Network Delay Time
You are given a network of n nodes, labeled from 1 to n. You are also given times, a list of travel times as directed edges times[i] = (ui, vi, wi), where ui is the source node, vi is the target node, and wi is the time it takes for a signal to travel from source to target.
We will send a signal from a given node k. Return the minimum time it takes for all the n nodes to receive the signal. If it is impossible for all the n nodes to receive the signal, return -1.
Example 1:
Input: times = [[2,1,1],[2,3,1],[3,4,1]], n = 4, k = 2
Output: 2
Example 2:
Input: times = [[1,2,1]], n = 2, k = 1
Output: 1
Example 3:
Input: times = [[1,2,1]], n = 2, k = 2
Output: -1
Constraints:
1 <= k <= n <= 1001 <= times.length <= 6000times[i].length == 31 <= ui, vi <= nui != vi0 <= wi <= 100- All the pairs
(ui, vi)are unique. (i.e., no multiple edges.)
Solution
We wish to find the shortest path from k to all nodes in the graph.
Dijkstra's algorithm is the best approach in finding shortest path from a single source.
We will keep track of the delay time from k to each node, and find the maximum in the end.
Implementation
1def networkDelayTime(self, times: List[List[int]], n: int, k: int) -> int:
2 graph = defaultdict(list)
3 for src, dst, time in times:
4 graph[src].append((time, dst))
5
6 queue = [(0, k)]
7 delay_time = [inf for _ in range(n+1)]
8 while queue:
9 cur_time, cur_node = heapq.heappop(queue) # pop min from min-heap
10 if cur_time > delay_time[cur_node]: # a shorter path exists
11 continue
12 for edge in graph[cur_node]:
13 new_time, new_node = edge
14 if delay_time[new_node] > cur_time + new_time:
15 delay_time[new_node] = cur_time + new_time
16 heapq.heappush(queue, (delay_time[new_node], new_node))
17
18 max_delay = max(delay_time)
19 return max_delay if max_delay != inf else -1
What's the relationship between a tree and a graph?
What's the output of running the following function using the following tree as input?
1def serialize(root):
2 res = []
3 def dfs(root):
4 if not root:
5 res.append('x')
6 return
7 res.append(root.val)
8 dfs(root.left)
9 dfs(root.right)
10 dfs(root)
11 return ' '.join(res)
121import java.util.StringJoiner;
2
3public static String serialize(Node root) {
4 StringJoiner res = new StringJoiner(" ");
5 serializeDFS(root, res);
6 return res.toString();
7}
8
9private static void serializeDFS(Node root, StringJoiner result) {
10 if (root == null) {
11 result.add("x");
12 return;
13 }
14 result.add(Integer.toString(root.val));
15 serializeDFS(root.left, result);
16 serializeDFS(root.right, result);
17}
181function serialize(root) {
2 let res = [];
3 serialize_dfs(root, res);
4 return res.join(" ");
5}
6
7function serialize_dfs(root, res) {
8 if (!root) {
9 res.push("x");
10 return;
11 }
12 res.push(root.val);
13 serialize_dfs(root.left, res);
14 serialize_dfs(root.right, res);
15}
16Solution Implementation
Which of the following is a min heap? 
What's the relationship between a tree and a graph?
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