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2436. Minimum Split Into Subarrays With GCD Greater Than One

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Description

You are given an array nums consisting of positive integers.

Split the array into one or more disjoint subarrays such that:

• Each element of the array belongs to exactly one subarray, and
• The GCD of the elements of each subarray is strictly greater than 1.

Return the minimum number of subarrays that can be obtained after the split.

Note that:

• The GCD of a subarray is the largest positive integer that evenly divides all the elements of the subarray.
• A subarray is a contiguous part of the array.

 

Example 1:

Input: nums = [12,6,3,14,8]
Output: 2
Explanation: We can split the array into the subarrays: [12,6,3] and [14,8].
- The GCD of 12, 6 and 3 is 3, which is strictly greater than 1.
- The GCD of 14 and 8 is 2, which is strictly greater than 1.
It can be shown that splitting the array into one subarray will make the GCD = 1.

Example 2:

Input: nums = [4,12,6,14]
Output: 1
Explanation: We can split the array into only one subarray, which is the whole array.

 

Constraints:

• 1 <= nums.length <= 2000
• 2 <= nums[i] <= 109

Solutions

Python3

class Solution:
    def minimumSplits(self, nums: List[int]) -> int:
        ans, g = 1, 0
        for x in nums:
            g = gcd(g, x)
            if g == 1:
                ans += 1
                g = x
        return ans

Java

class Solution {
    public int minimumSplits(int[] nums) {
        int ans = 1, g = 0;
        for (int x : nums) {
            g = gcd(g, x);
            if (g == 1) {
                ++ans;
                g = x;
            }
        }
        return ans;
    }

    private int gcd(int a, int b) {
        return b == 0 ? a : gcd(b, a % b);
    }
}

C++

class Solution {
public:
    int minimumSplits(vector<int>& nums) {
        int ans = 1, g = 0;
        for (int x : nums) {
            g = gcd(g, x);
            if (g == 1) {
                ++ans;
                g = x;
            }
        }
        return ans;
    }
};

Go

func minimumSplits(nums []int) int {
	ans, g := 1, 0
	for _, x := range nums {
		g = gcd(g, x)
		if g == 1 {
			ans++
			g = x
		}
	}
	return ans
}

func gcd(a, b int) int {
	if b == 0 {
		return a
	}
	return gcd(b, a%b)
}

TypeScript

function minimumSplits(nums: number[]): number {
    let ans = 1;
    let g = 0;
    for (const x of nums) {
        g = gcd(g, x);
        if (g == 1) {
            ++ans;
            g = x;
        }
    }
    return ans;
}

function gcd(a: number, b: number): number {
    return b ? gcd(b, a % b) : a;
}

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