在本教程中,我们将讨论使用中学程序查找两个数字的GCD或HCF的程序。
为此,我们将提供两个数字。我们的任务是找到给定值的GCD(最大公约数)或HCF(最高公因数)。
#include <bits/stdc++.h> #define MAXFACTORS 1024 using namespace std; //存储因式分解的结构 typedef struct{ int size; int factor[MAXFACTORS + 1]; int exponent[MAXFACTORS + 1]; } FACTORIZATION; void FindFactorization(int x, FACTORIZATION* factorization){ int i, j = 1; int n = x, c = 0; int k = 1; factorization->factor[0] = 1; factorization->exponent[0] = 1; for (i = 2; i <= n; i++) { c = 0; while (n % i == 0) { c++; n = n / i; } if (c > 0) { factorization->exponent[k] = c; factorization->factor[k] = i; k++; } } factorization->size = k - 1; } //打印因素 void DisplayFactorization(int x, FACTORIZATION factorization){ int i; cout << "Prime factor of << x << = "; for (i = 0; i <= factorization.size; i++) { cout << factorization.factor[i]; if (factorization.exponent[i] > 1) cout << "^" << factorization.exponent[i]; if (i < factorization.size) cout << "*"; else cout << "\n"; } } //使用中学程序的gcd- int gcdMiddleSchoolProcedure(int m, int n){ FACTORIZATION mFactorization, nFactorization; int r, mi, ni, i, k, x = 1, j; FindFactorization(m, &mFactorization); DisplayFactorization(m, mFactorization); FindFactorization(n, &nFactorization); DisplayFactorization(n, nFactorization); int min; i = 1; j = 1; while (i <= mFactorization.size && j <= nFactorization.size) { if (mFactorization.factor[i] < nFactorization.factor[j]) i++; else if (nFactorization.factor[j] < mFactorization.factor[i]) j++; else{ min = mFactorization.exponent[i] > nFactorization.exponent[j] ? nFactorization.exponent[j] : mFactorization.exponent[i]; x = x * mFactorization.factor[i] * min; i++; j++; } } return x; } int main(){ int m = 10, n = 15; cout << "GCD(" << m << ", " << n << ") = " << gcdMiddleSchoolProcedure(m, n); return (0); }
输出结果
GCD(10, 15) = Prime factor of << x << = 1*2*5 Prime factor of << x << = 1*3*5 5