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"]

• 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=============================

这道题我的第一个想法就是 这个好像和 letter combintion of phone number 那道题目很像，我们可以算出当lights number为k时所有可能的hours再算出相对应 num-k时所有可能minutes， 然后进行组合。 这样的话，我就想着我们应该分步进行。

• 第一步， 算出hours
• 第二步， 算出minutes
• 第三步， 结合hours 和 minutes
• 第四步， 改变 hours lights的个数， 继续上述

当然 我们需要注意的是亮灯个数， 因为hours毕竟一共才4灯，minutes一共才6灯，所以要根据传入的灯总数进行调整。同时， 我们也要注意时针不可以超过11，分针不可以超过59.

代码：

 

class Solution {
    int HOUR_LIMIT = 11;
    int MINUTE_LIMIT = 59;
    public List<String> readBinaryWatch(int num) {
        int[] hours = new int[]{1,2,4,8};
        int[] minutes = new int[]{1,2,4,8,16,32};
        List<String> hoursOptions = new ArrayList<>();
        List<String> minutesOptions = new ArrayList<>(); 
        List<String> results = new ArrayList<>();
        //separate the formation of hour and minute
        int options = num > hours.length ? hours.length : num;
        for (int index = 0; index <= options; index++) {
            formLightComb(index, hoursOptions, hours, 0, 0, HOUR_LIMIT);
            int option = minutes.length >= num - index ? num - index : minutes.length;
            formLightComb(option, minutesOptions, minutes, 0, 0, MINUTE_LIMIT);
            formTime(minutesOptions, hoursOptions, results, 0, "");
            hoursOptions.clear();
            minutesOptions.clear();
        }
        return results;
    }
    
    void formLightComb(int num, List<String> results, int[] times, int time, int index, int limit) {
        if (num == 0) {
            if (time <= limit) {
                if (limit == MINUTE_LIMIT && (time / 10 == 0)) {
                    results.add("0" + time);
                } else {
                    results.add(time + "");
                }
            }
            return;
        }
        for (int i = index; i < times.length; i++) { 
            formLightComb(num - 1, results, times, times[i] + time, i + 1, limit);
        }
    }
    
    void formTime(List<String> minutes, List<String> ls, List<String> results, int count, String time){
        if (count == 2) {
            results.add(time.substring(1, time.length()));
            return;
        }
        for (int i = 0; i < ls.size(); i++) {
             formTime(minutes, minutes, results, count + 1, time + ":" + ls.get(i));
        }           
    }
}