B.华华教月月做题--牛客小白月赛12 （快速幂+快速乘 或 大整数 或__int128）
链接：https://ac.nowcoder.com/acm/contest/392/B
来源：牛客网
时间限制：C/C++ 1秒，其他语言2秒
空间限制：C/C++ 32768K，其他语言65536K
64bit IO Format: %lld
题目描述
找到了心仪的小姐姐月月后，华华很高兴的和她聊着天。然而月月的作业很多，不能继续陪华华聊天了。华华为了尽快和月月继续聊天，就提出帮她做一部分作业。
月月的其中一项作业是：给定正整数A、B、P，求ABmodPABmodP的值。华华觉得这实在是毫无意义，所以决定写一个程序来做。但是华华并不会写程序，所以这个任务就交给你了。
因为月月的作业很多，所以有T组询问。
输入描述:
第一行一个正整数T表示测试数据组数。 接下来T行，每行三个正整数A、B、P，含义如上文。
输出描述:
输出T行，每行一个非负整数表示答案。
示例1
输入
复制
2 2 5 10 57284938291657 827493857294857 384729583748273
输出
复制
2 18924650048745
备注:
1≤T≤10^3，1≤A,B,P≤10^18
题意：求A^B%P 显然直接乘会爆long long
解法一：快速幂+快速乘
附代码：
#include
using namespace std;
typedef long long ll;
const double eps=1.0e-5;
const int maxn=200000+10;
const ll mod=1e9+7;
ll quick_mul(ll a,ll b,ll c)
{
ll ans=0;
while(b){
if(b&1) ans=(ans+a)%c;
a=(a+a)%c;
b>>=1;
}
return ans;
}
ll quick_pow(ll a,ll b,ll c)
{
ll ans=1;
while(b){
if(b&1) ans=quick_mul(ans,a,c);
a=quick_mul(a,a,c);
b>>=1;
}
return ans;
}
int t;
ll a,b,c;
int main()
{
scanf("%d",&t);
while(t--){
scanf("%lld %lld %lld",&a,&b,&c);
printf("%lld\n",quick_pow(a,b,c));
}
}
解法二：__int128 +快速幂 （需要手写输入输出
附代码：
#include
using namespace std;
template
E quick_pow(E a,E b,E c){
E ans=1;
while(b){
if(b&1) ans=ans*a%c;
a=a*a%c;b/=2;
}
return ans;
}
void scan(__int128 &x)//输入
{
x = 0;
int f = 1;
char ch;
if((ch = getchar()) == '-') f = -f;
else x = x*10 + ch-'0';
while((ch = getchar()) >= '0' && ch <= '9')
x = x*10 + ch-'0';
x *= f;
}
void _print(__int128 x)
{
if(x > 9) _print(x/10);
putchar(x%10 + '0');
}
void print(__int128 x)//输出
{
if(x < 0)
{
x = -x;
putchar('-');
}
_print(x);
}
int main()
{
__int128 t;scan(t);
while(t--){
__int128 a, b,c;
scan(a); scan(b);scan(c);
print(quick_pow(a,b,c));
printf("\n");
}
}
解法三：C++大整数类 + 快速幂
附代码：
#include
#define ll long long
using namespace std;
constexpr int base = 1000000000;
constexpr int base_digits = 9;
struct bigint {
// value == 0 is represented by empty z
vector z; // digits
// sign == 1 <==> value >= 0
// sign == -1 <==> value < 0
int sign;
bigint() : sign(1) {}
bigint(long long v) {
*this = v;
}
bigint& operator=(long long v) {
sign = v < 0 ? -1 : 1;
v *= sign;
z.clear();
for (; v > 0; v = v / base)
z.push_back((int)(v % base));
return *this;
}
bigint(const string& s) {
read(s);
}
bigint& operator+=(const bigint& other) {
if (sign == other.sign) {
for (int i = 0, carry = 0; i < other.z.size() || carry; ++i) {
if (i == z.size())
z.push_back(0);
z[i] += carry + (i < other.z.size() ? other.z[i] : 0);
carry = z[i] >= base;
if (carry)
z[i] -= base;
}
} else if (other != 0 /* prevent infinite loop */) {
*this -= -other;
}
return *this;
}
friend bigint operator+(bigint a, const bigint& b) {
return a += b;
}
bigint& operator-=(const bigint& other) {
if (sign == other.sign) {
if (sign == 1 && *this >= other || sign == -1 && *this <= other) {
for (int i = 0, carry = 0; i < other.z.size() || carry; ++i) {
z[i] -= carry + (i < other.z.size() ? other.z[i] : 0);
carry = z[i] < 0;
if (carry)
z[i] += base;
}
trim();
} else {
*this = other - *this;
this->sign = -this->sign;
}
} else {
*this += -other;
}
return *this;
}
friend bigint operator-(bigint a, const bigint& b) {
return a -= b;
}
bigint& operator*=(int v) {
if (v < 0)
sign = -sign, v = -v;
for (int i = 0, carry = 0; i < z.size() || carry; ++i) {
if (i == z.size())
z.push_back(0);
long long cur = (long long)z[i] * v + carry;
