#include <cstdio> #include <cstring> #include <cstdlib> #include <iostream> #include <algorithm> using namespace std;#define MAXN 9999 #define MAXSIZE 10 #define DLEN 4class BigInt { private:int a[500]; //可以控制大數的位數int len; //大數長度 public:BigInt(){ len = 1;memset(a,0,sizeof(a)); } //構造函數BigInt(const int); //將一個int類型的變量轉化為大數BigInt(const char*); //將一個字符串類型的變量轉化為大數BigInt(const BigInt &); //拷貝構造函數BigInt &operator=(const BigInt &); //重載賦值運算符，大數之間進行賦值運算friend istream& operator>>(istream&, BigInt&); //重載輸入運算符friend ostream& operator<<(ostream&, BigInt&); //重載輸出運算符BigInt operator+(const BigInt &) const; //重載加法運算符，兩個大數之間的相加運算BigInt operator-(const BigInt &) const; //重載減法運算符，兩個大數之間的相減運算BigInt operator*(const BigInt &) const; //重載乘法運算符，兩個大數之間的相乘運算BigInt operator/(const int &) const; //重載除法運算符，大數對一個整數進行相除運算BigInt operator^(const int &) const; //大數的n次方運算int operator%(const int &) const; //大數對一個int類型的變量進行取模運算bool operator>(const BigInt & T)const; //大數和另一個大數的大小比較bool operator<(const BigInt & T) const;bool operator==(const BigInt & T) const;bool operator>(const int & t)const; //大數和一個int類型的變量的大小比較bool operator<(const int &t) const;bool operator==(const int &t) const;void print(); //輸出大數 };bool BigInt::operator==(const BigInt & T) const {return !(*this > T) && !(T > *this); } bool BigInt::operator==(const int &t) const {BigInt T = BigInt(t);return *this == T; } bool BigInt::operator<(const BigInt & T) const {return T > *this; } bool BigInt::operator<(const int &t) const {return BigInt(t) > *this; } BigInt::BigInt(const int b) //將一個int類型的變量轉化為大數 {int c,d = b;len = 0;memset(a,0,sizeof(a));while(d > MAXN){c = d - (d / (MAXN + 1)) * (MAXN + 1);d = d / (MAXN + 1);a[len++] = c;}a[len++] = d; } BigInt::BigInt(const char*s) //將一個字符串類型的變量轉化為大數 {int t,k,index,l,i;memset(a,0,sizeof(a));l=strlen(s);len=l/DLEN;if(l%DLEN)len++;index=0;for(i=l-1;i>=0;i-=DLEN){t=0;k=i-DLEN+1;if(k<0)k=0;for(int j=k;j<=i;j++)t=t*10+s[j]-'0';a[index++]=t;} } BigInt::BigInt(const BigInt & T) : len(T.len) //拷貝構造函數 {int i;memset(a,0,sizeof(a));for(i = 0 ; i < len ; i++)a[i] = T.a[i]; } BigInt & BigInt::operator=(const BigInt & n) //重載賦值運算符，大數之間進行賦值運算 {int i;len = n.len;memset(a,0,sizeof(a));for(i = 0 ; i < len ; i++)a[i] = n.a[i];return *this; } istream& operator>>(istream & in, BigInt & b) //重載輸入運算符 {char ch[MAXSIZE*4];int i = -1;in>>ch;int l=strlen(ch);int count=0,sum=0;for(i=l-1;i>=0;){sum = 0;int t=1;for(int j=0;j<4&&i>=0;j++,i--,t*=10){sum+=(ch[i]-'0')*t;}b.a[count]=sum;count++;}b.len =count++;return in;} ostream& operator<<(ostream& out, BigInt& b) //重載輸出運算符 {int i;cout << b.a[b.len - 1];for(i = b.len - 2 ; i >= 0 ; i--){cout.width(DLEN);cout.fill('0');cout << b.a[i];}return out; }BigInt BigInt::operator+(const BigInt & T) const //兩個大數之間的相加運算 {BigInt t(*this);int i,big; //位數big = T.len > len ? T.len : len;for(i = 0 ; i < big ; i++){t.a[i] +=T.a[i];if(t.a[i] > MAXN){t.a[i + 1]++;t.a[i] -=MAXN+1;}}if(t.a[big] != 0)t.len = big + 1;elset.len = big;return t; } BigInt BigInt::operator-(const BigInt & T) const //兩個大數之間的相減運算 {int i,j,big;bool flag;BigInt t1,t2;if(*this>T){t1=*this;t2=T;flag=0;}else{t1=T;t2=*this;flag=1;}big=t1.len;for(i = 0 ; i < big ; i++){if(t1.a[i] < t2.a[i]){j = i + 1;while(t1.a[j] == 0)j++;t1.a[j--]--;while(j > i)t1.a[j--] += MAXN;t1.a[i] += MAXN + 1 - t2.a[i];}elset1.a[i] -= t2.a[i];}t1.len = big;while(t1.a[t1.len - 1] == 0 && t1.len > 1){t1.len--;big--;}if(flag)t1.a[big-1]=0-t1.a[big-1];return t1; }BigInt BigInt::operator*(const BigInt & T) const //兩個大數之間的相乘運算 {BigInt ret;int i,j,up;int temp,temp1;for(i = 0 ; i < len ; i++){up = 0;for(j = 0 ; j < T.len ; j++){temp = a[i] * T.a[j] + ret.a[i + j] + up;if(temp > MAXN){temp1 = temp - temp / (MAXN + 1) * (MAXN + 1);up = temp / (MAXN + 1);ret.a[i + j] = temp1;}else{up = 0;ret.a[i + j] = temp;}}if(up != 0)ret.a[i + j] = up;}ret.len = i + j;while(ret.a[ret.len - 1] == 0 && ret.len > 1)ret.len--;return ret; } BigInt BigInt::operator/(const int & b) const //大數對一個整數進行相除運算 {BigInt ret;int i,down = 0;for(i = len - 1 ; i >= 0 ; i--){ret.a[i] = (a[i] + down * (MAXN + 1)) / b;down = a[i] + down * (MAXN + 1) - ret.a[i] * b;}ret.len = len;while(ret.a[ret.len - 1] == 0 && ret.len > 1)ret.len--;return ret; } int BigInt::operator %(const int & b) const //大數對一個int類型的變量進行取模運算 {int i,d=0;for (i = len-1; i>=0; i--){d = ((d * (MAXN+1))% b + a[i])% b;}return d; } BigInt BigInt::operator^(const int & n) const //大數的n次方運算 {BigInt t,ret(1);int i;if(n<0)exit(-1);if(n==0)return 1;if(n==1)return *this;int m=n;while(m>1){t=*this;for( i=1;i<<1<=m;i<<=1){t=t*t;}m-=i;ret=ret*t;if(m==1)ret=ret*(*this);}return ret; } bool BigInt::operator>(const BigInt & T) const //大數和另一個大數的大小比較 {int ln;if(len > T.len)return true;else if(len == T.len){ln = len - 1;while(a[ln] == T.a[ln] && ln >= 0)ln--;if(ln >= 0 && a[ln] > T.a[ln])return true;elsereturn false;}elsereturn false; } bool BigInt::operator >(const int & t) const //大數和一個int類型的變量的大小比較 {BigInt b(t);return *this>b; }void BigInt::print() //輸出大數 {int i;printf("%d", a[len-1]);for (int i = len-2; i >= 0; --i) {printf("%04d", a[i]);}puts(""); } int main() {int t;char a[1000], b[1000];BigInt ans;scanf("%s%s",a,b);BigInt A(a), B(b);printf("%s + %s = ", a, b);ans = A + B;ans.print();printf("%s - %s = ", a, b);ans = A - B;ans.print();scanf("%d",&t);printf("%s * %d = ", a, t);ans = A * t;ans.print();printf("%s / %d = ", a, t);ans = A / t;ans.print();printf("%s ^ %d = ", a, t);ans = A ^ t;ans.print();printf("%s %% %d = ", a, t);ans = A % t;ans.print();return 0; }

