<p>A binary watch has 4 LEDs on the top to represent the hours (0-11), and 6 LEDs on the bottom to represent&nbsp;the minutes (0-59). Each LED represents a zero or one, with the least significant bit on the right.</p>

<ul>
	<li>For example, the below binary watch reads <code>&quot;4:51&quot;</code>.</li>
</ul>

<p><img alt="" src="https://assets.leetcode.com/uploads/2021/04/08/binarywatch.jpg" style="width: 500px; height: 500px;" /></p>

<p>Given an integer <code>turnedOn</code> which represents the number of LEDs that are currently on (ignoring the PM), return <em>all possible times the watch could represent</em>. You may return the answer in <strong>any order</strong>.</p>

<p>The hour must not contain a leading zero.</p>

<ul>
	<li>For example, <code>&quot;01:00&quot;</code> is not valid. It should be <code>&quot;1:00&quot;</code>.</li>
</ul>

<p>The minute must&nbsp;consist of two digits and may contain a leading zero.</p>

<ul>
	<li>For example, <code>&quot;10:2&quot;</code> is not valid. It should be <code>&quot;10:02&quot;</code>.</li>
</ul>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>
<pre><strong>Input:</strong> turnedOn = 1
<strong>Output:</strong> ["0:01","0:02","0:04","0:08","0:16","0:32","1:00","2:00","4:00","8:00"]
</pre><p><strong class="example">Example 2:</strong></p>
<pre><strong>Input:</strong> turnedOn = 9
<strong>Output:</strong> []
</pre>
<p>&nbsp;</p>
<p><strong>Constraints:</strong></p>

<ul>
	<li><code>0 &lt;= turnedOn &lt;= 10</code></li>
</ul>

class Solution {
public:
vector<string> results;

int time[10] = {1, 2, 4, 8, 1, 2, 4, 8, 16, 32};
int hourNow = 0;
int minNow = 0;

void changeToHour() {
    if (hourNow > 11 || minNow > 59)
    {
        return;
    }
    string oneT = to_string(hourNow) + ":";
    if (minNow < 10)
    {
        oneT += "0" + to_string(minNow);
    }
    else
    {
        oneT += to_string(minNow);
    }
    results.push_back(oneT);
}

void backTrack(int turnedOn, int index) {
    if (turnedOn == 0) {
        changeToHour();
        return;
    }   
    if (index == 10)
    {
        return;
    }
    backTrack(turnedOn, index + 1);
    if (index < 4)
    {
        hourNow += time[index];
    }
    else
    {
        minNow += time[index];
    }
    backTrack(turnedOn - 1, index + 1);
    if (index < 4)
    {
        hourNow -= time[index];
    }
    else
    {
        minNow -= time[index];
    }
    
}
vector<string> readBinaryWatch(int turnedOn) {
    backTrack(turnedOn, 0);
    return results;
}
};
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