carry = (int)(cur / base);
z[i] = (int)(cur % base);
}
trim();
return *this;
}
bigint operator*(int v) const {
return bigint(*this) *= v;
}
friend pair divmod(const bigint& a1, const bigint& b1) {
int norm = base / (b1.z.back() + 1);
bigint a = a1.abs() * norm;
bigint b = b1.abs() * norm;
bigint q, r;
q.z.resize(a.z.size());
for (int i = (int)a.z.size() - 1; i >= 0; i--) {
r *= base;
r += a.z[i];
int s1 = b.z.size() < r.z.size() ? r.z[b.z.size()] : 0;
int s2 = b.z.size() - 1 < r.z.size() ? r.z[b.z.size() - 1] : 0;
int d = (int)(((long long)s1 * base + s2) / b.z.back());
r -= b * d;
while (r < 0)
r += b, --d;
q.z[i] = d;
}
q.sign = a1.sign * b1.sign;
r.sign = a1.sign;
q.trim();
r.trim();
return {q, r / norm};
}
friend bigint sqrt(const bigint& a1) {
bigint a = a1;
while (a.z.empty() || a.z.size() % 2 == 1)
a.z.push_back(0);
int n = a.z.size();
int firstDigit = (int)::sqrt((double)a.z[n - 1] * base + a.z[n - 2]);
int norm = base / (firstDigit + 1);
a *= norm;
a *= norm;
while (a.z.empty() || a.z.size() % 2 == 1)
a.z.push_back(0);
bigint r = (long long)a.z[n - 1] * base + a.z[n - 2];
firstDigit = (int)::sqrt((double)a.z[n - 1] * base + a.z[n - 2]);
int q = firstDigit;
bigint res;
for (int j = n / 2 - 1; j >= 0; j--) {
for (;; --q) {
bigint r1 = (r - (res * 2 * base + q) * q) * base * base + (j > 0 ? (long long)a.z[2 * j - 1] * base + a.z[2 * j - 2] : 0);
if (r1 >= 0) {
r = r1;
break;
}
}
res *= base;
res += q;
if (j > 0) {
int d1 = res.z.size() + 2 < r.z.size() ? r.z[res.z.size() + 2] : 0;
int d2 = res.z.size() + 1 < r.z.size() ? r.z[res.z.size() + 1] : 0;
int d3 = res.z.size() < r.z.size() ? r.z[res.z.size()] : 0;
q = (int)(((long long)d1 * base * base + (long long)d2 * base + d3) / (firstDigit * 2));
}
}
res.trim();
return res / norm;
}
bigint operator/(const bigint& v) const {
return divmod(*this, v).first;
}
bigint operator%(const bigint& v) const {
return divmod(*this, v).second;
}
bigint& operator/=(int v) {
if (v < 0)
sign = -sign, v = -v;
for (int i = (int)z.size() - 1, rem = 0; i >= 0; --i) {
long long cur = z[i] + rem * (long long)base;
z[i] = (int)(cur / v);
rem = (int)(cur % v);
}
trim();
return *this;
}
bigint operator/(int v) const {
return bigint(*this) /= v;
}
int operator%(int v) const {
if (v < 0)
v = -v;
int m = 0;
for (int i = (int)z.size() - 1; i >= 0; --i)
m = (int)((z[i] + m * (long long)base) % v);
return m * sign;
}
bigint& operator*=(const bigint& v) {
*this = *this * v;
return *this;
}
bigint& operator/=(const bigint& v) {
*this = *this / v;
return *this;
}
bool operator<(const bigint& v) const {
if (sign != v.sign)
return sign < v.sign;
if (z.size() != v.z.size())
return z.size() * sign < v.z.size() * v.sign;
for (int i = (int)z.size() - 1; i >= 0; i--)
if (z[i] != v.z[i])
return z[i] * sign < v.z[i] * sign;
return false;
}
bool operator>(const bigint& v) const {
return v < *this;
}
bool operator<=(const bigint& v) const {
return !(v < *this);
}
bool operator>=(const bigint& v) const {
return !(*this < v);
}
bool operator==(const bigint& v) const {
return !(*this < v) && !(v < *this);
}
bool operator!=(const bigint& v) const {
return *this < v || v < *this;
}
void trim() {
while (!z.empty() && z.back() == 0)
z.pop_back();
if (z.empty())
sign = 1;
}
bool isZero() const {
return z.empty();
}
friend bigint operator-(bigint v) {
if (!v.z.empty())
v.sign = -v.sign;
return v;
}
bigint abs() const {
