Find the index of a given permutation in the sorted list of the permutations of a given string

Question

We\'re given a string and a permutation of the string.

For example, an input string sandeep and a permutation psdenae.

Find the pos

Answer 1

Building off @Algorithmist 's answer, and his comment to his answer, and using the principle discussed in this post for when there are repeated letters, I made the following algorithm in JavaScript that works for all letter-based words even with repeated letter instances.

function anagramPosition(string) {
  var index = 1;
  var remainingLetters = string.length - 1;
  var frequencies = {};
  var splitString = string.split("");
  var sortedStringLetters = string.split("").sort();

  sortedStringLetters.forEach(function(val, i) {
    if (!frequencies[val]) {
      frequencies[val] = 1;
    } else {
      frequencies[val]++;
    }
  })

  function factorial(coefficient) {
    var temp = coefficient;
    var permutations = coefficient;
    while (temp-- > 2) {
      permutations *= temp;
    }
    return permutations;
  }

  function getSubPermutations(object, currentLetter) {
    object[currentLetter]--;
    var denominator = 1;
    for (var key in object) {
      var subPermutations = factorial(object[key]);
      subPermutations !== 0 ? denominator *= subPermutations : null;
    }
    object[currentLetter]++;
    return denominator;
  }

  var splitStringIndex = 0;
  while (sortedStringLetters.length) {
    for (var i = 0; i < sortedStringLetters.length; i++) {
      if (sortedStringLetters[i] !== splitString[splitStringIndex]) {
        if (sortedStringLetters[i] !== sortedStringLetters[i+1]) {
          var permutations = factorial(remainingLetters);
          index += permutations / getSubPermutations(frequencies, sortedStringLetters[i]);
        } else {
          continue;
        }
      } else {
        splitStringIndex++;
        frequencies[sortedStringLetters[i]]--;
        sortedStringLetters.splice(i, 1);
        remainingLetters--;
        break;
      }
    }
  }
  return index;
}

anagramPosition("ARCTIC") // => 42

I didn't comment the code but I did try to make the variable names as explanatory as possible. If you run it through a debugger process using your dev tools console and throw in a few console.logs you should be able to see how it uses the formula in the above-linked S.O. post.