下面是用string類寫的模板

兩個大整數相加：

/*大整數加法調用方式:add(a, b);返回類型：string */string add(string a, string b) {string s;reverse(a.begin(), a.end());reverse(b.begin(), b.end());int i = 0;int m, k = 0;while(a[i] && b[i]){m = a[i] - '0' + b[i] - '0' + k;k = m / 10;s += (m % 10 + '0');i++;}if(i == a.size()){while(i != b.size()){m = k + b[i] - '0';k = m / 10;s += m % 10 + '0';i++;}if(k) s += k + '0';}else if(i == b.size()){while(i != a.size()){m = k + a[i] - '0';k = m / 10;s += m % 10 + '0';i++;}if(k) s += k + '0';}reverse(s.begin(), s.end());return s; }
兩個大整數相減：

/*大整數減法 */#include<cstdio> #include<cstring> #include<string> #include<iostream> using namespace std; string sub(string a, string b) {int i, j, k, s, flag = 1;int tmpa[10000], tmpb[10000], c[10000];string ans;if(a.size() < b.size() || (a.size() == b.size() && a.compare(b) < 0)){string tmp = a;a = b;b = tmp;flag = 0;}while(a.length() > b.length()) b = '0' + b;int len = a.length();for(i = 0; i < len; i++){tmpa[i] = a[i] - '0';tmpb[i] = b[i] - '0';}for(i = len - 1; i >= 0; i--){if(tmpa[i] >= tmpb[i])c[i] = tmpa[i] - tmpb[i];else{c[i] = 10 + tmpa[i] - tmpb[i];tmpa[i-1]--;}}for(i = 0; i < len - 1; i++)if(c[i] != 0)break;for(j = i; j < len; j++)ans = ans + (char)(c[j] + '0');if(!flag)ans = '-' + ans;return ans; }int main() {string a, b;while(cin >> a >> b){cout << sub(a, b) << endl;}return 0; }

大整數乘以一個小整數：

/*大整數乘以小整數（可以用整型變量表示的整數） */ string multi(string a, int k) {if(k == 0) return "0";int len = a.length(), carry = 0;reverse(a.begin(), a.end());for(int i = 0; i < len; i++){int s = (a[i] - '0') * k + carry;a[i] = s % 10 + '0';carry = s / 10;}while(carry != 0){a = a + (char)(carry % 10 + '0');carry /= 10;}reverse(a.begin(), a.end());return a; }

兩個不含前導0的大整數相乘：

/*兩個不含前導0的大整數相乘 */#include<string> #include<iostream> #include<algorithm> using namespace std;string multi_string_int(string a, int k) {if(k == 0) return "0";int len = a.length(), carry = 0;reverse(a.begin(), a.end());for(int i = 0; i < len; i++){int s = (a[i] - '0') * k + carry;a[i] = s % 10 + '0';carry = s / 10;}while(carry != 0){a = a + (char)(carry % 10 + '0');carry /= 10;}reverse(a.begin(), a.end());return a; }string add(string a, string b) {string s;reverse(a.begin(), a.end());reverse(b.begin(), b.end());int i = 0;int m, k = 0;while(a[i] && b[i]){m = a[i] - '0' + b[i] - '0' + k;k = m / 10;s += (m % 10 + '0');i++;}if(i == a.size()){while(i != b.size()){m = k + b[i] - '0';k = m / 10;s += m % 10 + '0';i++;}if(k) s += k + '0';}else if(i == b.size()){while(i != a.size()){m = k + a[i] - '0';k = m / 10;s += m % 10 + '0';i++;}if(k) s += k + '0';}reverse(s.begin(), s.end());return s; }string multi_string_string(string a, string b) {string ans = "";for(int i = a.size() - 1; i >= 0; i--){string tmp = multi_string_int(b, a[i] - '0');for(int j = 0; j < a.size() - 1 - i; j++)tmp += '0';ans = add(ans, tmp);}return ans; }int main() {string a, b;while(cin >> a >> b){cout << multi_string_string(a, b) << endl;}return 0; }

