Task description：
A prime is a positive integer X that has exactly two distinct divisors: 1 and X. The first few prime integers are 2, 3, 5, 7, 11 and 13.
A semiprime is a natural number that is the product of two (not necessarily distinct) prime numbers. The first few semiprimes are 4, 6, 9, 10, 14, 15, 21, 22, 25, 26.
You are given two non-empty arrays P and Q, each consisting of M integers. These arrays represent queries about the number of semiprimes within specified ranges.
Query K requires you to find the number of semiprimes within the range (P[K], Q[K]), where 1 ≤ P[K] ≤ Q[K] ≤ N.
For example, consider an integer N = 26 and arrays P, Q such that:
P[0] = 1 Q[0] = 26 P[1] = 4 Q[1] = 10 P[2] = 16 Q[2] = 20The number of semiprimes within each of these ranges is as follows:
- (1, 26) is 10,
- (4, 10) is 4,
- (16, 20) is 0.
Write a function:
class Solution { public int[] solution(int N, int[] P, int[] Q); }
that, given an integer N and two non-empty arrays P and Q consisting of M integers, returns an array consisting of M elements specifying the consecutive answers to all the queries.
For example, given an integer N = 26 and arrays P, Q such that:
P[0] = 1 Q[0] = 26 P[1] = 4 Q[1] = 10 P[2] = 16 Q[2] = 20the function should return the values [10, 4, 0], as explained above.
Assume that:
- N is an integer within the range [1..50,000];
- M is an integer within the range [1..30,000];
- each element of arrays P, Q is an integer within the range [1..N];
- P[i] ≤ Q[i].
Complexity:
- expected worst-case time complexity is O(N*log(log(N))+M);
- expected worst-case space complexity is O(N+M), beyond input storage (not counting the storage required for input arguments).
Solution：
要求时间复杂度是O(N)我的显然是O（N**3）了，不过正确度测试是百分百
def solution(n,p,q):#1,26 找到1到26之间的半素数 1,4,6 26,10,20
maxv = max(max(p,q)) #find all the semiprime between 0 and the max integer of these two arrays
num=[]
semiprime=[]
semipq=[]
result=[]
for i in range(2,maxv):#find all primes between 2 and maxv
j=2
for j in range(2,i):
if(i%j==0):
break
else:
num.append(i)
for i in num: #find all semiprimes between 2 and maxv
for j in num:
if i*j not in semiprime:
semiprime.append(i*j)
for i,j in zip(p,q):
semipq=[]
for k in range(i,j+1):
if k in semiprime :
if k not in semipq:
semipq.append(k)
result.append(len(semipq))
return result