Leetcode: 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".

Solution 1: Bit Manipulation

use   Integer.bitCount()

 public class Solution {
     public List<String> readBinaryWatch(int num) {
         List<String> res = new ArrayList<String>();
         for (int i=0; i<12; i++) {
             for (int j=0; j<60; j++) {
                 if (Integer.bitCount(i) + Integer.bitCount(j) == num) {
                     String str1 = Integer.toString(i);
                     String str2 = Integer.toString(j);
                     res.add(str1 + ":" + (j<10? "0"+str2 : str2));
                 }
             }
         }
         return res;
     }
 }

Solution 2: Backtracking, 非常精妙之处在于用了两个数组来帮助generate digit（例如：1011 -> 11）

 public class Solution {
     public List<String> readBinaryWatch(int num) {
         int[] nums1 = new int[]{8, 4, 2, 1}, nums2 = new int[]{32, 16, 8, 4, 2, 1};
         List<String> res = new ArrayList<String>();
         for (int i=0; i<=num; i++) {
             List<Integer> hours = getTime(nums1, i, 12);
             List<Integer> minutes = getTime(nums2, num-i, 60);
             for (int hour : hours) {
                 for (int minute : minutes) {
                     res.add(hour + ":" + (minute<10? "0"+minute : minute));
                 }
             }
         }
         return res;
     }
 
     public List<Integer> getTime(int[] nums, int count, int limit) {
         List<Integer> res = new ArrayList<Integer>();
         getTimeHelper(res, count, 0, 0, nums, limit);
         return res;
     }
 
     public void getTimeHelper(List<Integer> res, int count, int pos, int sum, int[] nums, int limit) {
         if (count == 0) {
             if (sum < limit)
                 res.add(sum);
             return;
         }
         for (int i=pos; i<nums.length; i++) {
             getTimeHelper(res, count-1, i+1, sum+nums[i], nums, limit);
         }
     }
 }