Longest Increasing Subsequence.cpp

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This is an implementation of Longest Increasing Subsequence in C++.

#include <vector>
using namespace std;
 
/* Finds longest strictly increasing subsequence. O(n log k) algorithm. */
void find_lis(vector<int> &a, vector<int> &b)
{
	vector<int> p(a.size());
	int u, v;
 
	if (a.empty()) return;
 
	b.push_back(0);
 
	for (size_t i = 1; i < a.size(); i++) 
        {
                // If next element a[i] is greater than last element of
                // current longest subsequence a[b.back()], just push it at back of "b" and continue
		if (a[b.back()] < a[i]) 
                {
			p[i] = b.back();
			b.push_back(i);
			continue;
		}
 
                // Binary search to find the smallest element referenced by b which is just bigger than a[i]
                // Note : Binary search is performed on b (and not a).
                // Size of b is always <=k and hence contributes O(log k) to complexity.    
		for (u = 0, v = b.size()-1; u < v;) 
                {
			int c = (u + v) / 2;
			if (a[b[c]] < a[i]) u=c+1; else v=c;
		}
 
                // Update b if new value is smaller then previously referenced value 
		if (a[i] < a[b[u]]) 
                {
			if (u > 0) p[i] = b[u-1];
			b[u] = i;
		}	
	}
 
	for (u = b.size(), v = b.back(); u--; v = p[v]) b[u] = v;
}
 
/* Example of usage: */
#include <cstdio>
int main()
{
	int a[] = { 1, 9, 3, 8, 11, 4, 5, 6, 4, 19, 7, 1, 7 };
	vector<int> seq(a, a+sizeof(a)/sizeof(a[0])); // seq : Input Vector
	vector<int> lis;                              // lis : Vector containing indexes of longest subsequence 
        find_lis(seq, lis);
 
        //Printing actual output 
	for (size_t i = 0; i < lis.size(); i++)
		printf("%d ", seq[lis[i]]);
        printf("\n");    
 
	return 0;
}