[LeetCode] Binary Watch 二进制表

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".

首先来看一种写法很简洁的解法，这种解法利用到了bitset这个类，可以将任意进制数转为二进制，而且又用到了count函数，用来统计1的个数。那么时针从0遍历到11，分针从0遍历到59，然后我们把时针的数组左移6位加上分针的数值，然后统计1的个数，即为亮灯的个数，我们遍历所有的情况，当其等于num的时候，存入结果res中，参见代码如下： 

class Solution {
public:
    vector<string> readBinaryWatch(int num) {
        vector<string> res;
        for (int h = 0; h < 12; ++h) {
            for (int m = 0; m < 60; ++m) {
                if (bitset<10>((h << 6) + m).count() == num) {
                    res.push_back(to_string(h) + (m < 10 ? ":0" : ":") + to_string(m));
                }
            }
        }
        return res;
    }
};

上面的方法之所以那么简洁是因为用了bitset这个类，如果我们不用这个类，那么应该怎么做呢？这个灯亮问题的本质其实就是在n个数字中取出k个，那么就跟之前的那道Combinations一样，我们可以借鉴那道题的解法，那么思路是，如果总共要取num个，我们在小时集合里取i个，算出和，然后在分钟集合里去num-i个求和，如果两个都符合题意，那么加入结果中即可，参见代码如下：

 解法二：

class Solution {
public:
    vector<string> readBinaryWatch(int num) {
        vector<string> res;
        vector<int> hour{8, 4, 2, 1}, minute{32, 16, 8, 4, 2, 1};
        for (int i = 0; i <= num; ++i) {
            vector<int> hours = generate(hour, i);
            vector<int> minutes = generate(minute, num - i);
            for (int h : hours) {
                if (h > 11) continue;
                for (int m : minutes) {
                    if (m > 59) continue;
                    res.push_back(to_string(h) + (m < 10 ? ":0" : ":") + to_string(m));
                }
            }
        }
        return res;
    }
    vector<int> generate(vector<int>& nums, int cnt) {
        vector<int> res;
        helper(nums, cnt, 0, 0, res);
        return res;
    }
    void helper(vector<int>& nums, int cnt, int pos, int out, vector<int>& res) {
        if (cnt == 0) {
            res.push_back(out);
            return;
        }
        for (int i = pos; i < nums.size(); ++i) {
            helper(nums, cnt - 1, i + 1, out + nums[i], res);
        }
    }
};