HDU_5748

描述

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.

输入格式

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).

输出格式

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

样例

输入

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

输出

1
1 1 1 1 1
1 2 3

思路

求每一位的最长上升子序列。

c++代码

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#include <iostream>  
#include <cstdio>
using namespace std;
#define inf 0x3f3f3f3f  
int const N = 1e5+5;
int a[N],sub[N],up[N];
int find(int *a,int len,int n)//若返回值为x,则a[x]>=n>a[x-1]  
{  
    int left=0,right=len,mid=(left+right)/2;  
    while(left<=right)  
    {  
        if(n>a[mid]) left=mid+1;  
        else if(n<a[mid]) right=mid-1;  
        else return mid;  
        mid=(left+right)/2;  
    }  
    return left;    
}  
       
void init(int *t,int n)  
{  
    for(int i=0;i<=n;i++)  
        t[i]=inf;  
    t[0]=-1;
    t[1]=a[0];
    sub[0]=1;
}  
       
int main()  
{  
    int max,i,j,n,t;  cin>>t;
    while(t--)  
    {        
        cin>>n;
        for(i=0;i<n;i++)  
            cin>>a[i]; 
        init(up,n+1);  
        for(i=1;i<n;i++)
        {  
            j=find(up,n+1,a[i]);
            up[j]=a[i];
            sub[i]=j; 
        }  
        for(int i=0;i<n;i++)
            printf("%d%c",sub[i],i==n-1?'\n':' ');
    }  
    return 0;  
}