NHAY - A Needle in the Haystack

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Write a program that finds all occurences of a given pattern in a given input string. This is often referred to as finding a needle in a haystack.

The program has to detect all occurences of the needle in the haystack. It should take the needle and the haystack as input, and output the positions of each occurence, as shown below. The suggested implementation is the KMP algorithm, but this is not a requirement. However, a naive approach will probably exceed the time limit, whereas other algorithms are more complicated... The choice is yours.

Input

The input consists of a number of test cases. Each test case is composed of three lines, containing:

  • the length of the needle,
  • the needle itself,
  • the haystack.

The length of the needle is only limited by the memory available to your program, so do not make any assumptions - instead, read the length and allocate memory as needed. The haystack is not limited in size, which implies that your program should not read the whole haystack at once. The KMP algorithm is stream-based, i.e. it processes the haystack character by character, so this is not a problem.

The test cases come one after another, each occupying three lines, with no additional space or line breaks in between.

Output

For each test case your program should output all positions of the needle's occurences within the haystack. If a match is found, the output should contain the position of the first character of the match. Characters in the haystack are numbered starting with zero.

For a given test case, the positions output should be sorted in ascending order, and each of these should be printed in a separate line. For two different test cases, the positions should be separated by an empty line.

Example

Sample input:
2
na
banananobano
6
foobar
foo
9
foobarfoo
barfoobarfoobarfoobarfoobarfoo
Sample output:
2
4

3
9
15
21

Note the double empty line in the output, which means that no match was found for the second test case.

Warning: large Input/Output data, be careful with certain languages

hide comments
anuragr135: 2021-10-19 06:29:26

Same prob in other sites got accepted__
but in SPOJ what happens!!!!!
it doesn't shows where is my error only tle or wa....what is this!!!!FRUSTRATEDDDD

aditya_das: 2021-07-30 23:55:22

is there something about input that I am unable to understand...do I need to take input or not?

Waseem Ahmed: 2021-07-04 04:53:18

Accepted first go with a simple brute-force 2-loop implementation - O(n*m). Was expecting a TLE.

Very very disappointed with level of problem.

parag_619: 2021-06-14 17:06:16

Used the string::find function works perfectly. Got accepted :)

kanisht09: 2021-02-03 20:33:00

for pre-computation take the size of dp array 10^6

satyam_656: 2021-01-30 06:17:25

Simply KMP

ashk77: 2020-08-25 12:10:37

input part is a bit confusing, rest is direct implementation.

mraatvik: 2020-08-09 17:13:58

for 0 occurences print a newline :)

rehank478: 2020-07-29 14:45:19

try this test case:
Input:
8
abcababd
abcababcababde

Output:
5

imposter_1729: 2020-07-24 10:37:17

can be solved by naive method, but try doing it with kmp or rolling hash function


Added by:mima
Date:2004-06-03
Time limit:5s
Source limit:50000B
Memory limit:1536MB
Cluster: Cube (Intel G860)
Languages:All