高精度运算模板
作者：互联网
为了模板化，我们用struct或class来定义高精度。
1 template<int SIZE>//用来限制最大表示位数
2 class bign(){
3 private://在class外不能调用
4 int a[SIZE],len;//高精度整数，用数组表示
5 public:
6 //一系列运算函数
7 }
输入输出：
1 bign(){len=1;memset(a,0,sizeof(a));}//初始化
2 void in(){
3 char s[SIZE];
4 scanf("%s",s);
5 len=strlen(s);
6 for(int i=0,j=len-1;i<len;i++,j--) a[i]=s[j]-48;
7 while(len>1&&a[len-1]==0) len--;//应对输入含前导0
8 }
9 void out(bool Entr=true){//默认输出换行
10 for(int i=len-1;i>=0;i--) putchar(a[i]+'0');
11 if(Entr) putchar('\n');
12 }
赋值：
1 void operator = (char *s){
2 len=strlen(s);
3 for(int i=0,j=len-1;i<len;i++,j--) a[i]=s[j]-48;
4 while(len>1&&a[len-1]==0) len--;
5 }
6 void operator = (int x){
7 len=0;if(x==0) len=1,a[0]=0;
8 while(x>0) a[len++]=x%10,x/=10;
9 }
10 void operator = (long long x){
11 len=0;if(x==0) len=1,a[0]=0;
12 while(x>0) a[len++]=x%10,x/=10;
13 }
大小比较：
1 friend bool operator < (bign a,bign b){
2 if(a.len!=b.len) return a.len<b.len;
3 for(int i=a.len-1;i>=0;i--)
4 if(a.a[i]!=b.a[i]) return a.a[i]<b.a[i];
5 return false;//表示a,b相等
6 }
7 friend bool operator > (bign a,bign b){
8 return b<a;
9 }
10 friend bool operator <= (bign a,bign b){
11 return !(a>b);
12 }
13 friend bool operator >= (bign a,bign b){
14 return !(a<b);
15 }
16 friend bool operator == (bign a,bign b){
17 return !(a>b&&b<a);
18 }
19 friend bool operator != (bign a,bign b){
20 return a<b||b<a;
21 }
加减乘除运算：
1 friend bign operator + (bign a,bign b){
2 bign c;
3 int lenth=max(a.len,b.len)+1;
4 for(int i=0;i<lenth;i++) c.a[i]=a.a[i]+b.a[i];
5 for(int i=0;i<lenth;i++){
6 if(c.a[i]>9) c.a[i]-=10,c.a[i+1]++;
7 }
8 while(lenth>1&&c.a[lenth-1]==0) lenth--;
9 c.len=lenth;
10 return c;
11 }
12 friend bign operator - (bign a,bign b){//求a-b的绝对值
13 bign c;
14 if(a<b) swap(a,b);
15 int len=a.len;
16 for(int i=0;i<len;i++)
17 c.a[i]=a.a[i]-b.a[i];
18 for(int i=0;i<len;i++)
19 if(c.a[i]<0) c.a[i+1]--, c.a[i]+=10;
20 while(len>1&&c.a[len-1]==0) len--;
21 c.len=len;
22 return c;
23 }
24 friend bign operator * (bign a,bign b){
25 bign ans;
26 int len=a.len+b.len;
27 for(int i=0;i<a.len;i++)
28 for(int j=0;j<b.len;j++)
29 ans.a[i+j]+=a.a[i]*b.a[j];//这里要思考一下
30 for(int i=0;i<len;i++)
31 if(ans.a[i]>9) ans.a[i+1]+=ans.a[i]/10,ans.a[i]%=10;
32 while(len>1&&ans.a[len-1]==0) len--;
33 ans.len=len;
34 return ans;
35 }
36 friend bign operator * (bign a,int x){//防溢出，x<=200,000,000
37 bign ans;
38 int len=a.len+20;
39 for(int i=0;i<len;i++) ans.a[i]=a.a[i]*x;
40 for(int i=0;i<len;i++)
41 if(ans.a[i]>9) ans.a[i+1]+=ans.a[i]/10,ans.a[i]%=10;
42 while(ans.a[len-1]==0&&len>1) len--;
43 ans.len=len;
44 return ans;
45 }
46 friend bign operator / (bign a,int b){//防溢出
47 bign c;
48 int d=0,len=a.len;
49 for(int i=len-1;i>=0;i--)
50 d=d*10+a.a[i],c.a[i]=d/b,d=d%b;
51 while(len>1&&c.a[len-1]==0) len--;
52 c.len=len;
53 return c;
54 }
55 friend bign operator / (bign a,bign b){
56 bign c,d;
57 int len=a.len;
58 for(int i=len-1;i>=0;i--){
59 d=d*10;
60 d.a[0]=a.a[i];
61 while(d>=b) c.a[i]++, d=d-b;//这里效率不是很高
62 }
63 while(len>1&&c.a[len-1]==0) len--;
64 c.len=len;
65 return c;
66 }
取模：
1 friend int operator % (bign a,int b){//注意返回值为int
2 int d=0,len=a.len;
3 for(int i=len-1;i>=0;i--)
4 d=d*10+a.a[i],d=d%b;
5 return d;
6 }
7 friend bign operator % (bign a,bign b){
8 bign d;
9 int len=a.len;
10 for(int i=len-1;i>=0;i--){
11 d=d*10;
12 d.a[0]=a.a[i];
13 while(d>=b) d=d-b;//同理，效率不够高
14 }
15 while(len>1&&d.a[len-1]==0) len--;
16 d.len=len;
17 return d;
18 }
完整代码：
1 template<int SIZE>
2 class bign{
3 private:
4 int a[SIZE],len;
5 public:
6 bign(){len=1;memset(a,0,sizeof(a));}
