public List<String> readBinaryWatch(int num) {

List<String> res = new ArrayList<>();

/* use a hashtable to represent digit lights for hours and minutes */

int[] nums1 = {8, 4, 2, 1}, nums2 = {32, 16, 8, 4, 2, 1};

for(int i = 0; i <= num; i++){

/* assign lights to hours and get hour comboniation time */

List<Integer> list1 = generateDigit(nums1, i);

/* assign rest to minutes and get all miniute combonation time */

List<Integer> list2 = generateDigit(nums2, num - i);

/* get the valid combonation of these two lists */

for(int num1 : list1){

if(num1 > 11) continue;/* hour represet 0-11 */

for(int num2 : list2){

if(num2 >= 60) continue;/* minute represts with 0-59 */

res.add(num1 + ":" + (num2 < 10 ? "0" + num2 : num2));

}

}

}

return res;

}

//generate all possible digit for the specified light number

public List<Integer> generateDigit(int[] num, int count){

List<Integer> res = new ArrayList<>();

generateDigitHelper(num, count, 0, 0, res);

return res;

}

//a helper method to combonation the digits

private void generateDigitHelper(int[] num, int count, int position, int calculated, List<Integer> res){

if(count == 0){

res.add(calculated);

} else {

for(int i = position; i < num.length; i++){

generateDigitHelper(num, count - 1, i + 1, calculated + num[i], res);

}

}

}