LeetCode in Kotlin
2709. Greatest Common Divisor Traversal
Hard
You are given a 0-indexed integer array nums, and you are allowed to traverse between its indices. You can traverse between index i and index j, i != j, if and only if gcd(nums[i], nums[j]) > 1, where gcd is the greatest common divisor.
Your task is to determine if for every pair of indices i and j in nums, where i < j, there exists a sequence of traversals that can take us from i to j.
Return true if it is possible to traverse between all such pairs of indices, or false otherwise.
Example 1:
Input: nums = [2,3,6]
Output: true
Explanation: In this example, there are 3 possible pairs of indices: (0, 1), (0, 2), and (1, 2). To go from index 0 to index 1, we can use the sequence of traversals 0 -> 2 -> 1, where we move from index 0 to index 2 because gcd(nums[0], nums[2]) = gcd(2, 6) = 2 > 1, and then move from index 2 to index 1 because gcd(nums[2], nums[1]) = gcd(6, 3) = 3 > 1. To go from index 0 to index 2, we can just go directly because gcd(nums[0], nums[2]) = gcd(2, 6) = 2 > 1. Likewise, to go from index 1 to index 2, we can just go directly because gcd(nums[1], nums[2]) = gcd(3, 6) = 3 > 1.
Example 2:
Input: nums = [3,9,5]
Output: false
Explanation: No sequence of traversals can take us from index 0 to index 2 in this example. So, we return false.
Example 3:
Input: nums = [4,3,12,8]
Output: true
Explanation: There are 6 possible pairs of indices to traverse between: (0, 1), (0, 2), (0, 3), (1, 2), (1, 3), and (2, 3). A valid sequence of traversals exists for each pair, so we return true.
Constraints:
1 <= nums.length <= 1051 <= nums[i] <= 105
Solution
@Suppress("NAME_SHADOWING")
class Solution {
private var map: MutableMap<Int, Int>? = null
private lateinit var set: IntArray
private fun findParent(u: Int): Int {
return if (u == set[u]) u else findParent(set[u]).also { set[u] = it }
}
private fun union(a: Int, b: Int) {
val p1 = findParent(a)
val p2 = findParent(b)
if (p1 != p2) {
set[b] = p1
}
set[p2] = p1
}
private fun solve(n: Int, index: Int) {
var n = n
if (n % 2 == 0) {
val x = map!!.getOrDefault(2, -1)
if (x != -1) {
union(x, index)
}
while (n % 2 == 0) n /= 2
map!!.put(2, index)
}
val sqrt = kotlin.math.sqrt(n.toDouble()).toInt()
for (i in 3..sqrt) {
if (n % i == 0) {
val x = map!!.getOrDefault(i, -1)
if (x != -1) {
union(x, index)
}
while (n % i == 0) n /= i
map!!.put(i, index)
}
}
if (n > 2) {
val x = map!!.getOrDefault(n, -1)
if (x != -1) {
union(x, index)
}
map!!.put(n, index)
}
}
fun canTraverseAllPairs(nums: IntArray): Boolean {
set = IntArray(nums.size)
map = HashMap()
for (i in nums.indices) set[i] = i
for (i in nums.indices) solve(nums[i], i)
val p = findParent(0)
for (i in nums.indices) if (p != findParent(i)) return false
return true
}
}