Algorithm

D. Bubble Sort Graph
time limit per test
1 second
memory limit per test
256 megabytes
Problem link- https://codeforces.com/contest/340/problem/D
input
standard input
output
standard output

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.

Examples
input
Copy
3
3 1 2
output
Copy
2
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].



 

Code Examples

#1 Code Example with C++ Programming

Code - C++ Programming

#include <bits/stdc++.h>

using namespace std;

int const N = 1e5 + 1;
int n, a[N], len, l[N];

int main() {
  scanf("%d", &n);
  for(int i = 0; i < n; ++i)
    scanf("%d", a + i);
  
  l[0] = a[0];
  len = 1;
  for(int i = 1; i < n; ++i) {
    if(a[i] < l[0])
      l[0] = a[i];
    else if(a[i] > l[len - 1])
      l[len++] = a[i];
    else
      l[lower_bound(l, l + len, a[i]) - l] = a[i];
  }

  printf("%d\n", len);

  return 0;
}
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Input

x
–
+
cmd
3
3 1 2

Output

x
–
+
cmd
2
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Demonstration

Codeforces Solution-Bubble Sort Graph-Solution in C, C++, Java, Python

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