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Formatted question description: https://leetcode.ca/all/2584.html

2584. Split the Array to Make Coprime Products

Description

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.

 

Example 1:

Input: nums = [4,7,8,15,3,5]
Output: 2
Explanation: 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
Explanation: 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 <= 104
• 1 <= nums[i] <= 106

Solutions

• Java
• C++
• Python
• Go

• class Solution {
      public int findValidSplit(int[] nums) {
          Map<Integer, Integer> first = new HashMap<>();
          int n = nums.length;
          int[] last = new int[n];
          for (int i = 0; i < n; ++i) {
              last[i] = i;
          }
          for (int i = 0; i < n; ++i) {
              int x = nums[i];
              for (int j = 2; j <= x / j; ++j) {
                  if (x % j == 0) {
                      if (first.containsKey(j)) {
                          last[first.get(j)] = i;
                      } else {
                          first.put(j, i);
                      }
                      while (x % j == 0) {
                          x /= j;
                      }
                  }
              }
              if (x > 1) {
                  if (first.containsKey(x)) {
                      last[first.get(x)] = i;
                  } else {
                      first.put(x, i);
                  }
              }
          }
          int mx = last[0];
          for (int i = 0; i < n; ++i) {
              if (mx < i) {
                  return mx;
              }
              mx = Math.max(mx, last[i]);
          }
          return -1;
      }
  }
  

• class Solution {
  public:
      int findValidSplit(vector<int>& nums) {
          unordered_map<int, int> first;
          int n = nums.size();
          vector<int> last(n);
          iota(last.begin(), last.end(), 0);
          for (int i = 0; i < n; ++i) {
              int x = nums[i];
              for (int j = 2; j <= x / j; ++j) {
                  if (x % j == 0) {
                      if (first.count(j)) {
                          last[first[j]] = i;
                      } else {
                          first[j] = i;
                      }
                      while (x % j == 0) {
                          x /= j;
                      }
                  }
              }
              if (x > 1) {
                  if (first.count(x)) {
                      last[first[x]] = i;
                  } else {
                      first[x] = i;
                  }
              }
          }
          int mx = last[0];
          for (int i = 0; i < n; ++i) {
              if (mx < i) {
                  return mx;
              }
              mx = max(mx, last[i]);
          }
          return -1;
      }
  };
  

• class Solution:
      def findValidSplit(self, nums: List[int]) -> int:
          first = {}
          n = len(nums)
          last = list(range(n))
          for i, x in enumerate(nums):
              j = 2
              while j <= x // j:
                  if x % j == 0:
                      if j in first:
                          last[first[j]] = i
                      else:
                          first[j] = i
                      while x % j == 0:
                          x //= j
                  j += 1
              if x > 1:
                  if x in first:
                      last[first[x]] = i
                  else:
                      first[x] = i
          mx = last[0]
          for i, x in enumerate(last):
              if mx < i:
                  return mx
              mx = max(mx, x)
          return -1
  
  

• func findValidSplit(nums []int) int {
  	first := map[int]int{}
  	n := len(nums)
  	last := make([]int, n)
  	for i := range last {
  		last[i] = i
  	}
  	for i, x := range nums {
  		for j := 2; j <= x/j; j++ {
  			if x%j == 0 {
  				if k, ok := first[j]; ok {
  					last[k] = i
  				} else {
  					first[j] = i
  				}
  				for x%j == 0 {
  					x /= j
  				}
  			}
  		}
  		if x > 1 {
  			if k, ok := first[x]; ok {
  				last[k] = i
  			} else {
  				first[x] = i
  			}
  		}
  	}
  	mx := last[0]
  	for i, x := range last {
  		if mx < i {
  			return mx
  		}
  		mx = max(mx, x)
  	}
  	return -1
  }
  
  func max(a, b int) int {
  	if a > b {
  		return a
  	}
  	return b
  }
  

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