Petr's blog

By Petr, history, 3 weeks ago, In English
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3 weeks ago, # |
  Vote: I like it +3 Vote: I do not like it

Auto comment: topic has been updated by Petr (previous revision, new revision, compare).

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3 weeks ago, # |
  Vote: I like it -22 Vote: I do not like it

OMG!Endless editorial!

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3 weeks ago, # |
  Vote: I like it 0 Vote: I do not like it

Thank you!

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3 weeks ago, # |
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Is there a dp solution for problem B

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3 weeks ago, # |
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Helpful. +1

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3 weeks ago, # |
Rev. 2   Vote: I like it 0 Vote: I do not like it

Did someone tried to solve B using binary search and maximum bipartite matching? I tried but got TLE (253131171).

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    3 weeks ago, # ^ |
      Vote: I like it +23 Vote: I do not like it

    I did :) I would not say I am proud of that but I thought about doing a binary search + checking Hall's theorem statement on the graph. It can be shown that it is enough to check Hall's condition only for subsegments of appetizers in the sorted order. However, $$$O(n^2 \log C)$$$ would probably be too slow, so I just initially set the answer to infinity and then looking at all subsegments decrease this value as long as Hall's condition does not hold. This leads to an $$$O(n^2)$$$ solution. Huge overkill though...

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      3 weeks ago, # ^ |
        Vote: I like it +39 Vote: I do not like it

      My approach was also using Hall's theorem; I thought about how to optimize $$$O(n^2$$$ $$$log$$$ $$$C)$$$ to $$$O(n^2)$$$ for a bit before realizing it's easier to optimize it to $$$O(n$$$ $$$log$$$ $$$C)$$$.

      For each element, let's say $$$x_i$$$ elements of $$$b$$$ are $$$\geq a_i+ans$$$ and $$$y_i$$$ elements of $$$b$$$ are $$$\leq a_i-ans$$$. Then, you want for all $$$i \leq j$$$, $$$x_i+y_j \geq j-i+1$$$, or $$$x_i+i \geq j+1-y_j$$$, which you can check by finding looking at the prefix minimum of $$$x_i+i$$$ and making sure that it's $$$\geq j+1-y_j$$$.

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      3 weeks ago, # ^ |
        Vote: I like it 0 Vote: I do not like it

      Thank you for replying. It would be really helpful if you can share your code.

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      3 weeks ago, # ^ |
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      I checked for hall in $$$O(n²\log{C})$$$ and it passed :). Maybe methods with a higher constant TLE.

      For all elements in $$$a$$$ you calculate $$$(l_i,r_i)$$$ such that $$$a_i$$$ can match with everyone from $$$b_1$$$ to $$$b_{l_i}$$$ and from $$$b_{r_i}$$$ to $$$b_n$$$. Now for each $$$(l,r)$$$ you want to calculate how many $$$(l_i,r_i)$$$ there are such that $$$l_i \leq l \leq r \leq r_i$$$, which is quite easy to do with a 2d prefix sum. I did have to do that prefix sum with a global array instead of a vector of vectors to get AC though.

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3 weeks ago, # |
Rev. 2   Vote: I like it -7 Vote: I do not like it

Poblem B, please, help me to figure out what's wrong with the code below:

 ull solve(){
            std::sort(A.begin(),A.end());
            std::sort(B.begin(),B.end());
            ull ans=-1;
            for (ull k=0;k<=n;++k){
                ull mi=1e15;
                
                // Pair k smallest ai's elements, with k largest bi's elements
                for(ull i=0;i<k;++i) mi=std::min(mi,abs(A[i]*1ll-B[n-1-i])*1ll);
                
                // Pair k largest (n-k) ai's elements, with (n-k) smallest bi's elements
                for(ull i=k+1;i<n;++i) mi=std::min(mi,abs(A[i]*1ll-B[i-k])*1ll);

                ans=std::max(ans,mi);
            }
            return ans;
        }

Thanks

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3 weeks ago, # |
  Vote: I like it -8 Vote: I do not like it

Is there any solution for problem F that use the alternate method they propose here? $$$O(K\sqrt(K)$$$ wouldn't enter with the k=10^6 right?

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3 weeks ago, # |
Rev. 2   Vote: I like it 0 Vote: I do not like it

Can someone explain the third paragraph of the proof in problem K("Now, note that if we swap free elements in A and C...")?I know the proof's idea is to swap the smallest $$$n_{b}$$$ numbers from A and C to B.I also agree with the solution about the truth that free elements in B and C can be swapped without break the conditions.But why the third paragraph swap free elements in A and C?I can't understand the necessity.I'm also doubt with the sentence at the end:"for the same reason.".Thank you.

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3 weeks ago, # |
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Auto comment: topic has been updated by dario2994 (previous revision, new revision, compare).

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11 days ago, # |
  Vote: I like it -20 Vote: I do not like it

i am studying this solution

can anyone explain this how we are calculating value of H in this solution like in this loop..

for(int i=x;i<=N;i+=x) xx+=cnt[i];

Your text to link here...

Here is the complete code 
#pragma GCC optimize("Ofast,unroll-loops")
#include<bits/stdc++.h>
using namespace std;
long long H,h[200003],gg;
int n,k;
vector<long long>V;
map<long long,int>mp;
bool cmp(long long A,long long B,long long C,long long D){
	return __int128(A)*D<__int128(B)*C;
}
long long A=3e18,B=1,X,Y;
int N=4e7;
//long long s[200003];
int cnt[40000003];
void add(int x,int y){
	if(cmp(A,B,H,1ll*x*y))
		return;
	long long xx=n-V.size(),yy=y;
	for(int i=x;i<=N;i+=x)
		xx+=cnt[i];
	for(auto i:V)
		xx+=(i+x-1)/x;
	if(cmp(xx,yy,A,B))
		A=xx,B=yy,X=x,Y=y;
}
int main(){
	ios::sync_with_stdio(0);
	cin.tie(0);
	cout.tie(0);
	cin>>n>>k;
	for(int i=0;i<n;i++){
		cin>>h[i];
		H+=h[i];
		if(h[i]>4e7)
			mp[h[i]]++,
			V.push_back(h[i]);
		else
			cnt[h[i]-1]++;
	}
//	for(auto i:mp)gg+=min(k,int(sqrt(i.first)));
	for(int i=N;i>0;i--)
		cnt[i]+=cnt[i+1];
	for(int i=k/2;i>0;i--){
		add(i,k-i);
		add(k-i,i);
	}
	cout<<X<<' '<<Y;
}