7 void in(){
8 char s[SIZE];
9 scanf("%s",s);
10 len=strlen(s);
11 for(int i=0,j=len-1;i<len;i++,j--) a[i]=s[j]-48;
12 while(len>1&&a[len-1]==0) len--;
13 }
14 void out(bool Entr=true){
15 for(int i=len-1;i>=0;i--) putchar(a[i]+'0');
16 if(Entr) putchar('\n');
17 }
18 void operator = (char *s){
19 len=strlen(s);
20 for(int i=0,j=len-1;i<len;i++,j--) a[i]=s[j]-48;
21 while(len>1&&a[len-1]==0) len--;
22 }
23 void operator = (int x){
24 len=0;if(x==0) len=1,a[0]=0;
25 while(x>0) a[len++]=x%10,x/=10;
26 }
27 void operator = (long long x){
28 len=0;if(x==0) len=1,a[0]=0;
29 while(x>0) a[len++]=x%10,x/=10;
30 }
31 friend bool operator < (bign a,bign b){
32 if(a.len!=b.len) return a.len<b.len;
33 for(int i=a.len-1;i>=0;i--)
34 if(a.a[i]!=b.a[i]) return a.a[i]<b.a[i];
35 return false;
36 }
37 friend bool operator > (bign a,bign b){
38 return b<a;
39 }
40 friend bool operator <= (bign a,bign b){
41 return !(a>b);
42 }
43 friend bool operator >= (bign a,bign b){
44 return !(a<b);
45 }
46 friend bool operator == (bign a,bign b){
47 return !(a>b&&b<a);
48 }
49 friend bool operator != (bign a,bign b){
50 return a<b||b<a;
51 }
52 friend bign operator + (bign a,bign b){
53 bign c;
54 int lenth=max(a.len,b.len)+1;
55 for(int i=0;i<lenth;i++) c.a[i]=a.a[i]+b.a[i];
56 for(int i=0;i<lenth;i++){
57 if(c.a[i]>9) c.a[i]-=10,c.a[i+1]++;
58 }
59 while(lenth>1&&c.a[lenth-1]==0) lenth--;
60 c.len=lenth;
61 return c;
62 }
63 friend bign operator - (bign a,bign b){
64 bign c;
65 if(a<b) std::swap(a,b);
66 int len=a.len;
67 for(int i=0;i<len;i++)
68 c.a[i]=a.a[i]-b.a[i];
69 for(int i=0;i<len;i++)
70 if(c.a[i]<0) c.a[i+1]--, c.a[i]+=10;
71 while(len>1&&c.a[len-1]==0) len--;
72 c.len=len;
73 return c;
74 }
75 friend bign operator * (bign a,bign b){
76 bign ans;
77 int len=a.len+b.len;
78 for(int i=0;i<a.len;i++)
79 for(int j=0;j<b.len;j++)
80 ans.a[i+j]+=a.a[i]*b.a[j];
81 for(int i=0;i<len;i++)
82 if(ans.a[i]>9) ans.a[i+1]+=ans.a[i]/10,ans.a[i]%=10;
83 while(len>1&&ans.a[len-1]==0) len--;
84 ans.len=len;
85 return ans;
86 }
87 friend bign operator * (bign a,int x){
88 bign ans;
89 int len=a.len+20;
90 for(int i=0;i<len;i++) ans.a[i]=a.a[i]*x;
91 for(int i=0;i<len;i++)
92 if(ans.a[i]>9) ans.a[i+1]+=ans.a[i]/10,ans.a[i]%=10;
93 while(ans.a[len-1]==0&&len>1) len--;
94 ans.len=len;
95 return ans;
96 }
97 friend bign operator / (bign a,int b){
98 bign c;
99 int d=0,len=a.len;
100 for(int i=len-1;i>=0;i--)
101 d=d*10+a.a[i],c.a[i]=d/b,d=d%b;
102 while(len>1&&c.a[len-1]==0) len--;
103 c.len=len;
104 return c;
105 }
106 friend bign operator / (bign a,bign b){
107 bign c,d;
108 int len=a.len;
109 for(int i=len-1;i>=0;i--){
110 d=d*10;
111 d.a[0]=a.a[i];
112 while(d>=b) c.a[i]++, d=d-b;
113 }
114 while(len>1&&c.a[len-1]==0) len--;
115 c.len=len;
116 return c;
117 }
118 friend int operator % (bign a,int b){
119 int d=0,len=a.len;
120 for(int i=len-1;i>=0;i--)
121 d=d*10+a.a[i],d=d%b;
122 return d;
123 }
124 friend bign operator % (bign a,bign b){
125 bign d;
126 int len=a.len;
127 for(int i=len-1;i>=0;i--){
128 d=d*10;
129 d.a[0]=a.a[i];
130 while(d>=b) d=d-b;
131 }
132 while(len>1&&d.a[len-1]==0) len--;
133 d.len=len;
134 return d;
135 }
136 friend bign gcd(bign a,bign b){
137 bign zero;
138 zero=0;
139 return b==zero?a:gcd(b,a%b);
140 }
141 friend bign pow_mod(int a,int n,bign m){
142 bign ret,X;
143 if(n==0){
144 ret=1;return ret;
145 }
146 X=pow_mod(a,n/2,m);
147 ret=(X*X)%m;
148 if(n%2) ret=(ret*a)%m;
149 return ret;
150 }
151 };
完整代码
标签：10,return,运算,高精度,int,len,--,bign,模板 来源： https://www.cnblogs.com/la-oj/p/14066052.html