/* 高精度模版 含大数开平方 */ #include <stdio.h> #include <math.h> #include <string.h> #include <iostream> #include <string> #include <algorithm> using namespace std; const int numlen = 105; // 位数 int max(int a,int b) { return a>b?a:b; } struct bign { int len,s[numlen]; bign() { memset(s,sizeof(s)); len = 1; } bign(int num) { *this = num; } bign(const char *num) { *this = num; } bign operator = (const int num) { char s[numlen]; sprintf(s,"%d",num); *this = s; return *this; } bign operator = (const char *num) { len = strlen(num); while(len > 1 && num[0] == '0') num++,len--; for(int i = 0;i < len; i++) s[i] = num[len-i-1] - '0'; return *this; } void deal() { while(len > 1 && !s[len-1]) len--; } bign operator + (const bign &a) const { bign ret; ret.len = 0; int top = max(len,a.len),add = 0; for(int i = 0;add || i < top; i++) { int Now = add; if(i < len) Now += s[i]; if(i < a.len) Now += a.s[i]; ret.s[ret.len++] = Now%10; add = Now/10; } return ret; } bign operator - (const bign &a) const { bign ret; ret.len = 0; int cal = 0; for(int i = 0;i < len; i++) { int Now = s[i] - cal; if(i < a.len) Now -= a.s[i]; if(Now >= 0) cal = 0; else { cal = 1; Now += 10; } ret.s[ret.len++] = Now; } ret.deal(); return ret; } bign operator * (const bign &a) const { bign ret; ret.len = len + a.len; for(int i = 0;i < len; i++) { for(int j = 0;j < a.len; j++) ret.s[i+j] += s[i]*a.s[j]; } for(int i = 0;i < ret.len; i++) { ret.s[i+1] += ret.s[i]/10; ret.s[i] %= 10; } ret.deal(); return ret; } //乘以小数,直接乘快点 bign operator * (const int num) { bign ret; ret.len = 0; int bb = 0; for(int i = 0;i < len; i++) { int Now = bb + s[i]*num; ret.s[ret.len++] = Now%10; bb = Now/10; } while(bb) { ret.s[ret.len++] = bb % 10; bb /= 10; } ret.deal(); return ret; } bign operator / (const bign &a) const { bign ret,cur = 0; ret.len = len; for(int i = len-1;i >= 0; i--) { cur = cur*10; cur.s[0] = s[i]; while(cur >= a) { cur -= a; ret.s[i]++; } } ret.deal(); return ret; } bign operator % (const bign &a) const { bign b = *this / a; return *this - b*a; } bign operator += (const bign &a) { *this = *this + a; return *this; } bign operator -= (const bign &a) { *this = *this - a; return *this; } bign operator *= (const bign &a) { *this = *this * a; return *this; } bign operator /= (const bign &a) { *this = *this / a; return *this; } bign operator %= (const bign &a) { *this = *this % a; return *this; } bool operator < (const bign &a) const { if(len != a.len) return len < a.len; for(int i = len-1;i >= 0; i--) if(s[i] != a.s[i]) return s[i] < a.s[i]; return false; } bool operator > (const bign &a) const { return a < *this; } bool operator <= (const bign &a) const { return !(*this > a); } bool operator >= (const bign &a) const { return !(*this < a); } bool operator == (const bign &a) const { return !(*this > a || *this < a); } bool operator != (const bign &a) const { return *this > a || *this < a; } string str() const { string ret = ""; for(int i = 0;i < len; i++) ret = char(s[i] + '0') + ret; return ret; } }; istream& operator >> (istream &in,bign &x) { string s; in >> s; x = s.c_str(); return in; } ostream& operator << (ostream &out,const bign &x) { out << x.str(); return out; } // 大数开平方 bign Sqrt(bign x) { int a[numlen/2]; int top = 0; for(int i = 0;i < x.len; i += 2) { if(i == x.len-1) { a[top++] = x.s[i]; } else a[top++] = x.s[i] + x.s[i+1]*10; } bign ret = (int)sqrt((double)a[top-1]); int xx = (int)sqrt((double)a[top-1]); bign pre = a[top-1] - xx*xx; bign cc; for(int i = top-2;i >= 0; i--) { pre = pre*100 + a[i]; cc = ret*20; for(int j = 9;j >= 0; j--) { bign Now = (cc + j)*j; if(Now <= pre) { ret = ret*10 + j; pre -= Now; break; } } } return ret; }
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