Class Solution
- java.lang.Object
-
- g1601_1700.s1627_graph_connectivity_with_threshold.Solution
-
public class Solution extends Object
1627 - Graph Connectivity With Threshold.Hard
We have
n
cities labeled from1
ton
. Two different cities with labelsx
andy
are directly connected by a bidirectional road if and only ifx
andy
share a common divisor strictly greater than somethreshold
. More formally, cities with labelsx
andy
have a road between them if there exists an integerz
such that all of the following are true:x % z == 0
,y % z == 0
, andz > threshold
.
Given the two integers,
n
andthreshold
, and an array ofqueries
, you must determine for eachqueries[i] = [ai, bi]
if citiesai
andbi
are connected directly or indirectly. (i.e. there is some path between them).Return an array
answer
, whereanswer.length == queries.length
andanswer[i]
istrue
if for theith
query, there is a path betweenai
andbi
, oranswer[i]
isfalse
if there is no path.Example 1:
Input: n = 6, threshold = 2, queries = [[1,4],[2,5],[3,6]]
Output: [false,false,true]
Explanation: The divisors for each number:
1: 1
2: 1, 2
3: 1, 3
4: 1, 2, 4
5: 1, 5
6: 1, 2, 3, 6
Using the underlined divisors above the threshold, only cities 3 and 6 share a common divisor, so they are the only ones directly connected. The result of each query:
[1,4] 1 is not connected to 4
[2,5] 2 is not connected to 5
[3,6] 3 is connected to 6 through path 3–6
Example 2:
Input: n = 6, threshold = 0, queries = [[4,5],[3,4],[3,2],[2,6],[1,3]]
Output: [true,true,true,true,true]
Explanation: The divisors for each number are the same as the previous example. However, since the threshold is 0, all divisors can be used. Since all numbers share 1 as a divisor, all cities are connected.
Example 3:
Input: n = 5, threshold = 1, queries = [[4,5],[4,5],[3,2],[2,3],[3,4]]
Output: [false,false,false,false,false]
Explanation: Only cities 2 and 4 share a common divisor 2 which is strictly greater than the threshold 1, so they are the only ones directly connected. Please notice that there can be multiple queries for the same pair of nodes [x, y], and that the query [x, y] is equivalent to the query [y, x].
Constraints:
2 <= n <= 104
0 <= threshold <= n
1 <= queries.length <= 105
queries[i].length == 2
1 <= ai, bi <= cities
ai != bi
-
-
Constructor Summary
Constructors Constructor Description Solution()
-
Method Summary
All Methods Instance Methods Concrete Methods Modifier and Type Method Description List<Boolean>
areConnected(int n, int threshold, int[][] queries)
-