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1697. Checking Existence of Edge Length Limited Paths

中文文档

Description

An undirected graph of n nodes is defined by edgeList, where edgeList[i] = [ui, vi, disi] denotes an edge between nodes ui and vi with distance disi. Note that there may be multiple edges between two nodes.

Given an array queries, where queries[j] = [pj, qj, limitj], your task is to determine for each queries[j] whether there is a path between pj and qj such that each edge on the path has a distance strictly less than limitj .

Return a boolean array answer, where answer.length == queries.length and the jth value of answer is true if there is a path for queries[j] is true, and false otherwise.

 

Example 1:

Input: n = 3, edgeList = [[0,1,2],[1,2,4],[2,0,8],[1,0,16]], queries = [[0,1,2],[0,2,5]]
Output: [false,true]
Explanation: The above figure shows the given graph. Note that there are two overlapping edges between 0 and 1 with distances 2 and 16.
For the first query, between 0 and 1 there is no path where each distance is less than 2, thus we return false for this query.
For the second query, there is a path (0 -> 1 -> 2) of two edges with distances less than 5, thus we return true for this query.

Example 2:

Input: n = 5, edgeList = [[0,1,10],[1,2,5],[2,3,9],[3,4,13]], queries = [[0,4,14],[1,4,13]]
Output: [true,false]
Exaplanation: The above figure shows the given graph.

 

Constraints:

  • 2 <= n <= 105
  • 1 <= edgeList.length, queries.length <= 105
  • edgeList[i].length == 3
  • queries[j].length == 3
  • 0 <= ui, vi, pj, qj <= n - 1
  • ui != vi
  • pj != qj
  • 1 <= disi, limitj <= 109
  • There may be multiple edges between two nodes.

Solutions

Union find.

Python3

class Solution:
    def distanceLimitedPathsExist(
        self, n: int, edgeList: List[List[int]], queries: List[List[int]]
    ) -> List[bool]:
        def find(x):
            if p[x] != x:
                p[x] = find(p[x])
            return p[x]

        p = list(range(n))
        edgeList.sort(key=lambda x: x[2])

        m = len(queries)
        indexes = list(range(m))
        indexes.sort(key=lambda i: queries[i][2])
        ans = [False] * m
        i = 0
        for j in indexes:
            pj, qj, limit = queries[j]
            while i < len(edgeList) and edgeList[i][2] < limit:
                u, v, _ = edgeList[i]
                p[find(u)] = find(v)
                i += 1
            ans[j] = find(pj) == find(qj)
        return ans

Java

class Solution {
    private int[] p;

    public boolean[] distanceLimitedPathsExist(int n, int[][] edgeList, int[][] queries) {
        p = new int[n];
        for (int i = 0; i < n; ++i) {
            p[i] = i;
        }
        int m = queries.length;
        Integer[] indexes = new Integer[m];
        for (int i = 0; i < m; ++i) {
            indexes[i] = i;
        }
        Arrays.sort(indexes, Comparator.comparingInt(i -> queries[i][2]));
        Arrays.sort(edgeList, Comparator.comparingInt(a -> a[2]));
        boolean[] ans = new boolean[m];
        int i = 0;
        for (int j : indexes) {
            int pj = queries[j][0], qj = queries[j][1], limit = queries[j][2];
            while (i < edgeList.length && edgeList[i][2] < limit) {
                int u = edgeList[i][0], v = edgeList[i][1];
                p[find(u)] = find(v);
                ++i;
            }
            ans[j] = find(pj) == find(qj);
        }
        return ans;
    }

    private int find(int x) {
        if (p[x] != x) {
            p[x] = find(p[x]);
        }
        return p[x];
    }
}

C++

class Solution {
public:
    vector<int> p;

    vector<bool> distanceLimitedPathsExist(int n, vector<vector<int>>& edgeList, vector<vector<int>>& queries) {
        p.resize(n);
        for (int i = 0; i < n; ++i) p[i] = i;
        sort(edgeList.begin(), edgeList.end(), [](const auto& e1, const auto& e2) {
            return e1[2] < e2[2];
        });
        int m = queries.size();
        vector<int> indexes(m);
        for (int i = 0; i < m; ++i) indexes[i] = i;
        sort(indexes.begin(), indexes.end(), [&](int i, int j) {
            return queries[i][2] < queries[j][2];
        });

        vector<bool> ans(m, false);
        int i = 0;
        for (int j : indexes) {
            int pj = queries[j][0], qj = queries[j][1], limit = queries[j][2];
            while (i < edgeList.size() && edgeList[i][2] < limit) {
                int u = edgeList[i][0], v = edgeList[i][1];
                p[find(u)] = find(v);
                ++i;
            }
            ans[j] = find(pj) == find(qj);
        }
        return ans;
    }

    int find(int x) {
        if (p[x] != x) p[x] = find(p[x]);
        return p[x];
    }
};

Go

func distanceLimitedPathsExist(n int, edgeList [][]int, queries [][]int) []bool {
	p := make([]int, n)
	for i := 0; i < n; i++ {
		p[i] = i
	}
	var find func(x int) int
	find = func(x int) int {
		if p[x] != x {
			p[x] = find(p[x])
		}
		return p[x]
	}
	sort.Slice(edgeList, func(i, j int) bool {
		return edgeList[i][2] < edgeList[j][2]
	})
	m := len(queries)
	indexes := make([]int, m)
	for i := 0; i < m; i++ {
		indexes[i] = i
	}
	sort.Slice(indexes, func(i, j int) bool {
		return queries[indexes[i]][2] < queries[indexes[j]][2]
	})
	ans := make([]bool, m)
	i := 0
	for _, j := range indexes {
		pj, qj, limit := queries[j][0], queries[j][1], queries[j][2]
		for i < len(edgeList) && edgeList[i][2] < limit {
			u, v := edgeList[i][0], edgeList[i][1]
			p[find(u)] = find(v)
			i++
		}
		ans[j] = find(pj) == find(qj)
	}
	return ans
}

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