Class Solution
Hard
You are given an integer array nums
. We call a subset of nums
good if its product can be represented as a product of one or more distinct prime numbers.
- For example, if
nums = [1, 2, 3, 4]
:[2, 3]
,[1, 2, 3]
, and[1, 3]
are good subsets with products6 = 2*3
,6 = 2*3
, and3 = 3
respectively.[1, 4]
and[4]
are not good subsets with products4 = 2*2
and4 = 2*2
respectively.
Return the number of different good subsets in nums
modulo 109 + 7
.
A subset of nums
is any array that can be obtained by deleting some (possibly none or all) elements from nums
. Two subsets are different if and only if the chosen indices to delete are different.
Example 1:
Input: nums = [1,2,3,4]
Output: 6
Explanation: The good subsets are:
-
[1,2]: product is 2, which is the product of distinct prime 2.
-
[1,2,3]: product is 6, which is the product of distinct primes 2 and 3.
-
[1,3]: product is 3, which is the product of distinct prime 3.
-
[2]: product is 2, which is the product of distinct prime 2.
-
[2,3]: product is 6, which is the product of distinct primes 2 and 3.
-
[3]: product is 3, which is the product of distinct prime 3.
Example 2:
Input: nums = [4,2,3,15]
Output: 5
Explanation: The good subsets are:
-
[2]: product is 2, which is the product of distinct prime 2.
-
[2,3]: product is 6, which is the product of distinct primes 2 and 3.
-
[2,15]: product is 30, which is the product of distinct primes 2, 3, and 5.
-
[3]: product is 3, which is the product of distinct prime 3.
-
[15]: product is 15, which is the product of distinct primes 3 and 5.
Constraints:
1 <= nums.length <= 105
1 <= nums[i] <= 30
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Constructor Summary
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Method Summary
Methods inherited from class java.lang.Object
clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait
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Constructor Details
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Solution
public Solution()
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Method Details
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numberOfGoodSubsets
public int numberOfGoodSubsets(int[] nums)
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