getAvailableTimes.js

const _ = require('lodash');

const parser = s => {
  const parts = s.split(':');
  return parts[0] * 60 + +parts[1]
};

const doesOverlap = (slot, booking) => {
  if (!slot || !booking) {
    return false;
  }
  return (slot[0] <= booking[1] && slot[1] >= booking[0])
    || (booking[0] <= slot[1] && booking[1] >= slot[0]);
};

const render = t => `${Math.floor(t / 60).toString().padStart(2, '0')}:${(t % 60).toString().padStart(2, '0')}`;

const getAvailableTime = (start, end, blocks, duration) => {
  blocks = blocks.map(b => b.map(parser));
  blocks = _.sortBy(blocks, '0');
  start = parser(start);
  end = parser(end);
  duration = parser(duration);

  const genBlocks = [];
  let blockI = 0;
  for (let i = start; i < end - duration; i++) {
    const possibleBlock = [i, i + duration - 1];
    if (doesOverlap(possibleBlock, blocks[blockI])) {
      i = blocks[blockI][1];
      blockI++;
    } else {
      genBlocks.push(possibleBlock);
      i += (duration - 1);
    }
  }

  return genBlocks.map(b => b.map(render));
};

getAvailableTime('8:00', '17:00', [['8:40', '9:20'], ['13:30', '14: 40']], '0:30');

// 08:00,08:29
// 09:21,09:50
// 09:51,10:20
// 10:21,10:50
// 10:51,11:20
// 11:21,11:50
// 11:51,12:20
// 12:21,12:50
// 12:51,13:20
// 14:41,15:10
// 15:11,15:40
// 15:41,16:10
// 16:11,16:40