Блог пользователя ShafinKhadem

Feature request: add github account to profile
Автор ShafinKhadem, история, 4 года назад, По-английски

Today I luckily discovered tourist's library from this comment. That made me think, it would be nice if github account could be added to profile, we could easily view many users' libraries and other public repos.

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Codeforces rating distribution over time
Автор ShafinKhadem, история, 4 года назад, По-английски

I was curious about rating inflation, so I generated a json object containing counts and percentiles and some plots of codeforces rating distribution over months, only counting active contestants:

Json object

Plot for Experts:

Spoiler

Codes and files are available here.

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python3 script to show problem difficulty rating without tags
Автор ShafinKhadem, история, 5 лет назад, По-английски

As I couldn't find any easy way to find problem difficulty rating without seeing tags, I have written a python3 script to do it:

Code

Usage: Run the script. Input the contestId (from URL, e.g. 1148) to view rating of all problems of that contests. Input contestId/problemIndex (e.g. 1108/E2) to view rating of only that problem.

If the problem has no rating yet, it will print None. Exception will be thrown if it fails to connect to codeforces server or invalid input is given.

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Binary Indexed Tree range increment and range query
Автор ShafinKhadem, 6 лет назад, По-английски

Though some articles of this topic are already available, as a beginner I found them quite hard. So I decided to write down my thoughts here, in case someone finds it useful. Sorry for poor formatting and poor English.

Using one BIT we can do range increment and point query: For increasing a[l...r] by val, tmp[l] += val, tmp[r+1] += -val. After any number of range updates, prefixSum(i) of tmp[] denotes total increment in a[i] till now. BIT supports both point increment and prefixSum query.

Using another BIT with this BIT, we can also calculate range query. Let, prefixSum(i) from first BIT is a[i] = a[i]*(i-(i-1)). Our target is to calculate prefixSumOFa(i) in O(logn).

Let, addend[i] = a[i - 1] * (i - 1) - a[i] * (i - 1). so, , assuming 1-based indexing and a[0] = a[n+1] = 0

if (a[i]==a[i-1]), addend[i] == 0. So, writing all non-zero elements of addend[] for an example a[]:

i                |   1   |   2   |   3   |   4   |   5   |   6   |   7   |   8   |   9   |

a[i]             |   0   |   3   |   3   |   0   |   0   |   2   |   2   |   2   |   0   |
addend[i]        |       | -3*1  |       |  3*3  |       | -2*5  |       |       |  2*8  |

Observation: prefixSumOFa(i) = a[i]*i + prefixSumOFaddend(i). In case you are confused about where a[i]*i come from, notice that if a[i] would be last element of a[], a[i]*i would be written in addend[i+1].

Now, to calculate prefixSumOFa(i), we can get a[i] from first BIT, for getting prefixSumOFaddend(i), we need to keep another BIT, BIT2. For increasing [l...r] by val, we need to update BIT2(l) += (-val*(l-1)) and BIT2(r+1) += val*r.

This method works even if updates overlap, as when updating [l...r], for i = [l+1...r], (a[i-1]-a[i]) remains the same, so append[i] = (a[i-1]-a[i])*(i-1) remains same. Just like previous example, only updating BIT2(l) and BIT2(r+1) is necessary. For example if we increase range [5...7] by 5 in previous example of a[]:

a[]              |   0   |   3   |   3   |   0   |   5   |   7   |   7   |   2   |   0   |
addend[]         |       | -3*1  |       |  3*3  | -5*4  | -2*5  |       |  5*7  |  2*8  |

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