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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.
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 a single integer — the answer to the problem.
3
3 1 2
2
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 <iostream> 6 #include <sstream> 7 #include <ios> 8 #include <iomanip> 9 #include <functional> 10 #include <algorithm> 11 #include <vector> 12 #include <string> 13 #include <list> 14 #include <queue> 15 #include <deque> 16 #include <stack> 17 #include <set> 18 #include <map> 19 #include <cstdio> 20 #include <cstdlib> 21 #include <cmath> 22 #include <cstring> 23 #include <climits> 24 #include <cctype> 25 using namespace std; 26 #define XINF INT_MAX 27 #define INF 0x3FFFFFFF 28 #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<N;X++) 31 #define REP2(X,L,R) for(int X=L;X<=R;X++) 32 #define DEP(X,R,L) for(int X=R;X>=L;X--) 33 #define CLR(A,X) memset(A,X,sizeof(A)) 34 #define IT iterator 35 typedef long long ll; 36 typedef pair<int,int> PII; 37 typedef vector<PII> VII; 38 typedef vector<int> VI; 39 #define MAXN 100010 40 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<n;i++) 48 cin>>a[i]; 49 fill(dp,dp+MAXN,INF); 50 for(int i=0;i<n;i++) 51 *lower_bound(dp,dp+n,a[i])=a[i]; 52 cout<<lower_bound(dp,dp+n,INF)-dp<<endl; 53 54 55 return 0; 56 }
codeforces 340D Bubble Sort Graph（dp,LIS）
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原文地址：http://www.cnblogs.com/fraud/p/4376961.html
