一、 最大公约数的写法:
int gcd(int a, int b){
return !b ? a : gcd(b, a % b);
}
二、 最小公倍数的写法:
//实质是在得到最大公约数的基础上求解
得到最大公约数d后,最小公倍数等于ab/d
int lcm(int a, int b){
return a / gcd(a, b) * b;
}
三、分数的四则运算:
//1.分数的表示与化简
struct Fraction{
int up, down;
};
Fraction reduction(Fraction result){
if(result.down < 0){
result.up = -result.up;
result.down = -result.down;
}
if(result.up == 0){
result.down = 1;
}else{
int d = gcd(abs(result.up), abs(result.down));
result.up /= d;
result.down /= d;
}
return result;
}
//2.分数加法
Fraction add(Fraction f1, Fraction f2){
Fraction result;
result.up = f1.up * f2.down + f1.down * f2.up;
result.down = f1.down * f2.down;
return reduction(result);
}
//3.分数减法
Fraction minu(Fraction f1, Fraction f2){
Fraction result;
result.up = f1.up * f2.down - f1.down * f2.up;
result.down = f1.down * f2.down;
return reduction(result);
}
//4.分数乘法
Fraction multi(Fraction f1, Fraction f2){
Fraction result;
result.up = f1.up * f2.up;
result.down = f1.down * f2.down;
return reduction(result);
}
//5.分数除法
Fraction divide(Fraction f1, Fraction f2){
Fraction result;
result.up = f1.up * f2.down;
result.down = f1.down * f2.up;
return reduction(result);
}
//分数的输出
void showResult(Fraction r){
r = reduction(r);
if(r.down == 1) printf("%lld", r.up);
else if(abs(r.up) > r.down){
printf("%d %d/%d", r.up / r.down, abs(r.up) % r.down, r.down);
}else{
printf("%d/%d", r.up, r.down);
}
}
四、素数:是指除了1和本身之外,不能被其他数整除的一类数;1既不是素数,也不是合数;
//1.素数的判断
bool isPrime(int n){
if(n <= 1) return false;
//int sqr = (int)sqrt(1.0 * n);
for(int i = 2; i <= n; i++){
if(n % i == 0) return false;
}
return true;
}
//2.素数表的获取
const int maxn = 101;//表长
int prime[maxn], pNum = 0;//prime数组存放所有素数,pNum为素数个数
bool p[maxn] = {0};//p[i] == true表示i是素数
void Find_Prime(){
for(int i = 0; i < maxn; i++){
if(isPrime(i) == true){
prime[pNum++] = i;
p[i] = true;
}
}
}
void Find_Prime(){
for(int i = 2; i < maxn; i++){
if(p[i] == false){
prime[pNum++] = i;
for(int j = i + i; j < maxn; j += i){
p[j] = true;
}
}
}
}
五、质因子分解
#include<iostream>
#include<cmath>
using namespace std;
const int maxn = 100010;
bool isPrime(int n){
if(n <= 1) return false;
int sqr = (int)sqrt(1.0 * n);
for(int i = 2; i <= sqr; i++){
if(n % i == 0) return false;
}
return true;
}
int prime[maxn], pNum = 0;
void Find_Prime(){
for(int i = 1; i < maxn; i++){
if(isPrime(i) == true){
prime[pNum++] = i;
}
}
}
struct factor{
int x, cnt;
}fac[10];
int main(){
Find_Prime();
int n, num = 0;
scanf("%d", &n);
if(n == 1) printf("1=1");
else{
printf("%d=", n);
int sqr = (int)sqrt(1.0*n);
//
for(int i = 0; i < pNum && prime[i] <= sqr; i++){
if(n % prime[i] == 0){
fac[num].x = prime[i];
fac[num].cnt = 0;
while(n % prime[i] == 0){
fac[num].cnt++;
n /= prime[i];
}
num++;
}
if(n == 1) break;
}
if(n != 1){
fac[num].x = n;
fac[num++].cnt = 1;
}
for(int i = 0; i < num; i++){
if(i > 0) printf("*");
printf("%d", fac[i].x);
if(fac[i].cnt > 1){
printf("^%d", fac[i].cnt);
}
}
}
//
return 0;
}