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Longest Monotonically Increasing Subsequence Size (N log N): Simple implementation

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  • Difficulty Level : Medium
  • Last Updated : 27 Dec, 2022
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Given an array of random numbers, find the longest monotonically increasing subsequence (LIS) in the array. If you want to understand the O(NlogN) approach, it’s explained very clearly here.

In this post, a simple and time-saving implementation of O(NlogN) approach using stl is discussed. Below is the code for LIS O(NlogN):

Implementation:

C++




// C++ implementation
// to find LIS
#include<iostream>
#include<algorithm>
#include<set>
using namespace std;
 
// Return length of LIS in arr[] of size N
int lis(int arr[], int N)
{
    int i;
    set<int> s;
    set<int>::iterator k;
    for (i=0; i<N; i++)
    {
        // Check if the element was actually inserted
        // An element in set is not inserted if it is
        // already present. Please see
        if (s.insert(arr[i]).second)
        {
            // Find the position of inserted element in iterator k
            k = s.find(arr[i]);
 
            k++;  // Find the next greater element in set
 
            // If the new element is not inserted at the end, then
            // remove the greater element next to it (This is tricky)
            if (k!=s.end()) s.erase(k);
        }
    }
 
    // Note that set s may not contain actual LIS, but its size gives
    // us the length of LIS
    return s.size();
}
 
int main()
{
    int arr[] = {8, 9, 12, 10, 11};
    int n = sizeof(arr)/sizeof(arr[0]);
    cout << lis(arr, n)<< endl;
}

Output

4

Time Complexity: O(N log N)
Auxiliary Space: O(N)


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