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计数器

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乱代码之右三角
N皇后问题

卡特兰数

Star posted @ 2010年8月08日 23:29 in C语言 with tags c 数学 递归式 高精度 排列组合 , 2093 阅读

$$C(0) = 1$$

$$C(n) = \frac{C(n-1)(4n-2)}{n+1} (n>0)$$

#include <stdio.h>
int C[101][101], len[101];

int main(void)
{
	int i, j, r, t, l;
	C[0][0] = 1;
	len[0]  = 1;
	l       = 1;        //长度
	
	for(i = 1; i <= 100; ++i)
	{
		for(j = 0; j < l; ++j)        //乘法
			C[i][j] = C[i-1][j] * (4*i-2);
		for(r=j = 0; j < l; ++j)
		{
			t       = C[i][j] + r;
			C[i][j] = t % 10;
			r       = t / 10;
		}
		while(r)
			C[i][l++] = r % 10, r /= 10;
		for(j = l-1, r = 0; j >= 0; --j)        //除法
		{
			t       = r*10 + C[i][j];
			C[i][j] = t / (i+1);
			r       = t % (i+1);
		}
		while(!C[i][l-1])
			--l;
		len[i] = l;
	}
			
	for(i = 1; i <= 100; ++i)
	{
		printf("%d:", i);
		for(j = len[i]-1; j >= 0; --j)
			printf("%d", C[i][j]);
		putchar(10);
	}
	
	return 0;
}
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