题目链接：http://acm.csu.edu.cn/OnlineJudge/problem.php?id=1561
题面：
1561: (More) Multiplication
Time Limit: 1 Sec Memory Limit: 128 MB
Submit: 180 Solved: 95
Description
Educators are always coming up with new ways to teach math to students. In 2011, an educational software company, All Computer Math (ACM), developed an application to display products in a traditional grade school math format. ACM is now working on an
updated version of the software that will display results in a lattice format that some students find to be easier when multiplying larger numbers.
An example would be when multiplying 345 * 56 = 19320 as given below, using a lattice grid with 2 rows and 3 columns, which appears inside a surrounding frame:
+---------------+
| 3 4 5 |
| +---+---+---+ |
| |1 /|2 /|2 /| |
| | / | / | / |5|
|1|/ 5|/ 0|/ 5| |
| +---+---+---+ |
|/|1 /|2 /|3 /| |
| | / | / | / |6|
|9|/ 8|/ 4|/ 0| |
| +---+---+---+ |
|/ 3 / 2 / 0 |
+---------------+
The first operand, 345, is displayed above the top of the grid with each digit centered horizontally above its column of the grid, and the second operand, 56, is displayed along the righthand side with each digit
centered vertically at the center of its row in the grid. A single cell of the grid, such as
+---+
|3 /|
| / |
|/ 0|
+---+
represents the product of the digit of the first operand that is above its column and the digit of the second operand that is to the right of its row. In our example, this cell represents the product 5 times 6 = 30 that results when multiplying the 5 in
345 and the 6 in 56. Note that the 10‘s digit of that product is placed in the upper left portion of this cell and the 1‘s digit in the lower right.
The overall product is then computed by summing along the diagonals in the lattice that represent the same place values in the result. For example, in our first problem the product 19320 was computed as:
| 1‘s digit | = 0 |
| 10‘s digit | = 5 + 3 + 4 = 12, thus 2 with a carry of 1 |
| 100‘s digit | = (1 carry) + 2 + 0 + 2 + 8 = 13, thus 3 with a carry of 1 |
| 1000‘s digit | = (1 carry) + 2 + 5 + 1 = 9 |
| 10000‘s digit | = 1 |
The resulting product is placed with the one‘s digit below the grid at the far right and, depending on its length, with the most significant digits wrapped around the left side of the grid. Each digit of the final product appears perfectly aligned with
the corresponding diagonal summands.
To provide an aesthetic view, we use a series of minus (-) characters for horizontal lines, pipe (|) characters for vertical lines, and slash (/) characters for diagonal lines. Furthermore, we use a plus (+) character wherever a horizontal and vertical line
meet. Each multiplication lattice is subsequently "boxed" by an outer border. There is a row containing the first operand which is between the topmost border and the top line of the grid, and a row between the bottom of the grid and the bottom border, which
contains some portion of the resulting product. There is one column between the leading | and the left edge of the inner grid, which may contain a portion of the resulting product, and one column after the right edge of the inner grid but before the rightmost
| border, which contains the second operand. If the product is not long enough to wrap around the bottom-left corner, the column between the left border and the left edge of the grid will containing only spaces. (See the later example of 3 x 3.)
Leading zeros should be displayed within lattice grid cells, but leading zeros should never be displayed in the product, nor should there ever be a slash (/) character prior to the leading digit of the product. For example, consider the product of 12 * 27 =
324 below:
+-----------+
| 1 2 |
| +---+---+ |
| |0 /|0 /| |
| | / | / |2|
| |/ 2|/ 4| |
| +---+---+ |
| |0 /|1 /| |
| | / | / |7|
|3|/ 7|/ 4| |
| +---+---+ |
|/ 2 / 4 |
+-----------+
Note that in the top-right grid of the lattice, the product 2 * 2 = 04 is displayed with the zero for the tens digit. However, there is no thousands digit displayed in the product 324, nor is there any slash displayed above the digit 3 in that product.
Input
The input contains one or more tests. Each test contains two positive integers, A and B, such that 1 ≤ A ≤ 9999 and 1 ≤ B ≤ 9999. The last data set will be followed by a line containing 0 0.
Output
For each data set, produce the grid that illustrates how to multiply the two numbers using the lattice multiplication technique.
