×

# Can't understand INOI problem "Periodic Strings"

 0 See title, here is the problem statement. Specifically I don't understand what is meant my "Output Format - the number of non-periodic strings of length N , modulo M" bit. Could someone give me an example to explain the output format? Here is the problem https://www.codechef.com/IOIPRAC/problems/INOI1502 I am also pasting this here in case someone doesn't want to click the link. A string is any nonempty sequence of 0s and 1s. Examples of strings are 00, 101, 111000, 1, 0, 01. The length of a string is the number of symbols in it. For example, the length of 111000 is 6. If u and v are strings, then uv is the string obtained by concatenating u and v. For example if u = 110 and v = 0010 then uv = 1100010. A string w is periodic if there exists a string v such that w = v n = vv · · · v (n times), for some n ≥ 2. Note that in this case the length of v is strictly less than that of w. For example, 110110 is periodic, because it is vv for v = 110. Given a positive integer N, find the number of strings of length N which are not periodic. Report the answer modulo M. The non-periodic strings of length 2 are 10 and 01. The nonperiodic strings of length 3 are 001, 010, 011, 100, 101, and 110. Input format: A single line, with two space-separated integers, N and M. Output format: A single integer, the number of non-periodic strings of length N, modulo M. Test Data In all subtasks, 2 ≤ M ≤ 108 The testdata is grouped into 4 subtasks. Subtask 1 (10 marks) 1 ≤ N ≤ 4000. N is the product of two distinct prime numbers. Subtask 2 (20 marks) 1 ≤ N ≤ 4000. N is a power of a prime number. Subtask 3 (35 marks) 1 ≤ N ≤ 4000. Subtask 4 (35 marks) 1 ≤ N ≤ 150000. asked 12 Sep '16, 17:03 56●3 accept rate: 11%

 4 Non-Periodic means the strings which cannot be broken down into some recurring sub-string. Lets take an example with N = 4 All possible periodic strings are: 0000, 0101, 1010, 1111 each with periodic sub-string '0','01','10','1' respectively. Lets take an example of a non-periodic string 1110. You cannot have a sub-string of it which you can repeat 2 or more times to get original string. So for N=4 your output should be 12%M. As there are 12 strings of length 4 which are non-periodic answered 13 Sep '16, 14:29 311●3 accept rate: 60%
 0 answered 30 Sep '16, 18:44 5★sholja 1 accept rate: 0%
 -2 it is impossible this problem. Gave a string from length N there are 2^N possible strings, which I have subtract the periodics one. But I can't compute 2^150000. Nobody can do it. There is something wrong. May be the problem requires the periodic one. answered 30 Sep '16, 16:58 2★jurhas -1●1 accept rate: 0% Rather than vote down, please explain your point of view. This is math. (30 Sep '16, 17:25) jurhas2★ Not fully accomplishing. The problems require (2^N - k)%M and not 2^N%M -k . For example N=3 : 2^3 =8 - 2(periodic)=6 Than compute modulo for 6. How can get ride of it? (30 Sep '16, 19:35) jurhas2★
 toggle preview community wiki:
Preview

By Email:

Markdown Basics

• *italic* or _italic_
• **bold** or __bold__
• image?![alt text](/path/img.jpg "title")
• numbered list: 1. Foo 2. Bar
• to add a line break simply add two spaces to where you would like the new line to be.
• basic HTML tags are also supported
• mathemetical formulas in Latex between \$ symbol

Question tags:

×2,167
×399
×242
×166
×38

question asked: 12 Sep '16, 17:03

question was seen: 1,731 times

last updated: 30 Sep '16, 19:35