demoralizer's blog

By demoralizer, history, 2 months ago, In English

Here's my (attempt at a) video solution of the all problems from yesterday's div 2 contest.

https://youtu.be/elOYwIx1fAM

(Fortunately there weren't many prerequisites for today's problems so it all went fine.)

I skipped the code because it would've taken very long, just explained the problems well. Do share your thoughts and opinions by commenting here (or on the video).

PS: I missed getting to red by 4 rating :(((

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By demoralizer, history, 2 months ago, In English

EDIT: As I'll be posting a lot of videos in this series, instead of writing a separate blog everytime, I'll just keep on adding the links on this blog itself

Here are the links of the videos currently available in the DP playlist on my channel.

I'll add the remaining editorials soon, keep checking the blog regularly if you're interested. Also do give me suggestions, if you want such series on some other topic.

If you have any doubts/feedback/suggestions, comment them here or on the youtube video.

Original Text of the blog:-

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By demoralizer, history, 3 months ago, In English

LATEST EDIT: The channel is created, read more in my new blog.

EDIT: I have decided I'm going to start the channel. If you want videos on some specific topics or editorials of some famous questions, please mention them in the comment section below.

Hello everyone,

I see a lot of content in russian or chinese language that gets translated or rewritten in english and then it gets introduced to the world. I believe that in my country (India), there are people who aren't very familiar with English either. I actually know a few people who are sometimes unable to understand blogs and editorials because of being weak in English. Even some of the people who understand English pretty well might feel more comfortable with Hindi.

Now I know that English is a pretty standard language and people should be good at it, but I still believe that Hindi videos would actually be helpful to some people, although I'm not very sure, that's why I wrote this blog.

Should I start a youtube channel in which I make videos about algorithms and/or problem solutions in Hindi? I have a few nice topics in mind.

Please comment your opinions/suggestions (your suggestions are valuable even if you can't speak/understand Hindi)

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By demoralizer, history, 6 months ago, In English

I was implementing a Trie for Google Kickstart earlier today and the code is malfunctioning in a very strange way. I have no idea why this is happening. I narrowed down the problem in a few hours.

#include <bits/stdc++.h>
using namespace std;
#define rep(i,a,b)        for(int i=a;i<b;i++)

struct node{
	int ends=0;
	int child[26]={0};
};

vector<node> trie;
int makenode(){
	trie.push_back(node());
	int x=(int)trie.size() - 1;
	cout<<x<<" ";
	return x;
}

void insert(string &s,int root=0,int pos=0){
	if(pos==(int)(s.size())){
		trie[root].ends++;
		return;
	}
	int next=s[pos]-'A';
	if(!trie[root].child[next]){
		// trie.push_back(node()); trie[root].child[next]=(int)trie.size()-1;    //THIS LINE WORKS FINE
		trie[root].child[next]=makenode();
		cout<<trie[root].child[next]<<"\n";
	}
	insert(s,trie[root].child[next],pos+1);
}

int main(){
	trie.clear();
	trie.push_back(node());
	string s;
	cin>>s;
	insert(s);
	return 0;
}

The function makenode() returns x. When I print x, the values are fine but after returning the values are getting changed.

One would expect the above code to print the same integers per line but the values aren't same.

These are the values of x before and after returning from the function makenode().

Does anybody have any idea why this is happening?

(I have noticed that only the values 1,2,4,8,16,32,etc are wrong)

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By demoralizer, history, 6 months ago, In English

There's another simple greedy solution to the problem using dfs trees.

First form a dfs tree of the graph with any vertex as its root. Now consider a vertex $$$P$$$ which has a backedge to vertex $$$Q$$$, if $$$depth(P)-depth(Q)+1 >= \lceil\sqrt{n}\rceil$$$ then we have found a cycle of at least $$$\lceil\sqrt{n}\rceil$$$ vertices.

If we cannot find such a cycle, we'll find an independent set, we know that the leaves of a dfs tree do not have an edge between them. So we'll take all the leaves in the independent set. But that may not be enough we need more vertices, so we'll choose each such vertex whose depth is at least $$$\left(\lceil\sqrt{n}\rceil - 1\right)$$$ less than the minimum depth of all the chosen vertices in it's subtree and insert it to the independent set (we can do so because if there is an edge between the current vertex and any of the previously chosen vertices, we would have found a cycle). How can we say that such an independent set will have at least $$$\lceil\sqrt{n}\rceil$$$ vertices? Here is an intuitive proof:-

Consider any linear chain in the dfs tree of length $$$L$$$ which terminates at a single leaf, we can pick $$$\lceil\frac{L}{\sqrt{n}}\rceil$$$ vertices from this chain. Whenever we put a vertex in the independent set, we can disconnect its entire subtree from the graph and consider it as a new leaf. After this we can select any other linear chain and repeat this process.

In total, we'll have $$$\sum{\lceil\frac{L}{\sqrt{n}}\rceil}$$$ vertices in our independent set which is at least $$$\lceil\frac{n}{\sqrt{n}}\rceil = \lceil\sqrt{n}\rceil$$$ (since $$$\sum{L} = n$$$).

I'd appreciate if someone can come up with a more concrete proof.

Here is my accepted solution: https://codeforces.com/contest/1325/submission/73328247

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