I'm not gonna let send pie down.

What do we have here?

Find duplicate number given an array numbs containing end plus one integers where each integer is between one and end inclusive proved that at least one duplicate number must exist.

Of course, because of the pigeonhole principle, Child's play assumed that there is only one duplicate number, but it could be repeated more than once.

Find a duplicate number.

I got it.

If the numbers are sorted than any duplicate numbers will be a Jason in this sordid array.

A simple sort and the linear scan would do as expected.

I knew it couldn't be that easy, but you think that would stop me then You underestimated me.

I have no choice but to use my secret weapon Hash Famous hash map.

One of the most powerful data structures for reducing your time complexity, taking advantage of its constant look of times.

However, using a Hashmat requires me to increase my power level.

So I need to wear these to suppress control my powers in case it gets out of control.

Also, my doctor told me to wear them to treat my carpal tunnel.

Wait, oh, expressions to show.

Too weak.

I'm running out of ideas.

I can't solve this.

Me and roll can even be real engineer homemaking against Google, it seems like you need some help.

This question is trivial.

Oh my God, he's so cool and jackets so big.

Solving this in linear time and constant space requires Floyd's Tortoise and Hare, a simple cycle detection algorithm where one point to traverse is twice as fast is another.

And once they meet, you can trace back to the point where the cycle began.

In our case, the values of the array is like a pointer pointing to Indices of the array, which is like notes in our case, because each number is from one to end, then each valley will have to point to a valid index.

And since there's a duplicate number, there will be a cycle.

Find that cycle and you will have your answer.

What are you waiting for?

Call yourself senior engineers on coding.

More also, my doctor said not to because of my carpal tunnel.

They're worse.