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挑战程序竞赛系列（15）：2.6快速幂运算
详细代码可以fork下Github上leetcode项目，不定期更新。
练习题如下：
- POJ 3641: Pseudoprime numbers
- POJ 1995: Raising Modulo Numbers
POJ 3641: Pseudoprime numbers
判断在当前基数a时，满足费马小定理的伪素数。
代码如下：
代码语言：javascript复制public static void main(String[] args) throws IOException {
Scanner in = new Scanner(System.in);
while (true) {
int p = in.nextInt();
int a = in.nextInt();
if (p == 0 && a == 0)
break;
if (a != quickPow(a, p, p)){
System.out.println("no");
continue;
}
if (isPrime(p)) System.out.println("no");
else System.out.println("yes");
}
}
public static boolean isPrime(int num){
for (int i = 2; i * i <= num; i){
if (num % i == 0) return false;
}
return true;
}
public static long quickMul(long a, long b, long mod) {
long ans = 0;
while (b != 0) {
if ((b & 1) != 0) {
ans = (ans a) % mod;
}
b >>= 1;
a = (a a) % mod;
}
return ans;
}
public static long quickPow(long a, long b, long mod) {
long ans = 1;
while (b != 0) {
if ((b & 1) != 0) {
ans = quickMul(ans, a, mod);
}
b >>= 1;
a = quickMul(a, a, mod);
}
return ans;
}POJ 1995: Raising Modulo Numbers
取模运算，水题。
代码如下：
代码语言：javascript复制public static void main(String[] args) throws IOException {
Scanner in = new Scanner(System.in);
int Z = in.nextInt();
while ((Z--) != 0){
int M = in.nextInt();
int N = in.nextInt();
long ans = 0;
for (int i = 0; i < N; i){
long a = in.nextLong();
long b = in.nextLong();
ans = (ans quickPow(a, b, M)) % M;
}
System.out.println(ans);
}
}
public static long quickMul(long a, long b, long mod){
long res = 0;
while (b != 0){
if ((b & 1) != 0){
res = (res a) % mod;
}
b >>= 1;
a = (a a) % mod;
}
return res;
}
public static long quickPow(long a, long b, long mod){
long res = 1;
while (b != 0){
if ((b & 1) != 0){
res = quickMul(res, a, mod);
}
b >>= 1;
a = quickMul(a, a, mod);
}
return res;
}
