初学者求助：入栈1234，出栈序列有几种？

[黑主理事长]

如题。或者告诉我怎么算也可以。先谢谢了。

[p0303230]

4321

[p0303230]

14种

[1/(n+1)]*[(2n)!/(n!)^2]

或者
f(0) = 1
f(1) = 1
f(2) = f(0)*f(1) + f(1)*f(0) = 2
f(3) = f(0)*f(2) + f(1)*f(1) + f(2)*f(0) = 5
..........
f(n) = f(0)*f(n - 1) + f(1)*f(n - 2) + ......... + f(n-2)*f(1) + f(n-1)*f(0)

#include<fstream.h>
#include<stdio.h>
int sin[]= {1, 2, 3, 4};
const int N = sizeof(sin) / sizeof(int);
int push[N*2];
int s[N];
ofstream out("xx.txt");

void calcout(int snum, int innum, int opNum)
{
if (innum) {
push[opNum]=true;
calcout(snum+1, innum-1, opNum+1);
if (snum>0) {
push[opNum]=false;
calcout(snum-1, innum, opNum+1);
}
}else {
static int num = 1;
out<<num++<<",";
int i;
for (i=opNum; i<N*2; i++) push[i]=false;
int spos=0, inpos=0;
// 打印出栈顺序
for (i=0; i<N*2; i++) {
if (push[i])
{
s[spos++] = sin[inpos++];
}
else {
out<<s[--spos];
}
}
// 打印出栈顺序对应的进出栈操作序列
for (i=0; i<N*2; i++) {
if (push[i]) out<<"<" ;
else out<<">";
}
out<<"\n";
}
}
int main(int argc, char* argv[])
{
calcout(0, N, 0);
return 0;
}

[p0303230]

14种

[1/(n+1)]*[(2n)!/(n!)^2]

或者
f(0) = 1
f(1) = 1
f(2) = f(0)*f(1) + f(1)*f(0) = 2
f(3) = f(0)*f(2) + f(1)*f(1) + f(2)*f(0) = 5
..........
f(n) = f(0)*f(n - 1) + f(1)*f(n - 2) + ......... + f(n-2)*f(1) + f(n-1)*f(0)
[code=C/C++]

#include<fstream.h>
#include<stdio.h>
int sin[]= {1, 2, 3, 4};
const int N = sizeof(sin) / sizeof(int);
int push[N*2];
int s[N];
ofstream out("xx.txt");

void calcout(int snum, int innum, int opNum)
{
if (innum) {
push[opNum]=true;
calcout(snum+1, innum-1, opNum+1);
if (snum>0) {
push[opNum]=false;
calcout(snum-1, innum, opNum+1);
}
}else {
static int num = 1;
out<<num++<<",";
int i;
for (i=opNum; i<N*2; i++) push[i]=false;
int spos=0, inpos=0;
// 打印出栈顺序
for (i=0; i<N*2; i++) {
if (push[i])
{
s[spos++] = sin[inpos++];
}
else {
out<<s[--spos];
}
}
// 打印出栈顺序对应的进出栈操作序列
for (i=0; i<N*2; i++) {
if (push[i]) out<<"<" ;
else out<<">";
}
out<<"\n";
}
}
int main(int argc, char* argv[])
{
calcout(0, N, 0);
return 0;
}[/code]

[p0303230]

[code=C/C++]#include<fstream.h>
#include<stdio.h>
int   sin[]=   {1,   2,   3,   4};   
  const   int   N   =   sizeof(sin)   /   sizeof(int);   
  int   push[N*2];   
  int   s[N];   
  ofstream out("xx.txt");   

void   calcout(int   snum,   int   innum,   int   opNum)   
  {
	if   (innum)   {
		push[opNum]=true;
		calcout(snum+1,   innum-1,   opNum+1); 
		if   (snum>0)   {
			push[opNum]=false;
			calcout(snum-1,   innum,   opNum+1);
		}
		}else   { 
			static int num = 1;
			out<<num++<<",";
			int   i;   
			for   (i=opNum;   i<N*2;   i++)   push[i]=false; 
			int   spos=0,   inpos=0;
			//   打印出栈顺序
			for   (i=0;   i<N*2;   i++)   {
				if   (push[i])  
				{
					s[spos++]   =   sin[inpos++];
				}
				else   {
					out<<s[--spos];
				}
			} 
			//   打印出栈顺序对应的进出栈操作序列 
			for   (i=0;   i<N*2;   i++)   {
				if   (push[i])   out<<"<"  ;
				else  out<<">";
			}  
			out<<"\n";
		}   
  }  
  int   main(int   argc,   char*   argv[])   
  {   
   calcout(0,   N,   0);
  return   0;   
  }

[/code]

[zimuqingyang]

楼上的弄得那么复杂阿，我就知道一种4321，呵呵，不知道其他的出栈顺序，麻烦楼上的赐教其他的出栈顺序，不胜感激

[p0303230]

把程序拷到你机子上运行一下就知道了
或者百度一下 这里不列出了

[liquid_7788]

只知道一种,其他十几种都是什么,想了解下

[p0303230]

1,4321
2,3421
3,3241
4,3214
5,2431
6,2341
7,2314
8,2143
9,2134
10,1432
11,1342
12,1324
13,1243
14,1234

[p0303230]

比如第二种情况
1 进
2 进
3 进
3 出 3
4 进
4 出 34
。。。。

[zimuqingyang]

明白.谢谢p0303230

[黑主理事长]

谢谢p0303230