g1901_2000.s1994_the_number_of_good_subsets.Solution Maven / Gradle / Ivy
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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%)
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;
}
}