Bellovin||HDU5748

link：http://acm.hdu.edu.cn/showproblem.php?pid=5748
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

题解：LIS，o（nlogn）算法，可以参考我的这个http://blog.youkuaiyun.com/csdn_muxin/article/details/76998459

中文题面：http://bestcoder.hdu.edu.cn/contests/contest_chineseproblem.php?cid=718&pid=1002

这道题要注意！！！！

s[i]=upper_bound(dp,dp+n,a[i])-dp;
            //要么这样用，要么用lower加a[i]然后数值加一，不能用lower加INF，不然WA 

AC代码

#include<cstdio>
#include<cstring>
#include<cstdlib>
#include<cmath>
#include<algorithm>
#include<iostream>
using namespace std;
const int MAX=100010;
int INF=1000000100;
int a[MAX],dp[MAX],s[MAX];
int main()
{
    int t,n,i; 
    scanf("%d",&t);
    while(t--)
    {
        scanf("%d",&n);
        for(i=0;i<n;i++)
        {
            scanf("%d",&a[i]);
//          dp[i]=INF;
//          s[MAX]=0;
        }
        fill(dp,dp+n,INF);
        for(i=0;i<n;i++)
        {
            *lower_bound(dp,dp+n,a[i])=a[i];
            s[i]=upper_bound(dp,dp+n,a[i])-dp;
            //要么这样用，要么用lower加a[i]然后数值加一，不能用lower加INF，不然WA 
        }
        for(i=0;i<n;i++)
        {
            printf("%d%c",s[i],i==(n-1)?'\n':' ');
        }
    }
return 0;
}