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2737. Find the Closest Marked Node

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

  • 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;
        }
    };
    
  • 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
    
    
  • 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
    }
    
    func min(a, b int) int {
    	if a < b {
    		return a
    	}
    	return b
    }
    
  • 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;
    }
    
    

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