401.Binary Watch

A binary watch has 4 LEDs on the top which represent the hours (0-11), and the 6 LEDs on the bottom represent the minutes (0-59).

Each LED represents a zero or one, with the least significant bit on the right.

For example, the above binary watch reads "3:25".

Given a non-negative integer n which represents the number of LEDs that are currently on, return all possible times the watch could represent.

Example:

Input: n = 1
Return: ["1:00", "2:00", "4:00", "8:00", "0:01", "0:02", "0:04", "0:08", "0:16", "0:32"]

Note:

• The order of output does not matter.
• The hour must not contain a leading zero, for example "01:00" is not valid, it should be "1:00".
• The minute must be consist of two digits and may contain a leading zero, for example "10:2" is not valid, it should be "10:02".

Analyze

题目可以转化为在 [1, 2, 4, 8, 1, 2, 4, 8, 16, 32] 中任意取 n 个数值, 有几种组合? 组合问题可以使用回溯法求解得到。

• 前置条件: 确认如果一个 led 灯都没亮着是否为 "0:00"。
• 小时位数范围为 [0, 11], 分钟范围为 [0, 59]。

/**
 * @param {number} num
 * @return {string[]}
 */
var readBinaryWatch = function(num) {
  const arr = [1, 2, 4, 8, 1, 2, 4, 8, 16, 32]
  const result = []
  backTrace(arr, num, 0, [0, 0], result)
  return result
};

var backTrace = function(arr, num, start, temp, result) {
  if (temp[0] >= 12 || temp[1] >= 60) return
  if (num === 0) {
    result.push(`${temp[0]}:${padding(temp[1])}`)
    return
  }

  for (let i = start; i < arr.length; i++) {
    if (i <= 3) {
      temp[0] = temp[0] + arr[i]
    } else {
      temp[1] = temp[1] + arr[i]
    }
    num = num - 1
    backTrace(arr, num, i + 1, temp, result)
    if (i <= 3) {
      temp[0] = temp[0] - arr[i]
    } else {
      temp[1] = temp[1] - arr[i]
    }
    num = num + 1
  }
}

var padding = function(num) {
  return num < 10 ? `0${num}` : num
}