Z-Saber's blog

By Z-Saber, history, 4 years ago, In English

Hi Codeforces community,

Recently I have come across a problem which turned out to be tough for me. I hope that I can get some help from you.

Problem Statement

A permutation A of first N integers from 1 to N is good if it has exactly K good positions. A position i is good only if abs(A[i] - i) = 1. The task is to count how many permutation of first N integers like that, modulo 109 + 7.


N and K, 1 ≤ N ≤ 1000, 0 ≤ K ≤ N


Number of permutation of first N integers from 1 to N that has exactly K good positions, modulo 109 + 7


For N = 3, K = 2, there are 4 permutations that has 2 good positions. They are (1, 3, 2) , (2, 1, 3) , (2, 3, 1) , (3, 1, 2).

You may want to submit your solution here (written in Vietnamese, required SPOJ account): http://www.spoj.com/PTIT/problems/P172PROI/

I think it is a DP problem although I could not come up with a solution or any idea. Any help will be appreciated.

Thanks in advance.

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By Z-Saber, history, 5 years ago, In English

I saw this submission of problem 678A - Johny Likes Numbers and tried to hack it with case n=1000000000 and k=1.


It passes within the problem's time limit 0.5s, but I thought it should be a TLE (I tested on ideone and it runs about 0.91s). I can't think of any reason but CF judge is really fast. Any other ideas?

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