Jagadish, K.

Find all anagrams of a string in another string

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Given a string s and a non-empty string p, find all the start indices of p’s anagrams in s.

Strings consists of lowercase English letters only and the length of both strings s and p will not be larger than 20,100.

The order of output does not matter.

Example 1:

s: "cbaebabacd" p: "abc"

[0, 6]

The substring with start index = 0 is "cba", which is an anagram of "abc".
The substring with start index = 6 is "bac", which is an anagram of "abc".
Example 2:

s: "abab" p: "ab"

[0, 1, 2]

The substring with start index = 0 is "ab", which is an anagram of "ab".
The substring with start index = 1 is "ba", which is an anagram of "ab".
The substring with start index = 2 is "ab", which is an anagram of "ab".


A naive approach for this problem would be to find all possible anagrams of the givcen string p and store them in an array, say pAnagrams. Since the length of all anagrams of this is going to be constant, say pLen, you can progressively extract substrings of length pLen from the string s. Now check if it is present in the array pAnagrams and if it is present (indexOf returns a value more than -1) then store the index position.

This approach can work, but it involves the additional cost of generating all permutations of the string p which is O(n^2 * n!);

So let’s take a look at how we can optimise this. What we want to ensure is that the the characters and their occurence sum between two points in the string s is exactly the same as the string p.

eg: if the string p is dfeghied , this implies a string of length 8 will be ana anagram of p if,

  • number of d = 2,
  • number of e = 2,
  • number of f = 1,
  • number of g = 1,
  • number of h = 1,
  • number of i = 1


We shall create 2 arrays of that can accomodate the character counts for each alphabet in the given strings. We shall use their distance from the letter a to identify which position in the array to use for that character.

viz. the letter e is the fifth letter in the alphabet, so its occurence count will be stored in the index position 4 since arrays are zero indexed in Javascript.

 * @param {string} s
 * @param {string} p
 * @return {number[]}
var findAnagrams = function(s, p) {
     * We get the ASCII value of the letter 'a' using the `charCodeAt` function.
     * We then deduct the ASCII value of 'a' from the ASCII value of any letter
     * to identify its index position.
    const CHAR_CODE_A = 'a'.charCodeAt(0);
    const NUM_ALPHA = 26;
    const output = [];
    const pArray = Array(NUM_ALPHA).fill(0);
    const sArray = Array(NUM_ALPHA).fill(0);
    const pLen = p.length;
    const sLen = s.length;

    let sumOfNumberOfChars = 0;
    let i = 0;
    let foundAt = -1;

     * We first get the occurence index for the string `p` and store it in
     * `pArray`
    while( i<pLen ){
        let pos = p.charCodeAt(i) - CHAR_CODE_A;
        pArray[pos] = pArray[pos] ? pArray[pos] + 1 : 1;


    let fast = 0;
    let slow = 0;

    while(fast < sLen){
        let pos = s.charCodeAt(slow) - CHAR_CODE_A;
         * We advance the `slow` pointer till it finds a character that is
         * present in the pArray;
        while(pArray[pos] == 0 && slow < sLen){
            pos = s.charCodeAt(slow) - CHAR_CODE_A;

         * As long as 'slow' is pointing at characters in the string `s` we try to find the anagrams.
        if( slow < sLen ){
            let sPos;
            let tmpSumOfCharsFound = 0

            fast = slow;
            foundAt = slow; // `foundAt` marks the position where the first character from the string 'p' was found

             * We advance the `fast` pointer beginning at the position of `slow` character by character
             * until the distance between them is less than the length of the string 'p'
             * At the same time, we fill the sArray character with the incidents of the characters
            while ( (fast - slow) < pLen ){
                sPos = s.charCodeAt(fast) - CHAR_CODE_A;
                if(pArray[sPos] == 0) break;
                sArray[sPos] = sArray[sPos] ? sArray[sPos] + 1 : 1;

            // Compare the two arrays, if they are same store the point at which the subtring was found to output
            if(tmpSumOfCharsFound == sumOfNumberOfChars && areArraysSame(sArray, pArray)){
            // Reset the sArray to find a new substring.
            foundAt = -1;

        } else {

    return output;

function areArraysSame(arr1, arr2){

    if(arr1.length == arr2.length){
        let i = 0;
        let len = arr1.length;

        while(arr1[i] == arr2[i] && i<len) i++;

        return i == len;

    return false

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