C++ 大數乘法?分別包括?普通大數乘法、分治法大數乘法、改進的分治法大數乘法。

#include<iostream> #include<iomanip> #include<random> #include<ctime> #include<cmath> using namespace std;int randint(int a, int b); int* rand_num(int n); void show_num(int* c, int n); void multiply_normal(int* c1, int* c2, int n, int flag); void multiply_n(int* c1, int* c2, int n, int flag); int bit_number(int* c, int n); int* high_num_2(int* c, int n); int* low_num_2(int* c, int n); void add_list(int* c1, int* c2, int n, int m); int* multiply_partition(int* c1, int* c2, int n); int* x_y(int c1, int c2); void multiply_p(int* c1, int* c2, int n, int f); void sub_list(int* c1, int* c2, int n, int m);int* multiply_partition_enhanced(int* c1, int* c2, int n); void multiply_p_e(int* c1, int* c2, int n, int f);int main() {cout << "輸入數字位數 n = ";int n;cin >> n;cout << endl;//生成兩個隨機 n 位數int* c1 = NULL;int* c2 = NULL;c1 = rand_num(n);c2 = rand_num(n);//show_num(c1, n);//show_num(c2, n);//cout <<"正確乘積： " << bit_number(c1, n) * bit_number(c2, n) << endl;//int a1[] = { 1, 2, 3, 4, 5, 6 };//int a2[] = { 3,6,8 };//show_num(a1, 6);//show_num(a2, 3);//sub_list(a1, a2, 3, 1);//show_num(a1, 6);cout << "是否顯示乘積結果？ 是：1； 否：0 ";int flag = 0;cout<< "flag = ";cin >> flag;cout << endl;multiply_n(c1, c2, n, flag);multiply_p(c1, c2, n, flag);multiply_p_e(c1, c2, n, flag);delete[]c1;delete[]c2;return 0; }int randint(int a, int b) {random_device rd;default_random_engine eng(rd());uniform_int_distribution<int> distr1(a, b);//均勻分布的方式產生隨機數return distr1(eng); }int* rand_num(int n) {int* c = new int[n];for (int i = 0; i < n - 1; i++){c[i] = randint(0, 9);}c[n - 1] = randint(1, 9);return c; }void show_num(int* c, int n) {/*cout << "生成的數字為：";*/if (c[n - 1] != 0){cout << c[n - 1];}for (int j = n - 2; j >= 0; j--){cout << c[j];}cout << endl; }void multiply_normal(int* c1, int* c2, int n, int flag) {clock_t start = clock(); //獲取當前系統時間int* c = new int[2 * n];int x = 0;for (int i = 0; i < 2 * n; i++){c[i] = 0;}for (int i = 0; i < n; i++){for (int j = 0; j < n; j++){x = c[i + j] + c1[i] * c2[j];c[i + j] = x % 10;c[i + j + 1] += x / 10;}}clock_t end = clock();double programTimes = ((double)end - start) / CLOCKS_PER_SEC;if (flag){cout << "Result." << setw(26) << "普通大數乘法乘積：";show_num(c, 2 * n);}cout << "Time." << setw(28) << "普通大數乘法時間：" << programTimes << " 秒" << endl << endl;delete[]c; }void multiply_n(int* c1, int* c2, int n, int flag) {multiply_normal(c1, c2, n, flag); }int bit_number(int* c, int n) {int x = 0;for (int i = 0; i < n; i++){x += c[i] * pow(10, i);}return x; }int* x_y(int c1, int c2) {int x = 0;int* c = new int[2];x = c1 * c2;c[0] = x % 10;c[1] = x / 10;return c; }int* high_num_2(int* c, int n) {int* k = new int[n / 2];for (int i = 0; i < n / 2; i++){k[i] = c[i + n / 2];}return k; }int* low_num_2(int* c, int n) {int* k = new int[n / 2];for (int i = 0; i < n / 2; i++){k[i] = c[i];}return k; }void add_list(int* c1, int* c2, int n, int m) //n為c2的長度，m為c2的進位 {int x = 0;for (int i = 0; i < n; i++){x = c1[i + m] + c2[i];c1[i + m] = x % 10;if (x / 10 != 0)c1[i + m + 1] += x / 10;} }int* multiply_partition(int* c1, int* c2, int n) {if (n == 1){return x_y(c1[0], c2[0]);}int* x = NULL;int* y = NULL;if (n % 2 != 0){x = new int[n + 1];y = new int[n + 1];for (int i = 0; i < n; i++){x[i] = c1[i];y[i] = c2[i];}x[n] = 0;y[n] = 0;n += 1;}else{x = new int[n];y = new int[n];for (int i = 0; i < n; i++){x[i] = c1[i];y[i] = c2[i];}}int* a1 = high_num_2(x, n);int* a0 = low_num_2(x, n);int* b1 = high_num_2(y, n);int* b0 = low_num_2(y, n);int* p = multiply_partition(a1, b1, n / 2);int n_p = p[n - 1] == 0 ? n - 1 : n;int* q = multiply_partition(a1, b0, n / 2);int n_q = q[n - 1] == 0 ? n - 1 : n;int* r = multiply_partition(a0, b1, n / 2);int n_r = r[n - 1] == 0 ? n - 1 : n;int* s = multiply_partition(a0, b0, n / 2);int n_s = s[n - 1] == 0 ? n - 1 : n;delete[]x;delete[]y;delete[]a1;delete[]a0;delete[]b1;delete[]b0;int* c = new int[2 * n];for (int i = 0; i < 2 * n; i++){c[i] = 0;}add_list(c, p, n_p, n);add_list(c, r, n_r, n / 2);add_list(c, q, n_q, n / 2);add_list(c, s, n_s, 0);delete[]p;delete[]q;delete[]r;delete[]s;return c; }void multiply_p(int* c1, int* c2, int n, int flag) {clock_t start = clock(); //獲取當前系統時間int* c = multiply_partition(c1, c2, n);clock_t end = clock();double programTimes = ((double)end - start) / CLOCKS_PER_SEC;if (flag){cout << "Result." << setw(26) << "分治法大數乘法乘積：";show_num(c, 2 * n);}cout << "Time." << setw(28) << "分治法大數乘法時間：" << programTimes << " 秒" << endl << endl;delete[]c; }void sub_list(int* c1, int* c2, int n, int m) {for (int i = 0; i < n; i++){if (c1[i + m] < c2[i]){c1[i + m] = c1[i + m] + 10 - c2[i];c1[i + m + 1] -= 1;}elsec1[i + m] -= c2[i];}if (c1[n + m] < 0){for (int i = 0;;i++){c1[n + m + i] += 10;c1[n + m + i + 1] -= 1;if (c1[n + m + i + 1] >= 0)break;}}}int* multiply_partition_enhanced(int* c1, int* c2, int n) {if (n == 1){return x_y(c1[0], c2[0]);}int* x = NULL;int* y = NULL;if (n % 2 != 0){x = new int[n + 1];y = new int[n + 1];for (int i = 0; i < n; i++){x[i] = c1[i];y[i] = c2[i];}x[n] = 0;y[n] = 0;n += 1;}else{x = new int[n];y = new int[n];for (int i = 0; i < n; i++){x[i] = c1[i];y[i] = c2[i];}}int* a1 = high_num_2(x, n);int* a0 = low_num_2(x, n);int* b1 = high_num_2(y, n);int* b0 = low_num_2(y, n);int* p = multiply_partition_enhanced(a1, b1, n / 2);int n_p = p[n - 1] == 0 ? n - 1 : n;int* a2 = new int[n / 2 + 1];int* b2 = new int[n / 2 + 1];for (int i = 0; i < n / 2 + 1; i++){a2[i] = 0;b2[i] = 0;}add_list(a2, a1, n / 2, 0);add_list(a2, a0, n / 2, 0);add_list(b2, b1, n / 2, 0);add_list(b2, b0, n / 2, 0);int m = n / 2;if (a2[n / 2] != 0 || b2[n / 2] != 0){m = n / 2 + 1;}int* q = multiply_partition_enhanced(a2, b2, m); // 如果 n = 2, m = 1 or 2 66*77 12*14 = 168 nq = 3 n / 2 = 1int n_q = q[2 * m - 1] == 0 ? 2 * m - 1 : 2 * m;int* s = multiply_partition_enhanced(a0, b0, n / 2);int n_s = s[n - 1] == 0 ? n - 1 : n;delete[]x;delete[]y;delete[]a1;delete[]a0;delete[]b1;delete[]b0;delete[]a2;delete[]b2;int* c = new int[2 * n + 1];for (int i = 0; i < 2 * n + 1; i++){c[i] = 0;}add_list(c, p, n_p, n);add_list(c, q, n_q, n / 2);add_list(c, s, n_s, 0);sub_list(c, p, n_p, n / 2);sub_list(c, s, n_s, n / 2);delete[]p;delete[]q;delete[]s;return c; }void multiply_p_e(int* c1, int* c2, int n, int flag) {clock_t start = clock(); //獲取當前系統時間int* c = multiply_partition_enhanced(c1, c2, n);clock_t end = clock();double programTimes = ((double)end - start) / CLOCKS_PER_SEC;if (flag){cout << "Result." << setw(26) << "改進的分治法大數乘法乘積：";show_num(c, 2 * n);}cout << "Time." << setw(28) << "改進的分治法大數乘法時間：" << programTimes << " 秒" << endl << endl;delete[]c; }

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