C++ Code to Get Shortest Distance from Circular Stations

Suppose we have two numbers s and t, and another array D with n elements. The circle line of the Dreamland subway has n different stations. We know the distances between all pairs of neighboring stations: D[i] is the distance between station i and i+1, and D[n-1] is the distance between (n-1) and 0th station. We have to find shortest distance from s to t.

So, if the input is like s = 1; t = 3; D = [2, 3, 4, 9], then the output will be 5.

Steps

To solve this, we will follow these steps −

n := size of D
Define an array arr of size (n + 1), and fill with 0
for initialize i := 1, when i <= n, update (increase i by 1), do:
   arr[i] := D[i - 1]
   sum1 := sum1 + arr[i]
if s > t, then:
   swap s and t
for initialize i := s, when i < t, update (increase i by 1), do:
   sum2 := sum2 + arr[i]
return minimum of sum2 and (sum1 - sum2)

Example

Let us see the following implementation to get better understanding −

#include <bits/stdc++.h>
using namespace std;
int solve(int s, int t, vector<int> D){
   int n = D.size(), sum1 = 0, sum2 = 0;
   vector<int> arr(n + 1, 0);
   for (int i = 1; i <= n; i++){
      arr[i] = D[i - 1];
      sum1 += arr[i];
   }
   if (s > t)
      swap(s, t);
   for (int i = s; i < t; i++)
      sum2 += arr[i];
   return min(sum2, sum1 - sum2);
}
int main(){
   int s = 1;
   int t = 3;
   vector<int> D = { 2, 3, 4, 9 };
   cout << solve(s, t, D) << endl;
}

Input

1, 3, { 2, 3, 4, 9 }

Output

5