转载:http://archive.cnblogs.com/a/2122079/
up[n][k] 长度为n以k开始的,前两个数呈上升趋势的数列的个数
down[n][k] 长度为n以k开始的,前两个数呈下降趋势的数列的个数
up[n][k] = sigma(down[n-1][i]) k<=i<=n-1
down[n][k]= sigma(up[n-1][i]) 1<=i<=k-1
第一个满足 sigma(up[n][i]+down[n][i])>=c 的i即为第一位a1
c1=c-(up[n][a1]+down[n][a1])
第一个满足 sigma(up[n-1][i])>=c1 1<=i<a1, sigma(down[n-1][i])>=c1 a1<=i<=n-1 为a2
一旦确定a1,a2就可以与确定下面是up还是down,两者交替.
for (long long i = 1; i < n; i++)
if (ans[i] >= t)
ans[i]++;
算法中的这三行非常精妙,虽然ans[n]已经使用,但是却不影响g[][]高低计数的特征,最后只需作如下处理:大于ans[n]的直接加1,以起到忽视掉选中的高度为t的效果,不影响局部正确性。递归之后,自然也不影响整体正确性。
#include <iostream>
#include <cstdio>
#include <cstdlib>
#include <cstring>
using namespace std;
#define maxn 30
struct Node
{
long long up, down;
} g[maxn][maxn];
long long n;
long long c;
long long ans[maxn];
void getfirst(long long n, long long c, bool u)
{
if (n == 0)
return;
long long t;
long long sum;
if (!u)
{
sum = 0;
t = ans[n + 1];
while (sum + g[n][t].down < c)
{
sum += g[n][t].down;
t++;
}
}
else
{
sum = 0;
t = 1;
while (sum + g[n][t].up < c)
{
sum += g[n][t].up;
t++;
}
}
ans[n] = t;
getfirst(n - 1, c - sum, !u);
for (long long i = 1; i < n; i++)
if (ans[i] >= t)
ans[i]++;
}
int main()
{
//freopen("t.txt", "r", stdin);
g[1][1].up = 1;
g[1][1].down = 1;
for (long long i = 2; i <= 20; i++)
{
for (long long j = 1; j <= i; j++)
{
g[i][j].up = g[i][j].down = 0;
for (long long k = j; k <= i - 1; k++)
g[i][j].up += g[i - 1][k].down;
for (long long k = 1; k <= j - 1; k++)
g[i][j].down += g[i - 1][k].up;
}
}
long long x;
scanf("%lld", &x);
while (x--)
{
scanf("%lld%lld", &n, &c);
long long t = 1, sum = 0;
while (sum + g[n][t].down + g[n][t].up < c)
{
sum += g[n][t].down + g[n][t].up;
t++;
}
ans[n] = t;
if (sum + g[n][t].down < c)
getfirst(n - 1, c - sum - g[n][t].down, false);
else
getfirst(n - 1, c - sum, true);
for (long long i = 1; i < n; i++)
if (ans[i] >= t)
ans[i]++;
printf("%lld", ans[n]);
for (int i = n - 1; i >= 1; i--)
printf(" %lld", ans[i]);
putchar('\n');
}
return 0;
}