10862 - Connect the Cable Wires

#include <map>
#include <set>
#include <cmath>
#include <stack>
#include <deque>
#include <queue>
#include <cctype>
#include <cstdio>
#include <string>
#include <vector>
#include <bitset>
#include <limits>
#include <cstdlib>
#include <cstring>
#include <cstring>
#include <iomanip>
#include <iostream>
#include <algorithm>
#include <utility>
#include <ctime>
// #define TEXTFILE
// #define RUN_TIME
using namespace std;

/*

题意：	一条直线上有n个点，直线外有1个圆圈，问把这n + 1个用n条线连起来有多少种方法

题解：	递推公式：f
= 3 * f[n - 1] - f[n - 2]
f[i][j]表示数列的第i个数从最低位0标到第j位高位的数字

*/

typedef long long LL;
const double eps = 1e-9;
const int INF = 1000000000;
const long long MOD = 1000000000000LL;
const int N = 1010;

int f[2010][1010];

int main(int argc, char const *argv[])
{
#ifdef TEXTFILE
freopen("test_in.txt", "r", stdin);
freopen("test_out.txt", "w", stdout);
#endif
#ifdef RUN_TIME
clock_t start_time = clock(), end_time;
#endif

memset(f, 0, sizeof(f));
f[1][0] = 1; f[2][0] = 3;
for(int i = 3; i < 2005; ++i) {
for(int j = 0; j < 1000; ++j)
f[i][j] = 3 * f[i - 1][j];
for(int j = 0; j < 1000; ++j) {
f[i][j + 1] += f[i][j] / 10;
f[i][j] %= 10;
}
for(int j = 0; j < 1000; ++j) {
while(f[i][j] < f[i - 2][j]) {
f[i][j] += 10;
--f[i][j + 1];
}
f[i][j] -= f[i - 2][j];
}
}
int n;
while(~scanf("%d", &n) && n) {
int i = 1000;
while(f
[i] == 0) --i;
while(i >= 0) printf("%d", f
[i--]);
puts("");
}

#ifdef RUN_TIME
end_time = clock();
cout<<double(end_time-start_time)/CLOCKS_PER_SEC<<endl;
#endif

return 0;
}