求大整數除以一個小整數的商：

string division(string str, int x) {string ans = "";int len = str.length();int y = 0;for(int i = 0; i < len; i++) {ans += char((y * 10 + (str[i] - '0')) / x + '0');y = (y * 10 + (str[i] - '0')) % x;}while(*(ans.begin()) == '0' && ans.size() > 1) ans.erase(ans.begin());return ans; }

求一個大整數對一個小整數的余數：

int Mod(string str, int x) {int len = str.length();int y = 0;for(int i = 0; i < len; i++)y = (y * 10 + (str[i] - '0')) % x;return y; }

兩個大數除法：

/* 大數除法 -- 高精度除高精度 */ #include <iostream> #include <string> #include <cstring> using namespace std; #define N 2000/* 1. a.size < b.size 返回-1 2. a.size == b.size && a - b < 0 返回-1 3. a.size == b.size && a - b == 0 返回0 */// 判斷a.size 與 b.size的關系，以及做減法 int Judge(char a[], int a1, char b[], int b1) {int i;if(a1 < b1) return -1; // a.size < b.sizebool flag = false;if(a1 == b1) { //a.size == b.size && a < bfor(i = a1 - 1; i >= 0; i--) {if(a[i] > b[i])flag = true;else if(a[i] < b[i]) {if(!flag) return -1;}}}for(i = 0; i < a1; i++) { //前提b中b1--a1部分必須為'0'a[i] = a[i] - b[i] + 48; //'0'的ASCII為48if((a[i] - '0') < 0) {a[i] = a[i] + 10;a[i+1] = a[i+1] - 1;}}for(i = a1 - 1; i >= 0; i--) { // 返回被除數的長度if(a[i] != '0')return (i + 1);}return 0; //a.size==b.size&&a==b的情況 }string division(string a, string b) {char x1[N], x2[N];int ans[N];int a_len, b_len, i, j;a_len = a.length();b_len = b.length();// 初始化memset(x1, '0', sizeof(x1));memset(x2, '0', sizeof(x2));memset(ans, 0, sizeof(ans));for(i = a_len - 1, j = 0; i >= 0; i--)x1[j++] = a[i];for(i = b_len - 1, j = 0; i >= 0; i--)x2[j++] = b[i];// 分析部分if(a_len < b_len) return "0";int temp_len = Judge(x1, a_len, x2, b_len);if(temp_len < 0) return "0";if(temp_len == 0) return "1";ans[0]++; // 減掉1位， 商加1int ntimes = temp_len - b_len;if(ntimes < 0) return "1";// 擴充數位， 加快減法else if(ntimes > 0) {for(i = temp_len - 1; i >= 0; i--) {if(i >= ntimes)x2[i] = x2[i - ntimes];elsex2[i] = '0';}}b_len = temp_len;// 加快除法的部分for(j = 0; j <= ntimes; j++) {int ntemp;while((ntemp = Judge(x1, temp_len, x2 + j, b_len - j)) >= 0) {temp_len = ntemp;ans[ntimes - j]++;}}for(i = 0; i < N; i++) {if(ans[i] >= 10) {ans[i+1] += ans[i] / 10;ans[i] %= 10;}}// 返回string類型int k = N - 1;string c = "";while(ans[k] == 0 && k > 0) k--;for(i = k; i >= 0; i--)c+= (ans[i] + '0');return c; }int main() {string a, b;while(cin >> a >> b) {cout << division(a, b) << endl;}return 0; }

總結

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