Misha Moroshko Misha Moroshko - 5 months ago 12
Javascript Question

How to sort an array in-place given an array of target indices?

How would you sort a given array

arr
in-place given an array of target indices
ind
?

For example:

var arr = ["A", "B", "C", "D", "E", "F"];
var ind = [ 4, 0, 5, 2, 1, 3 ];

rearrange(arr, ind);

console.log(arr); // => ["B", "E", "D", "F", "A", "C"]

arr = ["A", "B", "C", "D"];
ind = [ 2, 3, 1, 0 ];

rearrange(arr, ind);

console.log(arr); // => ["D", "C", "A", "B"]


I tried the following algorithm, but it fails on the second example above.

function swap(arr, i, k) {
var temp = arr[i];
arr[i] = arr[k];
arr[k] = temp;
}

function rearrange(arr, ind) {
for (var i = 0, len = arr.length; i < len; i++) {
if (ind[i] !== i) {
swap(arr, i, ind[i]);
swap(ind, i, ind[i]);
}
}
}


How would you solve this in O(n) time and O(1) extra space?

Could you provide a proof that your algorithm works?




Note: This question looks similar to this one, but here mutating
ind
is allowed.

OB1 OB1
Answer

The algorithm fails because it has only one loop over the indices of your list.

What happens in your algorithm is this :

i=0 -> ["A", "B", "C", "D"] , [ 2,   3,   1,   0 ]
i=1 -> ["C", "B", "A", "D"] , [ 1,   3,   2,   0 ]
i=2 -> ["C", "D", "A", "B"] , [ 1,   0,   2,   3 ]
i=3 -> ["C", "D", "A", "B"] , [ 1,   0,   2,   3 ]

Note how by the first swap, 1 is in position 0 and you will not visit it again unless you swap it with 0, which does not happen in this example.

What your algorithm misses is an internal loop that runs through sub-cycles of indexes. Try replacing the if by while in rearrange:

function rearrange(arr, ind) {
   for (var i = 0, len = arr.length; i < len; i++) {
      while (ind[i] !== i) {
         swap(arr, i, ind[i]);
         swap(ind, i, ind[i]);
      }
   }
}

Note on complexity: although this is a double loop, complexity does not change because at each swap, one element is correctly placed, and each element is read at most twice (once through the cycling, once though the for loop).

Note on proof: I will not do a complete proof of this algorithm here, but I can give leads. If ind is a permutation, then all elements belong to closed permutative sub-cycles. The while loop ensures that you're iterating entire cycles, the for loop ensures that you're checking for every possible cycle.