Sample Input
345 56 12 27 1 68 9999 7 3 3 0 0
Sample Output
+---------------+ | 3 4 5 | | +---+---+---+ | | |1 /|2 /|2 /| | | | / | / | / |5| |1|/ 5|/ 0|/ 5| | | +---+---+---+ | |/|1 /|2 /|3 /| | | | / | / | / |6| |9|/ 8|/ 4|/ 0| | | +---+---+---+ | |/ 3 / 2 / 0 | +---------------+ +-----------+ | 1 2 | | +---+---+ | | |0 /|0 /| | | | / | / |2| | |/ 2|/ 4| | | +---+---+ | | |0 /|1 /| | | | / | / |7| |3|/ 7|/ 4| | | +---+---+ | |/ 2 / 4 | +-----------+ +-------+ | 1 | | +---+ | | |0 /| | | | / |6| | |/ 6| | | +---+ | | |0 /| | | | / |8| |6|/ 8| | | +---+ | |/ 8 | +-------+ +-------------------+ | 9 9 9 9 | | +---+---+---+---+ | | |6 /|6 /|6 /|6 /| | | | / | / | / | / |7| |6|/ 3|/ 3|/ 3|/ 3| | | +---+---+---+---+ | |/ 9 / 9 / 9 / 3 | +-------------------+ +-------+ | 3 | | +---+ | | |0 /| | | | / |3| | |/ 9| | | +---+ | | 9 | +-------+
HINT
The tables must be formatted precisely as outlined by the rules and examples provided. Mistakes that involve solely errant whitespace will be categorized as Presentation Error; all other errors will be reported as Wrong Answer.
解题：
此题不仅看上去烦，其实是真烦。不过，要输出的值都可以先算出来，保存下来，输出的时候加以判断就好了。像结果保存在string和int中。中间过程保留在二维数组中。比较坑的一点是左边和左下角的”/“，如果之前没有值的话，是不需要的，这里写起来挺烦的。能够1A还是挺高兴的！
代码：
#include <iostream>
#include <string>
#include <algorithm>
#include <cstring>
using namespace std;
int store[5][5];
int toInt(string s)
{
int ans=0,t=1;
reverse(s.begin(),s.end());
for(int i=0;i<s.length();i++)
{
ans+=(s[i]-'0')*t;
t*=10;
}
return ans;
}
string toString(int x)
{
string res="";
if(x==0)
{
res+="0";
return res;
}
while(x)
{
res+=char(x%10+'0');
x/=10;
}
reverse(res.begin(),res.end());
return res;
}
int main()
{
string a,b,ans;
int ia,ib,ians,cnt;
bool flag;
while(cin>>a>>b)
{
cnt=0;
flag=false;
ia=toInt(a);
ib=toInt(b);
if(!(ia||ib))break;
ians=ia*ib;
ans=toString(ians);
for(int i=0;i<b.length();i++)
{
for(int j=0;j<a.length();j++)
store[i][j]=(b[i]-'0')*(a[j]-'0');
}
//1
cout<<"+"<<string((a.length()-1)*4+7,'-')<<"+\n";
//2
cout<<'|'<<string(3,' ');
for(int i=0;i<a.length();i++)
{
cout<<a[i]<<string(3,' ');
}
cout<<"|\n";
//3
cout<<"| +";
for(int i=0;i<a.length();i++)
{
cout<<"---+";
}
cout<<" |"<<"\n";
for(int i=0;i<b.length();i++)
{
//4+T*n
cout<<"|";
if(!flag)
{
if(ans.length()+i>=(a.length()+b.length()))
{
flag=true;
}
cout<<' ';
}
else cout<<'/';
for(int j=0;j<a.length();j++)
{
cout<<'|';
cout<<char(store[i][j]/10+'0')<<' '<<'/';
}
cout<<"| |\n";
//5+T*n
cout<<"| ";
for(int j=0;j<a.length();j++)
cout<<"| / ";
cout<<"|"<<b[i]<<"|\n";
//6+T*n
cout<<"|";
if((i+ans.length())>=(a.length()+b.length()))
cout<<ans[cnt++];
else cout<<" ";
for(int j=0;j<a.length();j++)
{
cout<<"|/ ";
cout<<char(store[i][j]%10+'0');
}
cout<<"| |\n";
//7+T*n
cout<<"| +";
for(int j=0;j<a.length();j++)
cout<<"---+";
cout<<" |\n";
}
//倒数第2行
cout<<"|";
if(ans.length()>a.length())
cout<<"/";
else cout<<" ";
for(int i=0;i<a.length()-1;i++)
{
cout<<" ";
cout<<ans[ans.length()-a.length()+i];
cout<<" /";
}
cout<<" "<<ans[ans.length()-1]<<string(4,' ')<<"|\n";
//最后一行
cout<<"+"<<string((a.length()-1)*4+7,'-')<<"+\n";
}
return 0;
}
1561: (More) Multiplication
Time Limit: 1 Sec Memory Limit: 128 MB
Submit: 180 Solved: 95
Description
Educators are always coming up with new ways to teach math to students. In 2011, an educational software company, All Computer Math (ACM), developed an application to display products in a traditional grade school math format. ACM is now working on an
updated version of the software that will display results in a lattice format that some students find to be easier when multiplying larger numbers.
