How can an array in Javascript be sorted and then represented by an array of indices that show the original positions of the sorted elements?

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One way to accomplish this is to create a new array of objects that hold the original value and the index it occupies in the original array. Sort this new array by the value attribute and then extract the index attribute into a new array.

Here is an example implementation:

const array = [5, 2, 8, 1, 9];
const indexedArray = array.map((value, index) => ({ value, index }));
// [{ value: 5, index: 0 }, { value: 2, index: 1 }, { value: 8, index: 2 }, { value: 1, index: 3 }, { value: 9, index: 4 }]
indexedArray.sort((a, b) => a.value - b.value);
// [{ value: 1, index: 3 }, { value: 2, index: 1 }, { value: 5, index: 0 }, { value: 8, index: 2 }, { value: 9, index: 4 }]
const indices = indexedArray.map(item => item.index);
// [3, 1, 0, 2, 4]

Note that this implementation assumes that the original array does not contain objects or values that have complex comparison rules. If that is the case, the sort function passed to sort() must be adapted to compare those values correctly.