# Why am I getting a TLE?

Here’s the problem https://www.spoj.com/problems/LOCKER/
I have coded the following solution (using some hints from different sources):

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

#define FASTIO ios_base::sync_with_stdio(false); cin.tie(NULL); cout.tie(NULL);
#define rep(i,a,b) for(int i=a; i<b; i++)
#define ll long long
#define mod 1000000007

int modpower(ll x, int y)
{
x %= mod;
if(!x) return 0;
int res = 1;
while(y)
{
if(y&1) res = (res*x)%mod;
x = (x*x)%mod;
y >>= 1;
}
return res;
}

int solve(ll n)
{
if(n == 0) return 1;
else if(n == 2) return 2;
else if(n == 3) return 3;
else
{
int rem = n%3;
if(rem == 0) return modpower(3,n/3);
else if(rem == 1) return 4*modpower(3,n/3 - 1);
else return 2*modpower(3,n/3);
}
}

int main()
{
FASTIO
int t;
cin >> t;
while(t--)
{
ll n;
cin >> n;
cout << solve(n) << "\n";
}
return 0;
}
``````

Integer overflow…
Calling function modpower(x,y) where u have taken y as int type, as per constraints mentioned in the question , n can be up to 10^12 so u clearly need to declare it as long long so as to avoid overflow.
Declare int y and return type of function both as ll and when returning something like x*modpower(a,b) ,u should take modulo again and return it %mod

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

#define FASTIO ios_base::sync_with_stdio(false); cin.tie(NULL); cout.tie(NULL);
#define rep(i,a,b) for(int i=a; i<b; i++)
#define ll long long
#define mod 1000000007

ll modpower(ll x, ll y)
{
x %= mod;
if(!x) return 0;
ll res = 1;
while(y)
{
if(y&1) res = (res*x)%mod;
x = (x*x)%mod;
y >>= 1;
}
return res;
}

ll solve(ll n)
{
if(n == 0) return 1;
else if(n == 2) return 2;
else if(n == 3) return 3;
else
{
int rem = n%3;
if(rem == 0) return modpower(3,n/3);
else if(rem == 1) return (4*modpower(3,n/3 - 1))%mod;
else return (2*modpower(3,n/3))%mod;
}
}

int main()
{
FASTIO
int t;
cin >> t;
while(t--)
{
ll n;
cin >> n;
cout << solve(n) << "\n";
}
return 0;
}
``````

I have edited the code, but I still get TLE.

I tried recursive version of modular exponentiation keeping everything same and it got WA.
So check your logic once and speaking about your code’s time complexity , it is perfectly fine with the constraints so u may check your logic again.
Function i used
ll fpower(ll x,ll y)
{
if(!y)
return 1;
x = x%mod ;
return (y&1) ? x * fpower(x * x%mod,y/2)%mod : fpower(x * x%mod,y/2)%mod ;
}

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@say_ch_ee_zz Thanks for looking into the matter. I tried finding any flaw in the logic by using some sample cases, but I got correct answers for all of them. And I certainly could not find any piece in this code that might be the cause for a TLE. Maybe there is something that I am unable to spot out. Can anyone please help?

The first test case where your code fails is n=1
And it is also the cause for TLE

1 Like

Thanks @say_ch_ee_zz

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