高精度模板
http://acm.xidian.edu.cn/problem.php?id=1046
1 #include<bits/stdc++.h> 2 using namespace std; 3 struct bign{ 4 int num[1000]; 5 int len,symbol; 6 }; 7 bign a,b; 8 9 bool init(bign &a){ 10 memset(&a,0,sizeof a); 11 string s; 12 if(!(cin>>s)) return false; 13 a.len=s.length(); 14 for(int i=0;i<a.len;i++){ 15 a.num[i]=s[a.len-i-1]-'0'; 16 } 17 return true; 18 } 19 20 int compare(bign &a,bign &b){ 21 if(a.len>b.len) return 1; 22 if(a.len<b.len) return -1; 23 for(int i=a.len-1;i>=0;i--){ 24 if(a.num[i]>b.num[i]) return 1; 25 if(a.num[i]<b.num[i]) return -1; 26 } 27 return 0; 28 } 29 30 void print(bign &a){ 31 if(a.len==0){ 32 printf("0"); 33 return; 34 } 35 if(a.symbol==-1) printf("-"); 36 for(int i=a.len-1;i>=0;i--){ 37 printf("%d",a.num[i]); 38 }; 39 return; 40 } 41 42 bign add(bign &a,bign &b){ 43 bign c={0}; 44 c.len=a.len>b.len?a.len:b.len; 45 for(int i=0;i<c.len;i++){ 46 c.num[i]+=a.num[i]+b.num[i]; 47 if(c.num[i]>=10){ 48 c.num[i+1]+=c.num[i]/10; 49 c.num[i]%=10; 50 } 51 } 52 if(c.num[c.len]>0) c.len++; 53 return c; 54 } 55 56 bign sub(bign a,bign b){ 57 int flag=compare(a,b); 58 if(flag==0){ 59 a.len=0; 60 return a; 61 } 62 if(flag==-1){ 63 swap(a,b); 64 a.symbol=-1; 65 } 66 67 for(int i=0;i<a.len;i++){ 68 if(a.num[i]<b.num[i]){ 69 a.num[i+1]--; 70 a.num[i]+=10; 71 } 72 a.num[i]-=b.num[i]; 73 } 74 while(a.num[a.len-1]==0) a.len--; 75 return a; 76 } 77 78 bign mul(bign &a,bign &b){ 79 bign c={0}; 80 for(int i=0;i<a.len;i++){ 81 for(int j=0;j<b.len;j++){ 82 c.num[i+j]+=a.num[i]*b.num[j]; 83 if(c.num[i+j]>=10){ 84 c.num[i+j+1]+=c.num[i+j]/10; 85 c.num[i+j]%=10; 86 } 87 } 88 } 89 c.len=a.len+b.len; 90 while(c.len>1&&c.num[c.len-1]==0) c.len--; 91 return c; 92 } 93 94 void mul10(bign &a){ 95 int i; 96 for(i=a.len-1;i>=0;i--){ 97 a.num[i+1]=a.num[i]; 98 } 99 a.num[i]=0; 100 a.len++; 101 while(a.len>1&&a.num[a.len-1]==0) a.len--; 102 } 103 104 void div(bign &a, bign &b,bign &c,bign &f){ 105 f.len = 1; 106 c.len=a.len; 107 for(int i=a.len-1;i>=0;i--){ 108 mul10(f); 109 f.num[0] = a.num[i]; 110 while(compare(f,b)>=0){ 111 f=sub(f, b); 112 c.num[i]++; 113 } 114 } 115 while(c.len>1&&c.num[c.len-1]==0) c.len--; 116 } 117 118 119 120 int main(){ 121 while(init(a)&&init(b)){ 122 bign g={0},f={0}; 123 g.len=1; 124 bign c=add(a,b),d=sub(a,b),e=mul(a,b); 125 div(a,b,g,f); 126 print(c);printf(" "); 127 print(d);printf(" "); 128 print(e);printf(" "); 129 print(g);printf(" "); 130 print(f); 131 printf("\n"); 132 } 133 return 0; 134 }
1 #include <stdio.h> 2 #include <string.h> 3 #include <stdlib.h> 4 #include <math.h> 5 #include <assert.h> 6 #include <ctype.h> 7 #include <map> 8 #include <string> 9 #include <set> 10 #include <bitset> 11 #include <utility> 12 #include <algorithm> 13 #include <vector> 14 #include <stack> 15 #include <queue> 16 #include <iostream> 17 #include <fstream> 18 #include <list> 19 using namespace std; 20 //三元运算符要常用，会很好的减少代码量 21 const int MAXL = 500; 22 struct BigNum{ 23 int num[MAXL]; 24 int len; 25 }; 26 27 //高精度比较 a > b return 1, a == b return 0; a < b return -1; 28 int Comp(BigNum &a, BigNum &b){ 29 int i; 30 if(a.len != b.len) return (a.len > b.len) ? 1 : -1; 31 for(i = a.len-1; i >= 0; i--) 32 if(a.num[i] != b.num[i]) return (a.num[i] > b.num[i]) ? 