squares_kata.js

function isSquare(a, b) {
  return Math.sqrt(a + b) % 1 === 0;
}

function remove_pair(a, b, _pairs) {
  _pairs[a] = _pairs[a].filter(s => s !== b);
  _pairs[b] = _pairs[b].filter(s => s !== a);
}

const clone = (obj) => JSON.parse(JSON.stringify(obj));

function square_sums_row(n) {
  const pairs = {};
  let arr = [];
  let all_seq = [];

  for (let i = 1; i <= n; i++) {
    arr[i - 1] = i;
  }

  for (let i = 0; i < n; i++) {
    for (let j = 0; j < n; j++) {
      if (isSquare(arr[i], arr[j])) {
        if (pairs[arr[i]]) {
          pairs[arr[i]].push(arr[j]);
        } else {
          pairs[arr[i]] = [arr[j]];
        }
      }
    }
  }

  for (let j = 0; j < n; j++) {
    const cloned_pairs = clone(pairs);
    const seq = [];

    seq[0] = arr[j];

    function addSeq(start = 1, _seq, offset = 0) {
      let i = start;

      while (true) {
        const prev = _seq[i - 1];

        let maybe_next = cloned_pairs[prev];

        let next = maybe_next[offset];

        if (offset === 0 && maybe_next.length > 1) {
          for (let k = 1; k < maybe_next.length; k++) {
            addSeq(_seq.length, clone(_seq), k);
          }
        }

        offset = 0;

        if (!next) break;

        _seq[i] = next;

        remove_pair(prev, _seq[i], cloned_pairs);

        i++;
      }

      for (let l = 0; l < _seq.length; l++) {
        if (_seq.indexOf(_seq[l]) !== l)
          _seq.splice(l, 1);
      }

      all_seq.push(_seq);
    }

    addSeq(1, seq);
  }

  all_seq.sort((a1, a2) => a1.length > a2.length);

  return all_seq[all_seq.length - 1];
}

console.log(square_sums_row(15));