return sign == 1 ? *this : -*this;
}
long long longValue() const {
long long res = 0;
for (int i = (int)z.size() - 1; i >= 0; i--)
res = res * base + z[i];
return res * sign;
}
friend bigint gcd(const bigint& a, const bigint& b) {
return b.isZero() ? a : gcd(b, a % b);
}
friend bigint lcm(const bigint& a, const bigint& b) {
return a / gcd(a, b) * b;
}
void read(const string& s) {
sign = 1;
z.clear();
int pos = 0;
while (pos < s.size() && (s[pos] == '-' || s[pos] == '+')) {
if (s[pos] == '-')
sign = -sign;
++pos;
}
for (int i = (int)s.size() - 1; i >= pos; i -= base_digits) {
int x = 0;
for (int j = max(pos, i - base_digits + 1); j <= i; j++)
x = x * 10 + s[j] - '0';
z.push_back(x);
}
trim();
}
friend istream& operator>>(istream& stream, bigint& v) {
string s;
stream >> s;
v.read(s);
return stream;
}
friend ostream& operator<<(ostream& stream, const bigint& v) {
if (v.sign == -1)
stream << '-';
stream << (v.z.empty() ? 0 : v.z.back());
for (int i = (int)v.z.size() - 2; i >= 0; --i)
stream << setw(base_digits) << setfill('0') << v.z[i];
return stream;
}
static vector convert_base(const vector& a, int old_digits, int new_digits) {
vector p(max(old_digits, new_digits) + 1);
p[0] = 1;
for (int i = 1; i < p.size(); i++)
p[i] = p[i - 1] * 10;
vector res;
long long cur = 0;
int cur_digits = 0;
for (int v : a) {
cur += v * p[cur_digits];
cur_digits += old_digits;
while (cur_digits >= new_digits) {
res.push_back(int(cur % p[new_digits]));
cur /= p[new_digits];
cur_digits -= new_digits;
}
}
res.push_back((int)cur);
while (!res.empty() && res.back() == 0)
res.pop_back();
return res;
}
typedef vector vll;
static vll karatsubaMultiply(const vll& a, const vll& b) {
int n = a.size();
vll res(n + n);
if (n <= 32) {
for (int i = 0; i < n; i++)
for (int j = 0; j < n; j++)
res[i + j] += a[i] * b[j];
return res;
}
int k = n >> 1;
vll a1(a.begin(), a.begin() + k);
vll a2(a.begin() + k, a.end());
vll b1(b.begin(), b.begin() + k);
vll b2(b.begin() + k, b.end());
vll a1b1 = karatsubaMultiply(a1, b1);
vll a2b2 = karatsubaMultiply(a2, b2);
for (int i = 0; i < k; i++)
a2[i] += a1[i];
for (int i = 0; i < k; i++)
b2[i] += b1[i];
vll r = karatsubaMultiply(a2, b2);
for (int i = 0; i < a1b1.size(); i++)
r[i] -= a1b1[i];
for (int i = 0; i < a2b2.size(); i++)
r[i] -= a2b2[i];
for (int i = 0; i < r.size(); i++)
res[i + k] += r[i];
for (int i = 0; i < a1b1.size(); i++)
res[i] += a1b1[i];
for (int i = 0; i < a2b2.size(); i++)
res[i + n] += a2b2[i];
return res;
}
bigint operator*(const bigint& v) const {
vector a6 = convert_base(this->z, base_digits, 6);
vector b6 = convert_base(v.z, base_digits, 6);
vll a(a6.begin(), a6.end());
vll b(b6.begin(), b6.end());
while (a.size() < b.size())
a.push_back(0);
while (b.size() < a.size())
b.push_back(0);
while (a.size() & (a.size() - 1))
a.push_back(0), b.push_back(0);
vll c = karatsubaMultiply(a, b);
bigint res;
res.sign = sign * v.sign;
for (int i = 0, carry = 0; i < c.size(); i++) {
long long cur = c[i] + carry;
res.z.push_back((int)(cur % 1000000));
carry = (int)(cur / 1000000);
}
res.z = convert_base(res.z, 6, base_digits);
res.trim();
return res;
}
};
bigint quick_qow(bigint a,bigint b,bigint p)///快速幂 a^b %p
{
bigint ans=1;
for(;b>0;b/=2)
{
if(b%2==1)
ans=(ans*a)%p ;
a=a*a%p ;
}
return ans%p;
}
int main(){
int t;
cin>>t;
while(t--){
bigint a,b,c;
cin>>a>>b>>c;
bigint ans=quick_qow(a,b,c);
cout<