1 : -1; 33 return 0; 34 } 35 36 //高精度加法 37 BigNum Add(BigNum &a, BigNum &b){ 38 BigNum c; 39 int i, len; 40 len = (a.len > b.len) ? a.len : b.len; 41 memset(c.num, 0, sizeof(c.num)); 42 for(i = 0; i < len; i++){ 43 c.num[i] += (a.num[i]+b.num[i]); 44 if(c.num[i] >= 10){ 45 c.num[i+1]++; 46 c.num[i] -= 10; 47 } 48 } 49 if(c.num[len]) 50 len++; 51 c.len = len; 52 return c; 53 } 54 55 //高精度减法,保证a >= b 56 BigNum Sub(BigNum &a, BigNum &b){ 57 BigNum c; 58 int i, len; 59 len = (a.len > b.len) ? a.len : b.len; 60 memset(c.num, 0, sizeof(c.num)); 61 for(i = 0; i < len; i++){ 62 c.num[i] += (a.num[i]-b.num[i]); 63 if(c.num[i] < 0){ 64 c.num[i] += 10; 65 c.num[i+1]--; 66 } 67 } 68 while(c.num[len] == 0 && len > 1) 69 len--; 70 c.len = len; 71 return c; 72 } 73 //高精度乘以低精度，当b很大时可能会发生溢出int范围,具体情况具体分析 74 //如果b很大可以考虑把b看成高精度 75 BigNum Mul1(BigNum &a, int &b) 76 { 77 BigNum c; 78 int i, len; 79 len = a.len; 80 memset(c.num, 0, sizeof(c.num)); 81 //乘以0，直接返回0 82 if(b == 0) 83 { 84 c.len = 1; 85 return c; 86 } 87 for(i = 0; i < len; i++) 88 { 89 c.num[i] += (a.num[i]*b); 90 if(c.num[i] >= 10) 91 { 92 c.num[i+1] = c.num[i]/10; 93 c.num[i] %= 10; 94 } 95 } 96 while(c.num[len] > 0) 97 { 98 c.num[len+1] = c.num[len]/10; 99 c.num[len++] %= 10; 100 } 101 c.len = len; 102 return c; 103 } 104 105 //高精度乘以高精度,注意要及时进位，否则肯能会引起溢出,但这样会增加算法的复杂度， 106 //如果确定不会发生溢出, 可以将里面的while改成if 107 BigNum Mul2(BigNum &a, BigNum &b) 108 { 109 int i, j, len = 0; 110 BigNum c; 111 memset(c.num, 0, sizeof(c.num)); 112 for(i = 0; i < a.len; i++) 113 { 114 for(j = 0; j < b.len; j++) 115 { 116 c.num[i+j] += (a.num[i]*b.num[j]); 117 if(c.num[i+j] >= 10) 118 { 119 c.num[i+j+1] += c.num[i+j]/10; 120 c.num[i+j] %= 10; 121 } 122 } 123 } 124 len = a.len+b.len-1; 125 while(c.num[len-1] == 0 && len > 1) 126 len--; 127 if(c.num[len]) 128 len++; 129 c.len = len; 130 return c; 131 } 132 133 //高精度除以低精度,除的结果为c, 余数为f 134 void Div1(BigNum &a, int &b, BigNum &c, int &f) 135 { 136 int i, len = a.len; 137 memset(c.num, 0, sizeof(c.num)); 138 f = 0; 139 for(i = a.len-1; i >= 0; i--) 140 { 141 f = f*10+a.num[i]; 142 c.num[i] = f/b; 143 f %= b; 144 } 145 while(len > 1 && c.num[len-1] == 0) 146 len--; 147 c.len = len; 148 } 149 //高精度*10 150 void Mul10(BigNum &a) 151 { 152 int i, len = a.len; 153 for(i = len; i >= 1; i--) 154 a.num[i] = a.num[i-1]; 155 a.num[i] = 0; 156 len++; 157 //if a == 0 158 while(len > 1 && a.num[len-1] == 0) 159 len--; 160 } 161 162 //高精度除以高精度，除的结果为c，余数为f 163 void Div2(BigNum &a, BigNum &b, BigNum &c, BigNum &f) 164 { 165 int i, len = a.len; 166 memset(c.num, 0, sizeof(c.num)); 167 memset(f.num, 0, sizeof(f.num)); 168 f.len = 1; 169 for(i = len-1;i >= 0;i--) 170 { 171 Mul10(f); 172 //余数每次乘10 173 f.num[0] = a.num[i]; 174 //然后余数加上下一位 175 ///利用减法替换除法 176 while(Comp(f, b) >= 0) 177 { 178 f = Sub(f, b); 179 c.num[i]++; 180 } 181 } 182 while(len > 1 && c.num[len-1] == 0) 183 len--; 184 c.len = len; 185 } 186 void print(BigNum &a) //输出大数 187 { 188 int i; 189 for(i = a.len-1; i >= 0; i--) 190 printf("%d", a.num[i]); 191 puts(""); 192 } 193 //将字符串转为大数存在BigNum结构体里面 194 BigNum ToNum(char *s) 195 { 196 int i, j; 197 BigNum a; 198 a.len = strlen(s); 199 for(i = 0, j = a.len-1; s[i] != '\0'; i++, j--) 200 a.num[i] = s[j]-'0'; 201 return a; 202 } 203 204 void Init(BigNum &a, char *s, int &tag) //将字符串转化为大数 205 { 206 int i = 0, j = strlen(s); 207 if(s[0] == '-') 208 { 209 j--; 210 i++; 211 tag *= -1; 212 } 213 a.len = j; 214 for(; s[i] != '\0'; i++, j--) 215 a.num[j-1] = s[i]-'0'; 216 } 217 218 int main() 219 { 220 BigNum a, b; 221 char s1[100], s2[100]; 222 while(scanf("%s %s", s1, s2) != EOF) 223 { 224 int tag = 1; 225 Init(a, s1, tag); //将字符串转化为大数 226 Init(b, s2, tag); 227 a = Mul2(a, b); 228 if(a.len == 1 && a.num[0] == 0) 229 { 230 puts("0"); 231 } 232 else 233 { 234 if(tag < 0) putchar('-'); 235 print(a); 236 } 237 } 238 return 0; 239 }
