既求从点(0,0)仅仅能向上或者向右而且不穿越y=x到达点(a,b)有多少总走法...

有公式: C(a+b,min(a,b))-C(a+b,min(a,b)-1)  ///

折纸法证明卡特兰数: http://blog.sina.com.cn/s/blog_6917f47301010cno.html

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Time Limit: 2000/1000 MS (Java/Others)    Memory Limit: 65536/65536 K (Java/Others)
Total Submission(s): 506    Accepted Submission(s): 120

/* ***********************************************
Author        :CKboss
Created Time  :2015年03月18日 星期三 20时10分21秒
File Name     :HDOJ5184.cpp
************************************************ */#include <iostream>
#include <cstdio>
#include <cstring>
#include <algorithm>
#include <string>
#include <cmath>
#include <cstdlib>
#include <vector>
#include <queue>
#include <set>
#include <map>using namespace std;typedef long long int LL;const int maxn=1001000;
const LL mod=1000000007LL;int n,len;
char str[maxn];LL inv[maxn];
LL jc[maxn],jcv[maxn];void init()
{inv[1]=1; jc[0]=1; jcv[0]=1;jc[1]=1; jcv[1]=1;for(int i=2;i<maxn;i++){inv[i]=inv[mod%i]*(mod-mod/i)%mod;jc[i]=(jc[i-1]*i)%mod;jcv[i]=(jcv[i-1]*inv[i])%mod;}
}LL COMB(LL n,LL m)
{if(m<0||m>n) return 0LL;if(m==0||m==n) return 1LL;LL ret=((jc[n]*jcv[n-m])%mod*jcv[m])%mod;return ret;
}int main()
{//freopen("in.txt","r",stdin);//freopen("out.txt","w",stdout);init();while(scanf("%d",&n)!=EOF){scanf("%s",str);len=strlen(str);bool flag=true;if(n%2==1) flag=false;int left=0,right=0;for(int i=0;i<len&&flag;i++){if(str[i]=='(') left++;else if(str[i]==')') right++;if(left>=right) continue;else flag=false;}if(flag==false) { puts("0"); continue; }int a=n/2-left; /// remain leftint b=n/2-right; /// remain rightif(b>a) swap(a,b);LL ans = (COMB(a+b,b)-COMB(a+b,b-1)+mod)%mod;cout<<ans<<endl;}return 0;
}