majaWalk.js

// (x, y)
let stepActionByType = {
  'down': [0, 1],
  'left down': [-1, 1],
  'left up': [-1, 0],
  'up': [0, -1],
  'right up': [1, -1],
  'right down': [1, 0]
};
let stepTypeOrder = [
  // 'down',
  'left down',
  'left up',
  'up',
  'right up',
  'right down',
  'down'
];

function stepsByRoundNumber(roundNumber) {
  if(roundNumber === 1) return [];

  let nMinus1 = roundNumber - 1;
  let nMinus2 = roundNumber - 2;

  return [
    // 1      // down
    nMinus2,  // left down
    nMinus1,  // left up
    nMinus1,  // up
    nMinus1,  // right up
    nMinus1,  // right down
    nMinus1   // down
  ];
}

function roundSize(roundNumber) {
  if(roundNumber === 1) return 0;

  return 6 + 6 * (roundNumber - 2);
}
function countNumberOfRounds(numberOfSteps) {
  let countSteps = 1;
  let countRounds = 0;
  while(countSteps < numberOfSteps) {
    countRounds++;
    countSteps += roundSize(countRounds);
  }

  return countRounds;
}

// if numberOfSteps is higher than roundSize, roundSize will be considered instead
function walkMajaInRound(majaCoord, roundNumber, numberOfSteps) {
  if(roundNumber === 1) return majaCoord;
  if(numberOfSteps <= 0) return majaCoord;

  let stepsByType = stepsByRoundNumber(roundNumber);

  for(let i = 0; i < 6; i++) {
    let stepType = stepTypeOrder[i];

    for(let j = 0; j < stepsByType[i]; j++) {
      majaCoord[0] += stepActionByType[stepType][0];
      majaCoord[1] += stepActionByType[stepType][1];

      numberOfSteps--;
      if(numberOfSteps <= 0) return majaCoord;
    }
  }

  return majaCoord;
}

function walkMaja(numberOfSteps) {
  let majaCoord = [0, 0];

  let rounds = countNumberOfRounds(numberOfSteps);

  numberOfSteps--;
  for(let i = 1; i <= rounds; i++) {
    let stepsInRound = roundSize(i);

    majaCoord = walkMajaInRound(majaCoord, i, numberOfSteps);

    numberOfSteps -= (!stepsInRound ? 0 : stepsInRound - 1);

    if(numberOfSteps > 0) {
      majaCoord[0] += stepActionByType['down'][0];
      majaCoord[1] += stepActionByType['down'][1];

      numberOfSteps--;
    } else return majaCoord;

  }

  return majaCoord;
}