num(i + 1, size - 1);
        swap(data, i, idx);
    }
}

void run(int gas[], int dist[], int size)
{
    vector path;
    int diff = 0, vidx, minidx = 0, minval = gas[0] - dist[0];

    path.resize(size);

    for (int i = 0; i < size; ++i) {
        diff += gas[i] - dist[i];
        if (i == size - 1){
            vidx = 0; //path[0] = diff;
        }
        else {
            vidx = i + 1; //path[i + 1] = diff;
        }

        path[vidx] = diff;
        if (diff < minval) {
            minval = diff;
            minidx = vidx;
        }
    }

    print_vector("PATHS   ", path);
    printf("MINIDX: %d\nMINVAL: %d\n", minidx, minval);
}

int main()
{
    int size = sizeof(stations)/sizeof(stations[0]);
    srand((unsigned)time(NULL));

    shuffle(gasoline, sizeof(gasoline)/sizeof(gasoline[0]));
    shuffle(stations, sizeof(stations)/sizeof(stations[0]));

    print_array("GASOLINE ", gasoline, sizeof(gasoline)/sizeof(gasoline[0]));
    print_array("STATIONS ", stations, sizeof(stations)/sizeof(stations[0]));

    run(gasoline, stations, size);

    return 0;
}