A X B 高精度乘法，分治(二分)加速——算法作业 2.2，EOJ 1070
Time Limit:1000MS Memory Limit:30000KB
Description
旺财的数学老师开始发威了，留了一道很大很大的整数之间乘法的问题。
Input
第1行有一个正整数N(0 < N < 11)，表示有几组测试数据，接下来的2……N+1行里，每行有两个无正负号非负整数(都在500位以内)，整数之间用一个空格
分开.
Output
输出每行非负整数的积，每个结果占一行。
Sample Input
3
1 1
100 200
12345678901234567890 1
Sample Output
1
20000
12345678901234567890
朴素的高精度乘法
1
#include
<
stdio.h
>
2#include
<
string
.h
>
3
4
#define
L 1009
5
6
int
a[ L ], b[ L ], c[ L ];
7
8
void
input(
int
a[] )
{
9
char s[ L ];
10 int len, i;
11 scanf( "%s", s );
12 len = strlen( s );
13 memset( a, 0, sizeof(int)*L );
14 a[ 0 ] = len;
15
for ( i = 0; i < len; ++i ) {
16 a[ len - i ] = (int)(s[ i ] - '0');
17
}
18
}
19
20
void
mul(
int
c[],
int
a[],
int
b[] )
{
21 int la = a[ 0 ], lb = b[ 0 ], i, j;
22 memset( c, 0, sizeof(int)*L );
23 for ( i = 1; i <= la; ++i ) {
24 for ( j = 1; j <= lb; ++j ) {
25 c[ i + j - 1 ] += a[ i ] * b[ j ];
26 c[ i + j ] += c[ i + j - 1 ] / 10;
27 c[ i + j - 1 ] %= 10;
28 }
29 }
30 c[ 0 ] = la + lb;
31 while ( (c[0]>1) && (c[c[0]]==0) ) {
32 --c[ 0 ];
33 }
34}
35
36
void
output(
int
a[] )
{
37 int i;
38 for ( i = a[ 0 ]; i >= 1; --i ) {
39 printf( "%d", a[ i ] );
40 }
41 printf( "\n" );
42}
43
44
int
main()
{
45 int td;
46 scanf( "%d", &td );
47 while ( td-- > 0 ) {
48 input( a );
49 input( b );
50 mul( c, a, b );
51 output( c );
52 }
53 return 0;
54}
55
#include
<
stdio.h
>
2
#include
<
string
.h
>
3
4
#define
L 1009
5
6
int
a[ L ], b[ L ], c[ L ];7
8
void
input(
int
a[] )
{9
char s[ L ];10
int len, i;11
scanf( "%s", s );12
len = strlen( s );13
memset( a, 0, sizeof(int)*L );14
a[ 0 ] = len;15
for ( i = 0; i < len; ++i ) {16
a[ len - i ] = (int)(s[ i ] - '0');17
}18
}
19
20
void
mul(
int
c[],
int
a[],
int
b[] )
{21
int la = a[ 0 ], lb = b[ 0 ], i, j;22
memset( c, 0, sizeof(int)*L );23
for ( i = 1; i <= la; ++i ) {24
for ( j = 1; j <= lb; ++j ) {25
c[ i + j - 1 ] += a[ i ] * b[ j ];26
c[ i + j ] += c[ i + j - 1 ] / 10;27
c[ i + j - 1 ] %= 10;28
}29
}30
c[ 0 ] = la + lb;31
while ( (c[0]>1) && (c[c[0]]==0) ) {32
--c[ 0 ];33
}34
}
35
36
void
output(
int
a[] )
{37
int i;38
for ( i = a[ 0 ]; i >= 1; --i ) {39
printf( "%d", a[ i ] );40
}41
printf( "\n" );42
}
43
44
int
main()
{45
int td;46
scanf( "%d", &td );47
while ( td-- > 0 ) {48
input( a );49
input( b );50
mul( c, a, b );51
output( c );52
}53
return 0;54
}
55
使用二分加速的高精度乘法
1
#include
<
iostream
>
2#include
<
cstdio
>
3#include
<
cstring
>
4
5
using
namespace
std;
6
7
#define
L 1002
8
#define
LIM 500
9
10typedef
int
BI[ L ];
11BI buf[ LIM ];
12
int
top;
13
14
#define
bi_copy(a,b) memcpy( (void*)(a), (void*)(b), sizeof(int)*L )
15
16
void
bi_out(
int
a[] )
{
17 char s[ L ];
18 int i;
19 for ( i = 0; i < a[0]; ++i ) {
20 s[ i ] = a[ a[0] - i ] + '0';
21 }
22 s[ a[0] ] = 0;
23 puts( s );
24}
25
26
void
bi_in(