An example would be when multiplying 345 * 56 = 19320 as given below, using a lattice grid with 2 rows and 3 columns, which appears inside a surrounding frame:
+---------------+
| 3 4 5 |
| +---+---+---+ |
| |1 /|2 /|2 /| |
| | / | / | / |5|
|1|/ 5|/ 0|/ 5| |
| +---+---+---+ |
|/|1 /|2 /|3 /| |
| | / | / | / |6|
|9|/ 8|/ 4|/ 0| |
| +---+---+---+ |
|/ 3 / 2 / 0 |
+---------------+
The first operand, 345, is displayed above the top of the grid with each digit centered horizontally above its column of the grid, and the second operand, 56, is displayed along the righthand side with each digit
centered vertically at the center of its row in the grid. A single cell of the grid, such as
+---+
|3 /|
| / |
|/ 0|
+---+
represents the product of the digit of the first operand that is above its column and the digit of the second operand that is to the right of its row. In our example, this cell represents the product 5 times 6 = 30 that results when multiplying the 5 in
345 and the 6 in 56. Note that the 10‘s digit of that product is placed in the upper left portion of this cell and the 1‘s digit in the lower right.
The overall product is then computed by summing along the diagonals in the lattice that represent the same place values in the result. For example, in our first problem the product 19320 was computed as:
| 1‘s digit | = 0 |
| 10‘s digit | = 5 + 3 + 4 = 12, thus 2 with a carry of 1 |
| 100‘s digit | = (1 carry) + 2 + 0 + 2 + 8 = 13, thus 3 with a carry of 1 |
| 1000‘s digit | = (1 carry) + 2 + 5 + 1 = 9 |
| 10000‘s digit | = 1 |
The resulting product is placed with the one‘s digit below the grid at the far right and, depending on its length, with the most significant digits wrapped around the left side of the grid. Each digit of the final product appears perfectly aligned with
the corresponding diagonal summands.
To provide an aesthetic view, we use a series of minus (-) characters for horizontal lines, pipe (|) characters for vertical lines, and slash (/) characters for diagonal lines. Furthermore, we use a plus (+) character wherever a horizontal and vertical line
meet. Each multiplication lattice is subsequently "boxed" by an outer border. There is a row containing the first operand which is between the topmost border and the top line of the grid, and a row between the bottom of the grid and the bottom border, which
contains some portion of the resulting product. There is one column between the leading | and the left edge of the inner grid, which may contain a portion of the resulting product, and one column after the right edge of the inner grid but before the rightmost
| border, which contains the second operand. If the product is not long enough to wrap around the bottom-left corner, the column between the left border and the left edge of the grid will containing only spaces. (See the later example of 3 x 3.)
Leading zeros should be displayed within lattice grid cells, but leading zeros should never be displayed in the product, nor should there ever be a slash (/) character prior to the leading digit of the product. For example, consider the product of 12 * 27 =
324 below:
+-----------+
| 1 2 |
| +---+---+ |
| |0 /|0 /| |
| | / | / |2|
| |/ 2|/ 4| |
| +---+---+ |
| |0 /|1 /| |
| | / | / |7|
|3|/ 7|/ 4| |
| +---+---+ |
|/ 2 / 4 |
+-----------+
Note that in the top-right grid of the lattice, the product 2 * 2 = 04 is displayed with the zero for the tens digit. However, there is no thousands digit displayed in the product 324, nor is there any slash displayed above the digit 3 in that product.
Input
The input contains one or more tests. Each test contains two positive integers, A and B, such that 1 ≤ A ≤ 9999 and 1 ≤ B ≤ 9999. The last data set will be followed by a line containing 0 0.
Output
For each data set, produce the grid that illustrates how to multiply the two numbers using the lattice multiplication technique.
Sample Input
345 56 12 27 1 68 9999 7 3 3 0 0
Sample Output
+---------------+ | 3 4 5 | | +---+---+---+ | | |1 /|2 /|2 /| | | | / | / | / |5| |1|/ 5|/ 0|/ 5| | | +---+---+---+ | |/|1 /|2 /|3 /| | | | / | / | / |6| |9|/ 8|/ 4|/ 0| | | +---+---+---+ | |/ 3 / 2 / 0 | +---------------+ +-----------+ | 1 2 | | +---+---+ | | |0 /|0 /| | | | / | / |2| | |/ 2|/ 4| | | +---+---+ | | |0 /|1 /| | | | / | / |7| |3|/ 7|/ 4| | | +---+---+ | |/ 2 / 4 | +-----------+ +-------+ | 1 | | +---+ | | |0 /| | | | / |6| | |/ 6| | | +---+ | | |0 /| | | | / |8| |6|/ 8| | | +---+ | |/ 8 | +-------+ +-------------------+ | 9 9 9 9 | | +---+---+---+---+ | | |6 /|6 /|6 /|6 /| | | | / | / | / | / |7| |6|/ 3|/ 3|/ 3|/ 3| | | +---+---+---+---+ | |/ 9 / 9 / 9 / 3 | +-------------------+ +-------+ | 3 | | +---+ | | |0 /| | | | / |3| | |/ 9| | | +---+ | | 9 | +-------+
HINT
The tables must be formatted precisely as outlined by the rules and examples provided. Mistakes that involve solely errant whitespace will be categorized as Presentation Error; all other errors will be reported as Wrong Answer.