杨辉三角形是形如:
1
1 1
1 2 1
1 3 3 1
1 4 6 4 1
的三角形,其实质是二项式(a+b)的n次方展开后各项的系数排成的三角形,它的特点是左右两边全是1,从第二行起,中间的每一个数是上一行里相邻两个数之和。这个题目常用于程序设计的练习。
下面给出六种不同的解法。
解法一
#include <stdio.h>
main()
{ int i,j,n=0,a[17][17]={0}
while(n<1 || n>16)
{ printf("请输入杨辉三角形的行数:"雀差)
scanf("%d",&n)
}
for(i=0i<ni++)
a[i][0]=1
for(i=1i<ni++)
for(j=1j<=ij++)
a[i][j]=a[i-1][j-1]+a[i-1][j]
for(i=0i<ni++)
{ for(j=0j<=ij++)
printf("%5d",a[i][j])
printf("\n")
}
}
点评:解法一是一般最容易想到的解法,各部分功能独立,程序浅显易懂。
解法二
#include <stdio.h>
main()
{ int i,j,n=0,a[17][17]={1}
while(n<1 || n>16)
{ printf("请输入杨辉三角形的行数:")
scanf("%d",&n)
}
for(i=1i<ni++)
{ a[i][0]=1
for(j=1j<=ij++)
a[i][j]=a[i-1][j-1]+a[i-1][j]
}
for(i=0i<ni++)
{ for(j=0j<=ij++)
printf("%5d",a[i][j])
printf("\n")
}
}
点评:解窢二是顷隐皮在解法一的基础上,把第一列置为1的命令移到下面的双重循环中,减少了一个循环。注意初始化携丛数组的变化。
解法三
#include <stdio.h>
main()
{ int i,j,n=0,a[17][17]={0,1}
while(n<1 || n>16)
{ printf("请输入杨辉三角形的行数:")
scanf("%d",&n)
}
for(i=1i<=ni++)
for(j=1j<=ij++)
a[i][j]=a[i-1][j-1]+a[i-1][j]
for(i=1i<=ni++)
{ for(j=1j<=ij++) printf("%5d",a[i][j])
printf("\n")
}
}
点评:解法三是在解法一、二的基础上,把第一列置为1的命令去掉了,注意初始化数组的变化。
解法四
#include <stdio.h>
main()
{ int i,j,n=0,a[17][17]={0,1}
while(n<1 || n>16)
{ printf("请输入杨辉三角形的行数:")
scanf("%d",&n)
}
for(i=1i<=ni++)
{ for(j=1j<=ij++)
{ a[i][j]=a[i-1][j-1]+a[i-1][j]
printf("%5d",a[i][j])
}
printf("\n")
}
}
点评:解法四是在解法三的基础上,把计算和打印合并在一个双重循环中。
解法五
#include <stdio.h>
main()
{ int i,j,n=0,a[17]={1},b[17]
while(n<1 || n>16)
{ printf("请输入杨辉三角形的行数:")
scanf("%d",&n)
}
for(i=0i<ni++)
{ b[0]=a[0]
for(j=1j<=ij++)
b[j]=a[j-1]+a[j]
for(j=0j<=ij++)
{ a[j]=b[j]
printf("%5d",a[j])
}
printf("\n")
}
}
点评:解法一到解法四都用了二维数组,占用的空间较多。而解法五只使用了两个一维数组。
解法六
#include <stdio.h>
main()
{ int i,j,n=0,a[17]={0,1},l,r
while(n<1 || n>16)
{ printf("请输入杨辉三角形的行数:")
scanf("%d",&n)
}
for(i=1i<=ni++)
{ l=0
for(j=1j<=ij++)
{ r=a[j]
a[j]=l+r
l=r
printf("%5d",a[j])
}
printf("\n")
}
}
点评:解法六只使用了一个一维数组和两个临时变量。
输出缓冲区只有300行,再多了就把最前面的覆盖了,这是正常现象。当然可以扩大输出缓冲区,但考虑没有:扩大到400行你的需求满足了,另一程序侍蔽需要输出1000行又怎么办?所以不管输出缓冲区有多老缺州大,但总是有限的扮镇,不能要求把所有输出都在屏幕上显示出来……供参考。<饥老团!--STATUS OK--><html><head><含液title>百度贴吧_c++吧 </title>
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<td class="s"><a class=t href="/f?kz=96689304" target=_blank >【隆重】C++吧开始招吧主啦!</a>[<font class="red">精品</font>] [<font class="red">置顶</font>] </td>
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<td class="s"><a class=t href="/f?kz=107989315" target=_blank >经典绝妙题目,考考你的C/C++应用能力</a> </td>
<td class="u"><a href="http://passport.baidu.com/?detail&aid=6&default_tab=1&un=lianlxz%5F518" target=_blank><font color='#000000'>lianlxz_518</font></a></td>
<td class="u">10:35 <a href="http://passport.baidu.com/?detail&aid=6&default_tab=1&un=robber%5Ftys" target=_blank><font color='#000000'>robber_tys</font></a></td>
</tr><script>c(3)</script>
<td class="d"> 5</td>
<td class="d">1</td>
<td class="s"><a class=t href="/f?kz=108115645" target=_blank >【长期招聘软件高手】,兼职或全职</a> </td>
<td class="u"><font color='#000000'>221.221.200.*</font></td>
<td class="u">10:28 <a href="http://passport.baidu.com/?detail&aid=6&default_tab=1&un=liujioure" target=_blank><font color='#000000'>liujioure</font></a></td>
</tr><script>c(4)</script>
