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".

backtracking 让bit自左至右往上加，需要注意时间格式的限定条件，小时不超过12点，分钟不超过60min。

 public IList<string> ReadBinaryWatch(int num) {
        var res = new List<string>();
        Backtracking(num,1,res,0,0);
        return res;
        
    } 
    
    private void Backtracking(int num,int bit, IList<string> res, int hr,int min)
    {
        if(num<0) return;
        if(bit == 11)
        {
            if(num == 0 && hr<12 && min<60)  res.Add(hr+":"+((min<10)?"0"+min: min+""));
            return ;
        }
        else
        {
            Backtracking(num,bit+1,res,hr,min);
            if(bit <=4 ) Backtracking(num-1,bit+1,res,hr+(int)Math.Pow(2,4-bit),min);
            else  Backtracking(num-1,bit+1,res,hr,min+(int)Math.Pow(2,10-bit));
        }
    }