# 401     Binary Watch

## 401. [Binary Watch](https://leetcode.com/problems/binary-watch/description/)

## 1. Question

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.

![](https://upload.wikimedia.org/wikipedia/commons/8/8b/Binary_clock_samui_moon.jpg)

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

Given a non-negative integernwhich 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".

## 2. Implementation

**(1) Backtracking**

思路: 根据给定的输入num，我们生成所有可能的hours和minutes值，其中要注意排除无效的值，比如hours必须小于12，minutes必须小于60

```java
public class Solution {
    /*
     * Given a num, find the combination from hours array {8, 4, 2, 1}
     * and minutes array {32, 16, 8, 4, 2, 1}
     */
    public List<String> readBinaryWatch(int num) {
        List<String> res = new ArrayList<>();
        int[] hours = {8, 4, 2, 1};
        int[] minutes = {32, 16, 8, 4, 2, 1};

        for (int i = 0; i <= num; i++) {
            // Get i elements from hours array and the remaining (num - i) from minutes
             List<Integer> hoursList = generateDigit(hours, i, 12);
             List<Integer> minutesList = generateDigit(minutes, num - i, 60);
             for (int hour : hoursList) {
                for (int min : minutesList) {
                    // Convert digit to correct time form
                    res.add(hour + ":" + (min < 10 ? "0" + min : min));
                }
             }
        }
        return res;
    }

    public List<Integer> generateDigit(int[] nums, int count, int max) {
        List<Integer> res = new ArrayList<>();
        recGenerateDigit(nums, count, 0, 0, max, res);
        return res;
    }

    public void recGenerateDigit(int[] nums, int count, int pos, int sum, int max, List<Integer> res) {
        // Exclude invalid value of hour (>= 12) and minute (>= 60)
        if (sum >= max) {
            return;
        }

        if (count == 0) {
            res.add(sum);
            return;
        }

        for (int i = pos; i < nums.length; i++) {
            recGenerateDigit(nums, count - 1, i + 1, sum + nums[i], max, res);
        }
    }
}
```

## 3. Time & Space Complexity

**Backtracking:** 时间复杂度O(12 \* 60) => O(1), 空间复杂度O(12 \* 60) => O(1)
