Tower of Hanoi Backup

print-backup-times.js

// given a number of intervals and number of backup slots, console log out each backup slots age for every interval
const printBackupIntervals = (intervals, backupSlots) => {
  let points = {};
  const pad = String(Math.pow(2, backupSlots - 1)).split("").map(c => "0").join("");
  for (let i = 1; i < intervals; i++) {
    Object.keys(points).forEach(k => points[k]++);

    const k = tower(i, backupSlots).charCodeAt(0);
    points[k] = 1;
    console.log("Day " + i + ": " + Object.keys(points).map(p => {
      const str = String(points[p]);
      return String.fromCharCode(p) + ": " + pad.substring(0, pad.length - str.length) + str;
    }).join(", "));
  }
}

// how many days range do we get from each slot?
const backupRange = (slot) => {
	if (slot === 1) return [0, 1];
	if (slot === 2) return [1, 2];
	if (slot === 3) return [2, 3];
	const base = Math.pow(2, slot - 2) - 1;
	const base2 = Math.pow(2, slot - 1) - 1;
	return [base, base2];
}
/*
1: 0 - 1 days
2: 1 - 2 days
3: 2 - 3 days
4: 3 - 7 days
5: 7 - 15 days
6: 15 - 31 days
7: 31 - 63 days
8: 63 - 127 days
9: 127 - 255 days
10: 255 - 511 days
11: 511 - 1,023 days
12: 1,023 - 2,047 days
13: 2,047 - 4,095 days
14: 4,095 - 8,191 days
15: 8,191 - 16,383 days
16: 16,383 - 32,767 days
17: 32,767 - 65,535 days
18: 65,535 - 131,071 days
19: 131,071 - 262,143 days
*/

tower-of-hanoi.js

// given an increment from the first backup and the number of backup slots available,
// provide which backup slot this backup belongs in.
// returns a letter fom "A" on up to denote which backup slot to use.
const tower = (backupNum, backupCount) => {
  const max = Math.pow(2, backupCount - 1);
  const backupDay = backupNum % max;

  if (backupDay === 1) { // begining of cycle
    return "A"; 
  } else if (backupDay === 0) { // end of cycle
    return String.fromCharCode(64 + backupCount);
  }
  return tower(backupDay, backupCount - 1);
};

/*
// first backup with 5 slots:
tower(1, 5) => "A"

// 8th backup done with 5 slots:
tower(8, 5) => "D"

// 2,398th backup with 5 slots
tower(2938, 5) => "B"
*/