Rooted Trees Problem
Time Limit: 2000/1000 MS (Java/Others) Memory Limit: 65536/32768 K (Java/Others)Total Submission(s): 337 Accepted Submission(s): 108
分情况,分为有 1, 2, 3, ..., n-1 个子树的情况,然后相加。
#include <cstdio>
#include <cstdlib>
#include <cassert>
#include <cstring>
#include <cmath>
#include <vector>
#include <algorithm>
using namespace std;
long long GCD (long long a, long long b) {
return b ? GCD (b, a % b) : a;
}
long long C (long long n, long long m) {
long long num = 1; // numerator
long long don = 1; // doneminator
if (n - m < m) {
m = n - m;
}
long long gcd;
while (m) {
gcd = GCD (num, don);
num /= gcd;
don /= gcd;
num *= n--;
don *= m--;
}
assert (num % don == 0);
return num / don;
}
int a [10000][50]; // once this array is accessed violation, variable sz's value may be modified!!!
int sz;
void Devide (int last, int len, int rest, int ind) {
#ifdef _DEBUG
//printf ("Devide (last = %d, len = %d, rest = %d, ind = %d)\n", last, len, rest, ind);
#endif
if (ind == len) {
assert (sz + 1 < 10000); // this assertion can catch the bug.
assert (rest == 0);
for (int i=0; i<len; ++i) {
a [sz + 1][i] = a [sz][i];
}
++sz;
return;
}
assert (sz < 100000); // this assertion cannot catch the bug, because ...
#ifdef _DEBUG
int t = lrint (ceil (1.0 * rest / (len - ind)));
assert (t * (len - ind) >= rest);
assert ((t - 1) * (len - ind) < rest);
#endif
for (int i=lrint(ceil(1.0*rest/(len-ind))); i<=last && len-ind-1<=rest-i; ++i) {
a [sz][ind] = i;
Devide (i, len, rest-i, ind+1);
}
}
void Make (int n, int len) {
#ifdef _DEBUG
//printf ("Make (n = %d, len = %d)\n", n, len);
#endif
sz = 0;
#ifdef _DEBUG
int t = lrint (ceil (1.0 * n / len));
assert (t * len >= n);
assert ((t - 1) * len < n);
#endif
for (int i=lrint(ceil(1.0*n/len)); i<=n-len+1; ++i) {
a [sz][0] = i;
Devide (i, len, n-i, 1);
}
#ifdef _DEBUG
for (int i=0; i<sz; ++i) {
for (int k=0; k<len; ++k) {
printf ("%d%s", a [i][k], k==len-1 ? "\n" : " ");
}
}
#endif
}
long long dp [50];
long long DP (long long n) { // it's no longer a dp!!! what it is named is just for historic reason.
#ifdef _DEBUG
//printf ("DP (n = %lld)\n", n);
#endif
for (int i=1; i<n; ++i) {
sz = 0;
Make (n - 1, i);
for (int s=0; s<sz; ++s) {
long long t = 1;
int k = 0, m = 0;
while (k < i && m < i) {
m = k;
while (++m < i && a [s][m] == a [s][k]) {}
t *= C (dp [a [s][k]] + m - k - 1, m - k);
k = m;
}
dp [n] += t;
#ifdef _DEBUG
printf ("dp [%lld] = %lld\n", n, dp [n]);
#endif
}
}
return dp [n];
}
void MakeDP () {
memset (dp, 0, sizeof (dp));
dp [1] = dp [2] = 1;
for (int i=3; i<=40; ++i) {
DP (i);
}
}
int main () {
MakeDP ();
int n;
while (scanf ("%d", &n) == 1) {
printf ("%lld\n", dp [n]);
}
return 0;
}