05.3 LIS (Segment Tree).cpp

/*
 * Problem : Longest Increasing Subsequence (using Segment Tree)
 * */

/** Which of the favors of your Lord will you deny ? **/

#include<bits/stdc++.h>
using namespace std;

#define LL long long
#define PII pair<int,int>
#define PLL pair<LL,LL>
#define F first
#define S second

#define ALL(x)      (x).begin(), (x).end()
#define READ        freopen("alu.txt", "r", stdin)
#define WRITE       freopen("vorta.txt", "w", stdout)

#ifndef ONLINE_JUDGE
#define DBG(x)      cout << __LINE__ << " says: " << #x << " = " << (x) << endl
#else
#define DBG(x)
#endif

template<class T1, class T2>
ostream &operator <<(ostream &os, pair<T1,T2>&p);
template <class T>
ostream &operator <<(ostream &os, vector<T>&v);
template <class T>
ostream &operator <<(ostream &os, set<T>&v);

inline void optimizeIO()
{
    ios_base::sync_with_stdio(false);
    cin.tie(NULL);
}

const int nmax = 2e5+7;
const LL LINF = 1e17;

/**
Segment Tree (Point Update , Range Query)
=========================================
1 based indexing
**/

struct Node
{
    int mx;

    Node() /// change here
    {
        mx = 0;
    }

    void create_leaf(int val) /// change here
    {
        mx = val;
    }
};

Node merge_nodes(Node &a,Node &b) /// change here
{
    Node temp;
    temp.mx = max(a.mx,b.mx);

    return temp;
}

struct SegTree
{
    int n;
    vector<int>data;
    vector<Node>Tree;

    SegTree(int n)
    {
        this->n = n;
        int len = n+1;

        data = vector<int>(len);
        Tree = vector<Node>(len<<2);
    }

    void build()
    {
        build(1,1,n);
        return;
    }

    void build(int cur,int start,int end)
    {
        if(start==end)
        {
            Tree[cur].create_leaf(data[start]);
            return;
        }

        int mid = (start+end)>>1;
        int lc = cur<<1 , rc = lc|1;

        build(lc,start,mid);
        build(rc,mid+1,end);

        Tree[cur] = merge_nodes(Tree[lc],Tree[rc]);
    }

    void update(int updex,int val)
    {
        update(1,1,n,updex,val);
    }

    void update(int cur,int start,int end,int updex,int val)
    {
        if(start==end)
        {
            Tree[cur].create_leaf(val);
            return;
        }

        int mid = (start+end)>>1;
        int lc = cur<<1 , rc = lc|1;

        /// binary search
        if(updex<=mid) update(lc,start,mid,updex,val);
        else update(rc,mid+1,end,updex,val);

        Tree[cur] = merge_nodes(Tree[lc],Tree[rc]); /// bottom up correction after update
    }

    Node query(int ql,int qr)
    {
        return query(1,1,n,ql,qr);
    }

    Node query(int cur,int start,int end,int ql,int qr)
    {
        if(ql>qr) return Node();

        if(end<ql || start>qr) return Node();

        if(start>=ql && end<=qr)
        {
            return Tree[cur];
        }

        int mid = (start+end)>>1;
        int lc = cur<<1 , rc = lc|1;

        /// query on both child
        Node ansL = query(lc,start,mid,ql,qr);
        Node ansR = query(rc,mid+1,end,ql,qr);

        return merge_nodes(ansL,ansR);
    }
};

int solveLIS(vector<PII>&v)
{
    int n = v.size();

    vector<PII> sorted = v;
    sort(ALL(sorted));

    SegTree s(n);
    s.build();

    for(auto el:sorted)
    {
        int id = -el.second;

        int mx_till_now = s.query(1,id-1).mx;

        s.update(id,mx_till_now+1);
    }

    int lis = s.query(1,n).mx;
    return lis;
}

int main()
{
    optimizeIO();

    int n;
    cin>>n;

    vector<PII>v(n);

    for(int i=0; i<n; i++)
    {
        int x;
        cin>>x;

        v[i] = {x,-(i+1)}; /* minus to handle overcounting for duplicates after sorting , so that the latter ones are calculated first */
    }

    int ans = solveLIS(v);
    cout<<ans<<endl;

    return 0;
}
/**
5
1 6 2 3 5
**/

template<class T1, class T2>
ostream &operator <<(ostream &os, pair<T1,T2>&p)
{
    os<<"{"<<p.first<<", "<<p.second<<"} ";
    return os;
}
template <class T>
ostream &operator <<(ostream &os, vector<T>&v)
{
    os<<"[ ";
    for(T i:v)
    {
        os<<i<<" " ;
    }
    os<<" ]";
    return os;
}

template <class T>
ostream &operator <<(ostream &os, set<T>&v)
{
    os<<"[ ";
    for(T i:v)
    {
        os<<i<<" ";
    }
    os<<" ]";
    return os;
}