# UVa 481 – What Goes Up

## Solution Idea:

This is a LIS problem. But in this problem input size/number of elements in the list is not mentioned. So we have to use faster solution like NlogK algorithm because if the input list is large then O(n^2) solution can give a TLE. So in this problem we use LIS NlogK approach. We need to just run the algorithm and print the solution.

```
/*
+-+ +-+ +-+
|R| |.| |S|
+-+ +-+ +-+
*/

#include &lt;bits/stdc++.h&gt;

#define pii             pair &lt;int,int&gt;
#define sc              scanf
#define pf              printf
#define Pi              2*acos(0.0)
#define ms(a,b)         memset(a, b, sizeof(a))
#define pb(a)           push_back(a)
#define MP              make_pair
#define db              double
#define ll              long long
#define EPS             10E-10
#define ff              first
#define ss              second
#define sqr(x)          (x)*(x)
#define D(x)            cout&lt;&lt;#x &quot; = &quot;&lt;&lt;(x)&lt;&lt;endl
#define VI              vector &lt;int&gt;
#define DBG             pf(&quot;Hi\n&quot;)
#define MOD             100007
#define MAX             10000
#define CIN             ios_base::sync_with_stdio(0); cin.tie(0)
#define SZ(a)           (int)a.size()
#define sf(a)           scanf(&quot;%d&quot;,&amp;a)
#define sfl(a)          scanf(&quot;%lld&quot;,&amp;a)
#define sff(a,b)        scanf(&quot;%d %d&quot;,&amp;a,&amp;b)
#define sffl(a,b)       scanf(&quot;%lld %lld&quot;,&amp;a,&amp;b)
#define sfff(a,b,c)     scanf(&quot;%d %d %d&quot;,&amp;a,&amp;b,&amp;c)
#define sfffl(a,b,c)    scanf(&quot;%lld %lld %lld&quot;,&amp;a,&amp;b,&amp;c)
#define loop(i,n)       for(int i=0;i&lt;n;i++)
#define REP(i,a,b)      for(int i=a;i&lt;b;i++)
#define TEST_CASE(t)    for(int z=1;z&lt;=t;z++)
#define PRINT_CASE      printf(&quot;Case %d: &quot;,z)
#define all(a)          a.begin(),a.end()
#define intlim          2147483648
#define inf             1000000
#define ull             unsigned long long

using namespace std;

/*----------------------Graph Moves----------------*/
//const int fx[]={+1,-1,+0,+0};
//const int fy[]={+0,+0,+1,-1};
//const int fx[]={+0,+0,+1,-1,-1,+1,-1,+1};   // Kings Move
//const int fy[]={-1,+1,+0,+0,+1,+1,-1,-1};  // Kings Move
//const int fx[]={-2, -2, -1, -1,  1,  1,  2,  2};  // Knights Move
//const int fy[]={-1,  1, -2,  2, -2,  2, -1,  1}; // Knights Move
/*------------------------------------------------*/

//int Set(int N,int pos){return N=N | (1&lt;&lt;pos);}
//int reset(int N,int pos){return N= N &amp; ~(1&lt;&lt;pos);}
//bool check(int N,int pos){return (bool)(N &amp; (1&lt;&lt;pos));}
/*------------------------------------------------*/

vector&lt;int&gt;v,print_ans;
int n=0;

int L[1000000];
int I[1000000];

int LIS_NlogK()
{
loop(i,n+2) I[i]=inf;
I[0]=-inf;

int length=0;

for(int i=1;i&lt;=n;i++)
{
int low=0, hi=length, mid;

while(low&lt;=hi)
{
mid=(low+hi)/2;
if(v[i]&gt;I[mid])
low=mid+1;
else
hi=mid-1;
}

I[low]=v[i];
L[i]=low;
length=max(length,low);
}
return length;
}

int main()
{
//    freopen(&quot;in.txt&quot;,&quot;r&quot;,stdin);
///freopen(&quot;out.txt&quot;,&quot;w&quot;,stdout);

v.pb(-100000);

int a;
while(sf(a)==1)
{
n++;
v.pb(a);
}

int ans=LIS_NlogK();

int i;

int temp=ans;

for(i=n;i&gt;0;i--)
{
if(L[i]==temp)
{
temp--;
print_ans.pb(v[i]);
break;
}
}

for(--i;i&gt;0 &amp;&amp; temp ;i--)
{
if(v[i]&lt;print_ans.back() &amp;&amp; L[i]==temp)
{
print_ans.pb(v[i]);
temp--;
}
}

printf(&quot;%d\n-\n&quot;,ans);

for(i=ans-1;i&gt;=0;i--)
printf(&quot;%d\n&quot;,print_ans[i]);

return 0;
}

```