<td class="d"> 1</td>
<td class="d">0</td>
<td class="s"><a class=t href="/f?kz=108115216" target=_blank >【长期招聘软件高手】,兼职或全职.工作地点在北京</a> </td>
<td class="u"><font color='#000000'>221.221.200.*</font></td>
<td class="u">10:08 <font color='#000000'>221.221.200.*</font></td>
</tr><script>c(5)</script>
<td class="d"> 0</td>
<td class="d">0</td>
<td class="s"><a class=t href="/f?kz=108114981" target=_blank >【长期招聘软件高手】,兼职或全职.工作地点在北京</a> </td>
<td class="u"><font color='#000000'>221.221.200.*</font></td>
<td class="u">10:06 <font color='#000000'>221.221.200.*</font></td>
</tr><script>c(6)</script>
<td class="d"> 1822</td>
<td class="d">103</td>
<td class="s"><a class=t href="/f?kz=101575892" target=_blank >我认为研究生以下学历的人就不应该学c++编程!!!</a> </td>
<td class="u"><font color='#000000'>220.249.106.*</font></td>
<td class="u">10:04 <font color='#000000'>218.88.210.*</font></td>
</tr><script>c(7)</script>
<td class="d"> 134</td>
<td class="d">9</td>
<td class="s"><a class=t href="/f?kz=106514175" target=_blank >寻找C++编程高手</a> </td>
<td class="u"><a href="http://passport.baidu.com/?detail&aid=6&default_tab=1&un=%D1%C6%D1%C6%B9%AB%D6%F7" target=_blank><font color='#000000'>哑哑公主</font></a></td>
<td class="u">09:59 <a href="http://passport.baidu.com/?detail&aid=6&default_tab=1&un=liujioure" target=_blank><font color='#000000'>liujioure</font></a></td>
</tr><script>c(8)</script>
<td class="d"> 2</td>
<td class="d">0</td>
<td class="s"><a class=t href="/f?kz=108108494" target=_blank >有谁能给我一个300-400多行的程序,啥都可以!!!</a> </td>
<td class="u"><a href="http://passport.baidu.com/?detail&aid=6&default_tab=1&un=%CB%E6%B1%E3%C0%B4%C0%B4" target=_blank><font color='#000000'>随便来来</font></a></td>
<td class="u">09:28 <a href="http://passport.baidu.com/?detail&aid=6&default_tab=1&un=%CB%E6%B1%E3%C0%B4%C0%B4" target=_blank><font color='#000000'>随便来来</font></a></td>
</tr><script>c(9)</script>
<td class="d"> 142</td>
<td class="d">11</td>
<td class="s"><a class=t href="/f?kz=106514738" target=_blank >怎么样才能找到四五百行的程序呢???</a> </td>
<td class="u"><a href="http://passport.baidu.com/?detail&aid=6&default_tab=1&un=%D1%C6%D1%C6%B9%AB%D6%F7" target=_blank><font color='#000000'>哑哑公主</font></a></td>
<td class="u">09:18 <a href="http://passport.baidu.com/?detail&aid=6&default_tab=1&un=%D1%C6%D1%C6%B9%AB%D6%F7" target=_blank><font color='#000000'>哑哑公主</font></a></td>
</tr><script>c(10)</script>
<td class="d"> 426</td>
<td class="d">9</td>
<td class="s"><a class=t href="/f?kz=42607000" target=_blank >跪求学生宿舍管理系统的c或c++语言源码,十万火急啊!!!!</a> </td>
<td class="u"><font color='#000000'>219.140.173.*</font></td>
<td class="u">09:07 <font color='#000000'>211.65.95.*</font></td>
</tr><script>c(11)</script>
<td class="d"> 3165</td>
<td class="d">499</td>
<td class="s"><a class=t href="/f?kz=89611693" target=_blank >C++QQ群加会友</a> </td>
<td class="u"><a href="http://passport.baidu.com/?detail&aid=6&default_tab=1&un=xldn2005" target=_blank><font color='#000000'>xldn2005</font></a></td>
<td class="u">08:55 <font color='#000000'>221.8.184.*</font></td>
</tr><script>c(12)</script>
<td class="d">
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