CSES - Flight Discount

Say I use the discount coupon on the edge between cities A and B.

There are two cases: I can go from $1\rightarrow A\rightarrow B\rightarrow N$, or $1\rightarrow B\rightarrow A\rightarrow N$. We need to know the distance between $1$ and $A$, and $N$ and $B$.

We can use Dijkstra's to compute the distance from $1$ and $N$ to every vertex. Then our answer is $\text{min}_{A\rightarrow B} dist1[A]+c(A,B)+distN[B]$, where $c(A,B)$ is the cost to travel from city A to city B after applying the coupon to that flight.

import java.io.*; 
import java.util.*;

public class FlightDiscount {

    /**
     * Author : Kai Wang
     */
    static class Pair implements Comparable<Pair>{
        int v; long w;