Cracking the Coding Interview: Palindrome Permutation

a wall covered in padlocks with a red double decker bus in the backgroundPhoto by Mayumi Maciel

This post is part of the Algorithms Problem Solving series and a problem from the Cracking the Coding Interview book.

Problem description

Given a string, write a function to check if it is a permutation of a palindrome. A palindrome is a word or phrase that is the same forwards and backwards. A permutation is a rearrangement of letters. The palindrome does not need to be limited to just dictionary words. You can ignore casing and non-letter characters.


input: 'Tact Coa'
output: true

input: 'tat'
output: true

input: 'abcd'
output: false

input: 'tactfcoa'
output: false

input: 'tactfffcoa'
output: false


The first thing we do is to a hashmap of characters. For each character, we want to check the number of their occurances in the string.

The character we add to the hashmaps are only alpha and downcased. So it's important to lower case the string and check if it is an alphabetic character.

To check if the string is a palindrome, we just need to check the number of characters. If we have only one character that has an odd count, that can be a palindrome. Otherwise, it's not a palindrome and we can have a permutation for that.

  • Runtime Complexity: O(N), where N = the true length of the string
  • Space Complexity: O(N), where N = the true length of the string in the hashmap
function isAlpha(char) {
  return /[_a-zA-Z]/.test(char);

function buildMapOsChars(string) {
  const charsMap = new Map();
  const downcasedString = string.toLowerCase();

  for (let char of downcasedString) {
    if (!isAlpha(char)) continue;
    if (charsMap.has(char)) charsMap.set(char, charsMap.get(char) + 1);
    else charsMap.set(char, 1);

  return charsMap;

function palindromePermutation(string) {
  let charsMap = buildMapOsChars(string);
  let numberOfCharsWithOneCount = 0;

  for (let [_, count] of charsMap.entries()) {
    numberOfCharsWithOneCount += count % 2;

  return numberOfCharsWithOneCount <= 1;


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