Split the Array to Make Coprime Products

arrayhash tablemath

Problem Statement

You are given a 0-indexed integer array nums of length n .

A split at an index i where 0 <= i <= n - 2 is called valid if the product of the first i + 1 elements and the product of the remaining elements are coprime.

For example, if nums = [2, 3, 3] , then a split at the index i = 0 is valid because 2 and 9 are coprime, while a split at the index i = 1 is not valid because 6 and 3 are not coprime. A split at the index i = 2 is not valid because i == n - 1 .

Return the smallest index i at which the array can be split validly or -1 if there is no such split .

Two values val1 and val2 are coprime if gcd(val1, val2) == 1 where gcd(val1, val2) is the greatest common divisor of val1 and val2 .

Examples

Example 1

Input: nums = [4,7,8,15,3,5]
Output: 2
The table above shows the values of the product of the first i + 1 elements, the remaining elements, and their gcd at each index i.
The only valid split is at index 2.

Example 2

Input: nums = [4,7,15,8,3,5]
Output: -1
The table above shows the values of the product of the first i + 1 elements, the remaining elements, and their gcd at each index i.
There is no valid split.

Constraints

n == nums.length

1 <= n <= 10 ^4

1 <= nums[i] <= 10 ^6

😤

Hard

Difficulty

Topic Info

ModuleDSA

CategoryArray

Sub-topicHash Table