int
a[] )
{
27 int len, i;
28 char s[ L ];
29 scanf( "%s", s );
30 len = strlen( s );
31 a[ 0 ] = len;
32 for ( i = 0; i < len; ++i ) {
33 a[ len - i ] = s[ i ] - '0';
34 }
35}
36
37
void
bi_add(
int
c[],
int
a[],
int
b[] )
{
38 int i, g = 0;
39 for ( i = 1; (i<=a[0])&&(i<=b[0]); ++i ) {
40 g += a[ i ] + b[ i ];
41 c[ i ] = g % 10;
42 g /= 10;
43 }
44 while ( i <= a[0] ) {
45 g += a[ i ];
46 c[ i ] = g % 10;
47 g /= 10;
48 ++i;
49 }
50 while ( i <= b[ 0 ] ) {
51 g += b[ i ];
52 c[ i ] = g % 10;
53 g /= 10;
54 ++i;
55 }
56 while ( g > 0 ) {
57 c[ i ] = g % 10;
58 g /= 10;
59 ++i;
60 }
61 c[ 0 ] = i - 1;
62}
63
64
void
bi_shiftL(
int
a[],
int
n )
{
65 int i;
66 if ( n <= 0 ) {
67 return;
68 }
69 for ( i = a[0]; i >= 1; --i ) {
70 a[ i+n ] = a[ i ];
71 }
72 for ( i = 1; i <= n; ++i ) {
73 a[ i ] = 0;
74 }
75 a[ 0 ] += n;
76}
77
78
//
c[0] >= 2
79
void
bi_half(
int
a[],
int
b[],
int
c[] )
{
80 int i;
81 b[ 0 ] = ( c[ 0 ] >> 1 );
82 for ( i = b[ 0 ]; i >= 1; --i ) {
83 b[ i ] = c[ i ];
84 }
85 a[ 0 ] = c[ 0 ] - b[ 0 ];
86 for ( i = a[ 0 ]; i >= 1; --i ) {
87 a[ i ] = c[ b[ 0 ] + i ];
88 }
89}
90
91
void
bi_mul(
int
c[],
int
a[],
int
b[] )
{
92#define ADD(x) BI &x = buf[ top++ ]
93#define ENTER ADD(w); ADD(x); ADD(y); ADD(z); ADD(r); ADD(s); ADD(t)
94#define LEAVE top -= 7; return
95#define MULONE( a, b ) { \
96 int i, x = a[ 1 ], g = 0; \
97 for ( i = 1; i <= b[ 0 ]; ++i ) { \
98 g += b[ i ] * x; \
99 c[ i ] = g % 10; \
100 g /= 10; \
101 } \
102 while ( g > 0 ) { \
103 c[ i++ ] = g % 10; \
104 g /= 10; \
105 } \
106 --i; \
107 while ( (i>1) && (c[i]==0) ) { \
108 --i; \
109 } \
110 c[ 0 ] = i; \
111 }
112
113
if
( (a[
0
]
<
1
)
||
(b[
0
]
<
1
) )
{
114 return;
115 }
116
117 ENTER;
118
119
//
for debug
120
if
( top
>=
LIM )
{
121 fprintf( stderr, "buf overflow" );
122 LEAVE;
123 }
124
125
if
( a[
0
]
==
1
)
{
126 MULONE( a, b );
127 LEAVE;
128 }
129
if
( b[
0
]
==
1
)
{
130 MULONE( b, a );
131 LEAVE;
132 }
133 bi_half( w, x, a );
134 bi_half( y, z, b );
135 bi_mul( r, w, y );
136 bi_shiftL( r, (a[
0
]
>>
1
)
+
(b[
0
]
>>
1
) );
137 bi_mul( s, z, w );
138 bi_shiftL( s, (a[
0
]
>>
1
) );
139 bi_add( t, r, s );
140 bi_mul( r, x, y );
141 bi_shiftL( r, (b[
0
]
>>
1
) );
142 bi_mul( s, x, z );
143 bi_add( c, t, r );
144 bi_add( t, c, s );
145 bi_copy( c, t );
146 LEAVE;
147
148
#undef
ADD
149
#undef
ENTER
150
#undef
LEAVE
151
#undef
MULONE
152}
153
154
int
main()
{
155 int td, a[ L ], b[ L ], c[ L ];
156 scanf( "%d", &td );
157 while ( td-- > 0 ) {
158 top = 0;
159 bi_in( a );
160 bi_in( b );
161 bi_mul( c, a, b );
162 bi_out( c );
163 }
164 return 0;
165}
166
#include
<
iostream
>
2
#include
<
cstdio
>
3
#include
<
cstring
>
4
5
using
namespace
std;6
7
#define
L 1002
8
#define
LIM 500
9
10
typedef
int
BI[ L ];11
BI buf[ LIM ];12
int
top;13
