Scheduling algorithm for a round-robin tournament?

Here is the code for it in JavaScript.

function makeRoundRobinPairings(players) {
  if (players.length % 2 == 1) {
    players.push(null);
  }

  const playerCount = players.length;
  const rounds = playerCount - 1;
  const half = playerCount / 2;

  const tournamentPairings = [];

  const playerIndexes = players.map((_, i) => i).slice(1);

  for (let round = 0; round < rounds; round++) {
    const roundPairings = [];

    const newPlayerIndexes = [0].concat(playerIndexes);

    const firstHalf = newPlayerIndexes.slice(0, half);
    const secondHalf = newPlayerIndexes.slice(half, playerCount).reverse();

    for (let i = 0; i < firstHalf.length; i++) {
      roundPairings.push({
        white: players[firstHalf[i]],
        black: players[secondHalf[i]],
      });
    }

    // rotating the array
    playerIndexes.push(playerIndexes.shift());
    tournamentPairings.push(roundPairings);
  }

  return tournamentPairings;
}

UPDATED: Fixed a bug reported in the comments

I made an updated solution for this with reusable functions (inspired by varun):

const testData = [
  "Red",
  "Orange",
  "Yellow",
  "Green",
  "Blue",
  "Indigo",
  "Violet",
];

const matchParticipants = (participants) => {
  const p = Array.from(participants);
  if (p % 2 == 1) {
    p.push(null);
  }
  const pairings = [];
  while (p.length != 0) {
    participantA = p.shift();
    participantB = p.pop();
    if (participantA != undefined && participantB != undefined) {
      pairings.push([participantA, participantB]);
    }
  }
  return pairings;
};

const rotateArray = (array) => {
  const p = Array.from(array);
  const firstElement = p.shift();
  const lastElement = p.pop();
  return [firstElement, lastElement, ...p];
};

const generateTournament = (participants) => {
  const tournamentRounds = [];
  const rounds = Math.ceil(participants.length / 2);
  let p = Array.from(participants);
  for (let i = 0; i < rounds; i++) {
    tournamentRounds.push(matchParticipants(p));
    p = rotateArray(p);
  }
  return tournamentRounds;
};

console.log(generateTournament(testData));

I made this code, regarding the Okasaki explanation

const roundRobin = (participants) => {
  const tournament = [];

  const half = Math.ceil(participants.length / 2);
  const groupA = participants.slice(0, half);
  const groupB = participants.slice(half, participants.length);
  groupB.reverse();

  tournament.push(getRound(groupA, groupB));


  for(let i=1; i < participants.length - 1; i ++) {
    groupA.splice(1, 0, groupB.shift());
    groupB.push(groupA.pop())
    tournament.push(getRound(groupA, groupB));
  }

  console.log(tournament)
  console.log("Number of Rounds:", tournament.length)
  return tournament;
}

const getRound = (groupA, groupB) => {
  const total = [];
  groupA.forEach((p, i) => {
    total.push([groupA[i], groupB[i]]);
  });
  return total;
}

roundRobin([1,2,3,4,5,6,7])

P.S.: I put an example with an odd amount, so there is a team doesn't play every round, dueling with undefined, you can customize it the way you want

The classic algorithm works like this:

Number the teams 1..n. (Here I'll take n=8.)

Write all the teams in two rows.

1 2 3 4
8 7 6 5

The columns show which teams will play in that round (1 vs 8, 2 vs 7, ...).

Now, keep 1 fixed, but rotate all the other teams. In week 2, you get

1 8 2 3
7 6 5 4

and in week 3, you get

1 7 8 2
6 5 4 3

This continues through week n-1, in this case,

1 3 4 5
2 8 7 6

If n is odd, do the same thing but add a dummy team. Whoever is matched against the dummy team gets a bye that week.