Cheapest Flights Within K Stops

There are n cities connected by m flights. Each flight starts from city u and arrives at v with a price w.

Now given all the cities and flights, together with starting city src and the destination dst, your task is to find the cheapest price from src to dst with up to k stops. If there is no such route, output -1.

Example 1:
Input: 
n = 3, edges = [[0,1,100],[1,2,100],[0,2,500]]
src = 0, dst = 2, k = 1
Output: 200
Explanation: 
The graph looks like this:


The cheapest price from city 0 to city 2 with at most 1 stop costs 200, 
as marked red in the picture.

Example 2:
Input: 
n = 3, edges = [[0,1,100],[1,2,100],[0,2,500]]
src = 0, dst = 2, k = 0
Output: 500
Explanation: 
The graph looks like this:


The cheapest price from city 0 to city 2 with at most 0 stop costs 500, 
as marked blue in the picture.

Constraints:

• The number of nodes n will be in range [1, 100], with nodes labeled from 0 to n - 1.
• The size of flights will be in range [0, n * (n - 1) / 2].
• The format of each flight will be (src, dst, price).
• The price of each flight will be in the range [1, 10000].
• k is in the range of [0, n - 1].
• There will not be any duplicated flights or self cycles.

 class Solution {
   public int findCheapestPrice(int n, int[][] flights, int src, int dst, int K) {
        int[] dist = new int[n];
        Arrays.fill(dist, Integer.MAX_VALUE);
        dist[src] = 0;
        for (int i = 0; i <= K; i++) {
            int[] tmpDist = Arrays.copyOf(dist, dist.length);
            for (int[] edge : flights) {
                int u = edge[0];
                if (dist[u] == Integer.MAX_VALUE) continue;
                int v = edge[1];
                int w = edge[2];
                tmpDist[v] = Math.min(tmpDist[v], dist[u] + w);
            }
            dist = tmpDist;
        }
        return dist[dst] == Integer.MAX_VALUE ? -1 : dist[dst];
    }
}

Try it on Leetcode

Here we are going to use Bellman Ford Algorithm.

1) Initially create dist array and fill with INTEGER.MAX_VALUE and dist[src]=0.

2) For K times,

 a) Create temporary array (i.e., tmpDist) and fill it with copy of dist array.

 b) Iterate with all flights value u, v, w.

 c) If dist[u] is INTEGER.MAX_VALUE, then continue because those nodes are not reachable and thus no need to check for distance.

 d) Else find minimum distance using tmpDist[v] = Math.min(tmpDist[v], dist[u] + w) [values used are tmpDist[v] and dist[u]+w (i.e.,) from u to v using distance w]

 e) Store tmpDist to dist array.3.

3) Repeat above steps for K times.

4) Finally if dist[dst] is INTEGER.MAX_VALUE return -1 else return value present at dist[dst].

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