Given the number, you are to answer the question: "Is it prime?"
Solutions to this problem can be submitted in C, C++, Pascal, Perl, Python, Ruby, Lisp, Hask, Ocaml, Prolog, Whitespace, Brainf**k and Intercal only.
Input
t – the number of test cases, then t test cases follows. [t <= 500]
Each line contains one integer: N [2 <= N <= 2^63-1]
Output
For each test case output string "YES" if given number is prime and "NO" otherwise.
Example
Input: 5 2 3 4 5 6 Output: YES YES NO YES NO
题目大意是说，给你一个能够用有符号64位整型存储的数，判断它是否是素数。
用费马小定理，多次随机生成一个底数a，然后n - 1次幂，判断模n意义下是否是1。
为了充分表示对rand()的嫌弃，于是手写了一个随机数生成器。详细请见[here]
Code
1 /**
2 * SPOJ
3 * Problem#PON
4 * Accepted
5 * Time:180ms
6 * Memory:15360k
7 */
8 #include<iostream>
9 #include<cstdio>
10 #include<cctype>
11 #include<cmath>
12 #include<ctime>
13 #include<cstring>
14 #include<cstdlib>
15 #include<fstream>
16 #include<sstream>
17 #include<algorithm>
18 #include<map>
19 #include<set>
20 #include<queue>
21 #include<vector>
22 #include<stack>
23 using namespace std;
24 typedef bool boolean;
25 #define INF 0xfffffff
26 #define smin(a, b) a = min(a, b)
27 #define smax(a, b) a = max(a, b)
28 template<typename T>
29 inline boolean readInteger(T& u){
30 char x;
31 int aFlag = 1;
32 while(!isdigit((x = getchar())) && x != ‘-‘ && x != -1);
33 if(x == -1) {
34 ungetc(x, stdin);
35 return false;
36 }
37 if(x == ‘-‘){
38 x = getchar();
39 aFlag = -1;
40 }
41 for(u = x - ‘0‘; isdigit((x = getchar())); u = (u << 1) + (u << 3) + x - ‘0‘);
42 ungetc(x, stdin);
43 u *= aFlag;
44 return true;
45 }
46
47 #define LL long long
48
49 typedef class Random {
50 public:
51 unsigned int pre;
52 unsigned int seed;
53
54 Random():pre(0), seed((unsigned) time (NULL)) { }
55 Random(int seed):pre(0), seed(seed) { }
56
57 /**
58 * Generate a random number.
59 * @return this function will return the random number it gernerated
60 */
61 unsigned int rand() {
62 // unsigned int ret = (seed * 7361238 + seed % 20037 * 1244 + pre * 12342 + 378211) * (seed + 134543);
63 // unsigned int ret = (seed * 7361238 + seed % 20037 * 1244 + pre * 12342 + 378211 + time(NULL) * pre) * (seed + 134543);
64 unsigned int ret;
65 if(ret & 1)
66 ret = (seed * 7361238 + seed % 20037 * 1245 + pre * 456451 + (time(NULL) * (pre * 5 + seed * 3 + 37)) + 156464);
67 else
68 ret = (seed * 7361238 + seed % 20037 * 1241 + pre * 456454 + (time(NULL) * (pre * 7 + seed * 3 + 18)) + 156464);
69 pre = seed;
70 seed = ret;
71 return ret;
72 }
73 }Random;
74
75 inline void setLLhighBit(long long& x, int a) {
76 int* p = (int*)&x;
77 *(p + 1) = a;
78 }
79
80 inline void setLLlowBit(long long& x, int a) {
81 int* p = (int*)&x;
82 *p = a;
83 }
84
85 inline void cleanLLSignFlag(long long& a) {
86 a &= (1ull << 63) - 1;
87 }
88
89 template<typename T>
90 T mul_mod(T a, T b, T& moder) {
91 if(b == 1) return a;
92 T temp = mul_mod(a, b >> 1, moder);
93 if(b & 1) return (((temp + temp) % moder) + a) % moder;
94 return (temp + temp) % moder;
95 }
96
97 template<typename T>
98 T pow_mod(T a, T pos, T& moder) {
99 if(pos == 1) return a;
100 T temp = pow_mod(a, pos >> 1, moder);
101 if(pos & 1) return mul_mod(mul_mod(temp, temp, moder), a, moder);
102 return mul_mod(temp, temp, moder);
103 }
104
105 int T;
106 LL n;
107 Random r;
108
109 inline void work() {
110 readInteger(n);
111 if((n & 1) == 0) {
112 if(n == 2) puts("YES");
113 else puts("NO");
114 return;
115 }
116 unsigned int l, h;
117 LL a, r1;
118 for(int t = 0; t < 20; t++) {
119 l = r.rand();
120 h = r.rand();
121 setLLhighBit(a, h);
122 setLLlowBit(a, l);
123 cleanLLSignFlag(a);
124 a = (a % (n - 2)) + 2;
125 r1 = pow_mod(a, n - 1, n);
126 if(r1 != 1) {
127 puts("NO");
128 return;
129 }
130 }
131 puts("YES");
132 }
133
134 int main() {
135 readInteger(T);
136 while(T--) {
137 work();
138 }
139 return 0;
140 }
时间： 2024-11-05 06:10:10