computational-combinatorics/permutation

import {_invert} from './_invert.js';
import {permutation} from './permutation.js';

/**
 * Computes the inverse <code>tau</code> of the input permutation
 * <code>sigma</code>, that is, the permutation such that <code>compose(sigma,
 * tau)</code> returns <code>identity(sigma.length)</code>. Alternatives
 * include using {@link _invertcycles} and {@link itranspositions}.
 *
 * @param {Array} sigma The input permutation.
 * @returns {Array} The inverse of the input permutation.
 */
export function invert(sigma) {
    const tau = permutation(sigma.length);

    _invert(sigma, sigma.length, tau);

    return tau;
}