codeforces 340D Bubble Sort Graph（dp,LIS）-白红宇

codeforces 340D Bubble Sort Graph（dp,LIS）

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发布时间：2019-06-09

本文共 2903 字，大约阅读时间需要 9 分钟。

转载请注明出处： ——by fraud

Iahub recently has learned Bubble Sort, an algorithm that is used to sort a permutation with n elements a1, a2, ..., an in ascending order. He is bored of this so simple algorithm, so he invents his own graph. The graph (let's call it G) initially has n vertices and 0 edges. During Bubble Sort execution, edges appear as described in the following algorithm (pseudocode).

procedure bubbleSortGraph()     build a graph G with n vertices and 0 edges     repeat         swapped = false         for i = 1 to n - 1 inclusive do:             if a[i] > a[i + 1] then                 add an undirected edge in G between a[i] and a[i + 1]                 swap( a[i], a[i + 1] )                 swapped = true             end if         end for     until not swapped     /* repeat the algorithm as long as swapped value is true. */ end procedure

For a graph, an independent set is a set of vertices in a graph, no two of which are adjacent (so there are no edges between vertices of an independent set). A maximum independent set is an independent set which has maximum cardinality. Given the permutation, find the size of the maximum independent set of graph G, if we use such permutation as the premutation a in procedure bubbleSortGraph.

Input

The first line of the input contains an integer n (2 ≤ n ≤ 105). The next line contains n distinct integers a1, a2, ..., an (1 ≤ ai ≤ n).

Output

Output a single integer — the answer to the problem.

Sample test(s)

input

3 3 1 2

output

Note

Consider the first example. Bubble sort swaps elements 3 and 1. We add edge (1, 3). Permutation is now [1, 3, 2]. Then bubble sort swaps elements 3 and 2. We add edge (2, 3). Permutation is now sorted. We have a graph with 3 vertices and 2 edges (1, 3) and (2, 3). Its maximal independent set is [1, 2].

考虑到可以转化成最长上升子序列的问题。。。然后就O（nlogn）搞一下就好

1 //##################### 2 //Author:fraud 3 //Blog: http://www.cnblogs.com/fraud/ 4 //##################### 5 #include 
      
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                       22 #include 
                       
                        23 #include 
                        
                         24 #include 
                         
                          25 using namespace std;26 #define XINF INT_MAX27 #define INF 0x3FFFFFFF28 #define MP(X,Y) make_pair(X,Y)29 #define PB(X) push_back(X)30 #define REP(X,N) for(int X=0;X
                          
                           =L;X--)33 #define CLR(A,X) memset(A,X,sizeof(A))34 #define IT iterator35 typedef long long ll;36 typedef pair
                           
                             PII;37 typedef vector
                            
                              VII;38 typedef vector
                             
                               VI;39 #define MAXN 10001040 int a[MAXN];41 int dp[MAXN];42 int main()43 {44 ios::sync_with_stdio(false);45 int n;46 cin>>n;47 for(int i=0;i
                              
                               >a[i];49 fill(dp,dp+MAXN,INF);50 for(int i=0;i

代码君

转载于:https://www.cnblogs.com/fraud/p/4376961.html

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