![JAR search and dependency download from the Maven repository](/logo.png)
g1901_2000.s1994_the_number_of_good_subsets.Solution Maven / Gradle / Ivy
Go to download
Show more of this group Show more artifacts with this name
Show all versions of leetcode-in-java21 Show documentation
Show all versions of leetcode-in-java21 Show documentation
Java-based LeetCode algorithm problem solutions, regularly updated
package g1901_2000.s1994_the_number_of_good_subsets;
// #Hard #Array #Dynamic_Programming #Math #Bit_Manipulation #Bitmask
// #2022_05_12_Time_15_ms_(94.29%)_Space_125_MB_(11.43%)
/**
* 1994 - The Number of Good Subsets\.
*
* 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 products `6 = 2*3`, `6 = 2*3`, and `3 = 3` respectively.
* * `[1, 4]` and `[4]` are not **good** subsets with products `4 = 2*2` and `4 = 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`
**/
public class Solution {
private static final long MOD = (long) (1e9 + 7);
private long add(long a, long b) {
a += b;
return a < MOD ? a : a - MOD;
}
private long mul(long a, long b) {
a *= b;
return a < MOD ? a : a % MOD;
}
private long pow(long a, long b) {
// a %= MOD;
// b%=(MOD-1);//if MOD is prime
long res = 1;
while (b > 0) {
if ((b & 1) == 1) {
res = mul(res, a);
}
a = mul(a, a);
b >>= 1;
}
return add(res, 0);
}
public int numberOfGoodSubsets(int[] nums) {
int[] primes = {2, 3, 5, 7, 11, 13, 17, 19, 23, 29};
int[] mask = new int[31];
int[] freq = new int[31];
for (int x : nums) {
freq[x]++;
}
for (int i = 1; i <= 30; i++) {
for (int j = 0; j < primes.length; j++) {
if (i % primes[j] == 0) {
if ((i / primes[j]) % primes[j] == 0) {
mask[i] = 0;
break;
}
mask[i] |= (int) pow(2, j);
}
}
}
long[] dp = new long[1024];
dp[0] = 1;
for (int i = 1; i <= 30; i++) {
if (mask[i] != 0) {
for (int j = 0; j < 1024; j++) {
if ((mask[i] & j) == 0 && dp[j] > 0) {
dp[(mask[i] | j)] = add(dp[(mask[i] | j)], mul(dp[j], freq[i]));
}
}
}
}
long ans = 0;
for (int i = 1; i < 1024; i++) {
ans = add(ans, dp[i]);
}
ans = mul(ans, pow(2, freq[1]));
ans = add(ans, 0);
return (int) ans;
}
}