Question

2737. Find the Closest Marked Node

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Description

You are given a positive integer n which is the number of nodes of a 0-indexed directed weighted graph and a 0-indexed 2D array edges where edges[i] = [ui, vi, wi] indicates that there is an edge from node ui to node vi with weight wi.

You are also given a node s and a node array marked; your task is to find the minimum distance from s to any of the nodes in marked.

Return _an integer denoting the minimum distance from _s_ to any node in _marked_ or _-1_ if there are no paths from s to any of the marked nodes_.

 

Example 1:

Input: n = 4, edges = [[0,1,1],[1,2,3],[2,3,2],[0,3,4]], s = 0, marked = [2,3]
Output: 4
Explanation: There is one path from node 0 (the green node) to node 2 (a red node), which is 0->1->2, and has a distance of 1 + 3 = 4.
There are two paths from node 0 to node 3 (a red node), which are 0->1->2->3 and 0->3, the first one has a distance of 1 + 3 + 2 = 6 and the second one has a distance of 4.
The minimum of them is 4.

Example 2:

Input: n = 5, edges = [[0,1,2],[0,2,4],[1,3,1],[2,3,3],[3,4,2]], s = 1, marked = [0,4]
Output: 3
Explanation: There are no paths from node 1 (the green node) to node 0 (a red node).
There is one path from node 1 to node 4 (a red node), which is 1->3->4, and has a distance of 1 + 2 = 3.
So the answer is 3.

Example 3:

Input: n = 4, edges = [[0,1,1],[1,2,3],[2,3,2]], s = 3, marked = [0,1]
Output: -1
Explanation: There are no paths from node 3 (the green node) to any of the marked nodes (the red nodes), so the answer is -1.

 

Constraints:

• 2 <= n <= 500
• 1 <= edges.length <= 104
• edges[i].length = 3
• 0 <= edges[i][0], edges[i][1] <= n - 1
• 1 <= edges[i][2] <= 106
• 1 <= marked.length <= n - 1
• 0 <= s, marked[i] <= n - 1
• s != marked[i]
• marked[i] != marked[j] for every i != j
• The graph might have repeated edges.
• The graph is generated such that it has no self-loops.

Solutions

Solution 1

class Solution:
  def minimumDistance(
    self, n: int, edges: List[List[int]], s: int, marked: List[int]
  ) -> int:
    g = [[inf] * n for _ in range(n)]
    for u, v, w in edges:
      g[u][v] = min(g[u][v], w)
    dist = [inf] * n
    vis = [False] * n
    dist[s] = 0
    for _ in range(n):
      t = -1
      for j in range(n):
        if not vis[j] and (t == -1 or dist[t] > dist[j]):
          t = j
      vis[t] = True
      for j in range(n):
        dist[j] = min(dist[j], dist[t] + g[t][j])
    ans = min(dist[i] for i in marked)
    return -1 if ans >= inf else ans

class Solution {
  public int minimumDistance(int n, List<List<Integer>> edges, int s, int[] marked) {
    final int inf = 1 << 29;
    int[][] g = new int[n][n];
    for (var e : g) {
      Arrays.fill(e, inf);
    }
    for (var e : edges) {
      int u = e.get(0), v = e.get(1), w = e.get(2);
      g[u][v] = Math.min(g[u][v], w);
    }
    int[] dist = new int[n];
    Arrays.fill(dist, inf);
    dist[s] = 0;
    boolean[] vis = new boolean[n];
    for (int i = 0; i < n; ++i) {
      int t = -1;
      for (int j = 0; j < n; ++j) {
        if (!vis[j] && (t == -1 || dist[t] > dist[j])) {
          t = j;
        }
      }
      vis[t] = true;
      for (int j = 0; j < n; ++j) {
        dist[j] = Math.min(dist[j], dist[t] + g[t][j]);
      }
    }
    int ans = inf;
    for (int i : marked) {
      ans = Math.min(ans, dist[i]);
    }
    return ans >= inf ? -1 : ans;
  }
}

class Solution {
public:
  int minimumDistance(int n, vector<vector<int>>& edges, int s, vector<int>& marked) {
    const int inf = 1 << 29;
    vector<vector<int>> g(n, vector<int>(n, inf));
    vector<int> dist(n, inf);
    dist[s] = 0;
    vector<bool> vis(n);
    for (auto& e : edges) {
      int u = e[0], v = e[1], w = e[2];
      g[u][v] = min(g[u][v], w);
    }
    for (int i = 0; i < n; ++i) {
      int t = -1;
      for (int j = 0; j < n; ++j) {
        if (!vis[j] && (t == -1 || dist[t] > dist[j])) {
          t = j;
        }
      }
      vis[t] = true;
      for (int j = 0; j < n; ++j) {
        dist[j] = min(dist[j], dist[t] + g[t][j]);
      }
    }
    int ans = inf;
    for (int i : marked) {
      ans = min(ans, dist[i]);
    }
    return ans >= inf ? -1 : ans;
  }
};

func minimumDistance(n int, edges [][]int, s int, marked []int) int {
  const inf = 1 << 29
  g := make([][]int, n)
  dist := make([]int, n)
  for i := range g {
    g[i] = make([]int, n)
    for j := range g[i] {
      g[i][j] = inf
    }
    dist[i] = inf
  }
  dist[s] = 0
  for _, e := range edges {
    u, v, w := e[0], e[1], e[2]
    g[u][v] = min(g[u][v], w)
  }
  vis := make([]bool, n)
  for _ = range g {
    t := -1
    for j := 0; j < n; j++ {
      if !vis[j] && (t == -1 || dist[j] < dist[t]) {
        t = j
      }
    }
    vis[t] = true
    for j := 0; j < n; j++ {
      dist[j] = min(dist[j], dist[t]+g[t][j])
    }
  }
  ans := inf
  for _, i := range marked {
    ans = min(ans, dist[i])
  }
  if ans >= inf {
    return -1
  }
  return ans
}

function minimumDistance(n: number, edges: number[][], s: number, marked: number[]): number {
  const inf = 1 << 29;
  const g: number[][] = Array(n)
    .fill(0)
    .map(() => Array(n).fill(inf));
  const dist: number[] = Array(n).fill(inf);
  const vis: boolean[] = Array(n).fill(false);
  for (const [u, v, w] of edges) {
    g[u][v] = Math.min(g[u][v], w);
  }
  dist[s] = 0;
  for (let i = 0; i < n; ++i) {
    let t = -1;
    for (let j = 0; j < n; ++j) {
      if (!vis[j] && (t == -1 || dist[t] > dist[j])) {
        t = j;
      }
    }
    vis[t] = true;
    for (let j = 0; j < n; ++j) {
      dist[j] = Math.min(dist[j], dist[t] + g[t][j]);
    }
  }
  let ans = inf;
  for (const i of marked) {
    ans = Math.min(ans, dist[i]);
  }
  return ans >= inf ? -1 : ans;
}