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| // @Title: 好子集的数目 (The Number of Good Subsets)
// @Author: 15816537946@163.com
// @Date: 2022-02-22 15:26:55
// @Runtime: 196 ms
// @Memory: 8.1 MB
var primes = []int{2, 3, 5, 7, 11, 13, 17, 19, 23, 29}
func numberOfGoodSubsets(nums []int) (ans int) {
const mod int = 1e9 + 7
freq := [31]int{}
for _, num := range nums {
freq[num]++
}
f := make([]int, 1<<len(primes))
f[0] = 1
for i := 0; i < freq[1]; i++ {
f[0] = f[0] * 2 % mod
}
next:
for i := 2; i < 31; i++ {
if freq[i] == 0 {
continue
}
// 检查 i 的每个质因数是否均不超过 1 个
subset := 0
for j, prime := range primes {
if i%(prime*prime) == 0 {
continue next
}
if i%prime == 0 {
subset |= 1 << j
}
}
// 动态规划
for mask := 1 << len(primes); mask > 0; mask-- {
if mask&subset == subset {
f[mask] = (f[mask] + f[mask^subset]*freq[i]) % mod
}
}
}
for _, v := range f[1:] {
ans = (ans + v) % mod
}
return
}
|