Yeah, at first when I didnt notice that the array has to start from 1 and consecutive from there I was confuse too, since it mean we need a sorted array first to even check how many swap we will need in the end. Your 3rd step is basically a sort by itself, and if we have to sort anyway we can skip the whole normalize thing by doing this (in JS)

var origArray = arr.slice(0); // to keep a copy of the original array
var sortedArray = arr.sort();

for(var i = 0; i < origArray.length; i++) {
	if (origArray[i] != sortedArray[i]) {
		for (var j = i+1; j < origArray.length; j++) {
			if(origArray[j] === origArray[i]) {
				swap(origArray[i],origArray[j]
				numberOfSwap++
				break;
			}
		}
	}
}

This way we dont have to worry about normalization at all since we know exactly where each value should be after the mandatory sort either way.