Given a strings s and p, count the anagrams of s that occur in p.

For example, given s = “hello” and p = “ellohello”, the count of anagrams is 5.

Input. The input file consists of one or more pair of lines where the first line is string s and the second string p. The input file is terminated by an EOF character. Consider the following example.

hello
ellohello

Output. The output file consists the count anagrams of s that occur in p. The following output corresponds to the previous example input.

5

Solution

Consider the 5 anagrams of s = “hello” that occur in p = “ellohello”.

ellohello
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Each anagram is a substring of p and has the frequency of letters that s has (one “h”, one “e”, two “l”, and one “o”). Therefore, to count the anagrams in p, consider each substring of p of length 5 and check that the frequency of letters is the same as that of s.

To consider all substrings of length 5, it suffices to place a window of length 5 on the left of p (in other words, underline the first 5 characters) and then move the window to the right one position at a time.

To check the frequency of letters for every position of the window, do the following. For the first position, determine how many letters of s occur in the window. If that frequency is the same as the frequency of letters in s, count one anagram. In the example, the substring given by the first window (elloh) passes the check. For the rest of the positions, decrement the counter for the letter that exits the window through the left and increase the counter for the letter that enters the window from the right. In the example, for the second position of the window (llohe), decrement the counter for e (because e exits the window through the left) and then increment the counter for e (because another e enters the window from the right).

Finally, to avoid iterating over the counters every time you do the frequency check, give the counters the following meaning. Each counter is not how many times a letter occurs in a given window, but how many more occurrences of the letter you need to make an anagram. In the example, for the first position of the window, the counter for each letter of s is 0 because the first position is an anagram. Then, have an additional counter for how many counters have reached zero. Decrement that counter every time a letter that enters makes a counter reach zero and increment the counter every time a letter that exits makes a counter go above zero.

Ruby implementation

#!/usr/bin/env ruby

def count_anagrams s, p
ac = 0 # anagram count
f = {} # counters for the characters in `s`
s.chars.each { |c| f[c] = (f[c] || 0) + 1 }
cl = f.length # counters left to reach zero
p.chars.each_with_index do |c, i|
# contract window
if i >= s.length
ec = p[i - s.length] # the letter that exits
if !!f[ec] # is the letter that exits in `s`?
f[ec] += 1 # it is and we note that it left the window
if f[ec] == 1 # do we lack instances of the letter?
cl += 1 # we do and we note that
end
end
end
# expand window
if !!f[c] # is the letter that enters in `s`?
f[c] -= 1 # it is and we make a note that it is in the window
if f[c] == 0 # have we found enough instances of the letter?
cl -= 1 # we have and we note that
if cl == 0 # have we found all the letters of `s`?
ac += 1 # we have, this window position is an anagram
end
end
end
end
return ac
end

while true
s = readline.strip rescue break
p = readline.strip
puts count_anagrams s, p
end

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