14
#define
bi_copy(a,b) memcpy( (void*)(a), (void*)(b), sizeof(int)*L )
15
16
void
bi_out(
int
a[] )
{17
char s[ L ];18
int i;19
for ( i = 0; i < a[0]; ++i ) {20
s[ i ] = a[ a[0] - i ] + '0';21
}22
s[ a[0] ] = 0;23
puts( s );24
}
25
26
void
bi_in(
int
a[] )
{27
int len, i;28
char s[ L ];29
scanf( "%s", s );30
len = strlen( s );31
a[ 0 ] = len;32
for ( i = 0; i < len; ++i ) {33
a[ len - i ] = s[ i ] - '0';34
}35
}
36
37
void
bi_add(
int
c[],
int
a[],
int
b[] )
{38
int i, g = 0;39
for ( i = 1; (i<=a[0])&&(i<=b[0]); ++i ) {40
g += a[ i ] + b[ i ];41
c[ i ] = g % 10;42
g /= 10;43
}44
while ( i <= a[0] ) {45
g += a[ i ];46
c[ i ] = g % 10;47
g /= 10;48
++i;49
}50
while ( i <= b[ 0 ] ) {51
g += b[ i ];52
c[ i ] = g % 10;53
g /= 10;54
++i;55
}56
while ( g > 0 ) {57
c[ i ] = g % 10;58
g /= 10;59
++i;60
}61
c[ 0 ] = i - 1;62
}
63
64
void
bi_shiftL(
int
a[],
int
n )
{65
int i;66
if ( n <= 0 ) {67
return;68
}69
for ( i = a[0]; i >= 1; --i ) {70
a[ i+n ] = a[ i ];71
}72
for ( i = 1; i <= n; ++i ) {73
a[ i ] = 0;74
}75
a[ 0 ] += n;76
}
77
78
//
c[0] >= 2
79
void
bi_half(
int
a[],
int
b[],
int
c[] )
{80
int i;81
b[ 0 ] = ( c[ 0 ] >> 1 );82
for ( i = b[ 0 ]; i >= 1; --i ) {83
b[ i ] = c[ i ];84
}85
a[ 0 ] = c[ 0 ] - b[ 0 ];86
for ( i = a[ 0 ]; i >= 1; --i ) {87
a[ i ] = c[ b[ 0 ] + i ];88
}89
}
90
91
void
bi_mul(
int
c[],
int
a[],
int
b[] )
{92
#define ADD(x) BI &x = buf[ top++ ]93
#define ENTER ADD(w); ADD(x); ADD(y); ADD(z); ADD(r); ADD(s); ADD(t)94
#define LEAVE top -= 7; return95
#define MULONE( a, b ) { \96
int i, x = a[ 1 ], g = 0; \97
for ( i = 1; i <= b[ 0 ]; ++i ) { \98
g += b[ i ] * x; \99
c[ i ] = g % 10; \100
g /= 10; \101
} \102
while ( g > 0 ) { \103
c[ i++ ] = g % 10; \104
g /= 10; \105
} \106
--i; \107
while ( (i>1) && (c[i]==0) ) { \108
--i; \109
} \110
c[ 0 ] = i; \111
}
112
113
if
( (a[
0
]
<
1
)
||
(b[
0
]
<
1
) )
{114
return;115
}
116
117
ENTER;118
119
//
for debug
120
if
( top
>=
LIM )
{121
fprintf( stderr, "buf overflow" );122
LEAVE;123
}
124
125
if
( a[
0
]
==
1
)
{126
MULONE( a, b );127
LEAVE;128
}
129
if
( b[
0
]
==
1
)
{130
MULONE( b, a );131
LEAVE;132
}
133
bi_half( w, x, a );134
bi_half( y, z, b );135
bi_mul( r, w, y );136
bi_shiftL( r, (a[
0
]
>>
1
)
+
(b[
0
]
>>
1
) );137
bi_mul( s, z, w );138
bi_shiftL( s, (a[
0
]
>>
1
) );139
bi_add( t, r, s );140
bi_mul( r, x, y );141
bi_shiftL( r, (b[
0
]
>>
1
) );142
bi_mul( s, x, z );143
bi_add( c, t, r );144
bi_add( t, c, s );145
bi_copy( c, t );146
LEAVE;147
148
#undef
ADD
149
#undef
ENTER
150
#undef
LEAVE
151
#undef
MULONE
152
}153
154
int
main()
{155
int td, a[ L ], b[ L ], c[ L ];156
scanf( "%d", &td );157
while ( td-- > 0 ) {158
top = 0;159
bi_in( a );160
bi_in( b );161
bi_mul( c, a, b );162
bi_out( c );163
}164
return 0;165
}
166
我的二分实现太挫了，加之这题数据规模太小，二分加速的反而慢一些，o(╯□╰)o