LightOj 1307 (Counting Triangles)

#lightoj #cp #problem_solving #binary_search

Idea

Binary Search

  • For a triangle , the sum of any 2 side should be greater than the third side , which is to say the sum of the 2 shorter sides should be greater than the third side.
    i.e a + b > c [where a<=b<=c]
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/** 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 MP make_pair
#define F first
#define S second
#define INF INT_MAX

#define ALL(x) (x).begin(), (x).end()
#define DBG(x) cerr << __LINE__ << " says: " << #x << " = " << (x) << endl

#include <ext/pb_ds/assoc_container.hpp>
#include <ext/pb_ds/tree_policy.hpp>
using namespace __gnu_pbds;

template<class TIn>using indexed_set = tree<TIn, null_type, less<TIn>,rb_tree_tag, tree_order_statistics_node_update>;

/**
PBDS
-------------------------------------------------
1) insert(value)
2) erase(value)
3) order_of_key(value) // 0 based indexing
4) *find_by_order(position) // 0 based indexing
**/

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 = 2e3+7;
const LL LINF = 1e17;

string to_str(LL x)
{
    stringstream ss;
    ss<<x;
    return ss.str();
}

//bool cmp(const PII &A,const PII &B)
//{
//
//}

int ara[nmax];

int main()
{
    //freopen("out.txt","w",stdout);

    optimizeIO();

    int tc;
    cin>>tc;

    for(int q=1;q<=tc;q++)
    {
        int n;
        cin>>n;

        for(int i=1;i<=n;i++)
            cin>>ara[i];

        sort(ara+1,ara+n+1);

        LL ans = 0;

        for(int i=1;i<=n;i++)
        {
            for(int j=i+1;j<=n;j++)
            {
                int s = ara[i] + ara[j];
                int val = lower_bound(ara+1,ara+n+1,s) - ara -1;

                val -= j;
                ans = ans + val;

            }
        }

        cout<<"Case "<<q<<": ";
        cout<<ans<<endl;

    }

    return 0;
}

/**
3
5
3 12 5 4 9
6
1 2 3 4 5 6
4
100 211 212 121
**/

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(int i=0; i<v.size(); i++)
    {
        os<<v[i]<<" " ;
    }
    os<<" ]";
    return os;
}

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