hdu 1131 Count the Trees(catalan数的应用)

catalan数

/*Author: ACb0yDate: 2010年11月13日17:16:51Type: catalan数的应用 递推公式为：C( n ) = n * (4*n - 2)* C(n - 1)/(n + 1);ProblemId: hdu 1131 Count the TreesResult: 31903602010-11-13 17:13:59Accepted11310MS588K1123 BG++ACb0y*/#include <iostream>using namespace std;struct node {int digit[800];int len;};node ans[101];void print_ans(int pos) {node & cur = ans[pos];for (int i = cur.len - 1; i >= 0; --i) {printf("%d", cur.digit[i]);}printf("/n");}void get_ans() {int i, j;int up;ans[1].len = 1;ans[1].digit[0] = 1;for (i = 2; i <= 100; ++i) {node & pre = ans[i - 1];node & cur = ans[i];for (j = 0; j < pre.len; ++j) {cur.digit[j] = pre.digit[j] * (4 * i - 2) * i;}cur.len = pre.len;for (j = up = 0; j < cur.len; ++j) {up += cur.digit[j];cur.digit[j] = up % 10;up /= 10;}while (up) {cur.digit[cur.len] = up % 10;up /= 10;cur.len++;}up = 0;for (j = cur.len - 1; j >= 0; --j) {up *= 10;up += cur.digit[j];cur.digit[j] = up / (i + 1);up %= i + 1;}while (cur.digit[cur.len - 1] == 0) {cur.len--;}}}int main() {#ifndef ONLINE_JUDGEfreopen("in.txt", "r", stdin);#endifint n;get_ans();while (scanf("%d", &n) != EOF) {if (n == 0) {break;} else {print_ans(n);}}return 0;}