HDU - 5748 Bellovin —— 最长上升子序列

Bellovin

Time Limit: 6000/3000 MS (Java/Others)    Memory Limit: 131072/131072 K (Java/Others)

Total Submission(s): 2063    Accepted Submission(s): 808


Problem Description

Peter has a sequence a1,a2,...,an and
he define a function on the sequence -- F(a1,a2,...,an)=(f1,f2,...,fn),
where fi is
the length of the longest increasing subsequence ending with ai.

Peter would like to find another sequence b1,b2,...,bn in
such a manner that F(a1,a2,...,an) equals
to F(b1,b2,...,bn).
Among all the possible sequences consisting of only positive integers, Peter wants the lexicographically smallest one.

The sequence a1,a2,...,an is
lexicographically smaller than sequence b1,b2,...,bn,
if there is such number i from 1 to n,
that ak=bk for 1≤k<i and ai<bi.

 

Input

There are multiple test cases. The first line of input contains an integer T,
indicating the number of test cases. For each test case:

The first contains an integer n (1≤n≤100000) --
the length of the sequence. The second line contains n integers a1,a2,...,an (1≤ai≤109).

 

Output

For each test case, output n integers b1,b2,...,bn (1≤bi≤109) denoting
the lexicographically smallest sequence.

 

Sample Input

3
1
10
5
5 4 3 2 1
3
1 3 5

 

Sample Output

1
1 1 1 1 1
1 2 3

题意：给定一个数组，下标1~n，问到每个i位置的最长上升子序列的长度

思路：和找整个数组的最长子序列相似，只不过在寻找过程中不断记录下到每个位置的最长上升子序列的长度

#include <iostream>
#include <cstdio>
#include <cmath>
#include <vector>
#include <stack>
#include <cstring>
#include <queue>
#include <algorithm>
#define ll long long
#define max_ 100100
#define les 1e-6
#define inf 0x3f3f3f3f
using namespace std;
int n;
int num[max_],dp[max_],ans[max_];
int main(int argc, char const *argv[]) {
int t;
scanf("%d",&t);
while(t--)
{
scanf("%d",&n);
for(int i=1;i<=n;i++)
{
scanf("%d",&num[i]);
dp[i]=inf;
}
for(int i=1;i<=n;i++)
{
int k=lower_bound(dp+1,dp+1+n,num[i])-dp;
ans[i]=k;
dp[k]=num[i];
}
printf("%d",ans[1]);
for(int i=2;i<=n;i++)
printf(" %d",ans[i]);
printf("\n" );
}
return 0;
}