<p>Given a sentence&nbsp;<code>text</code> (A&nbsp;<em>sentence</em>&nbsp;is a string of space-separated words) in the following format:</p>

<ul>
	<li>First letter is in upper case.</li>
	<li>Each word in <code>text</code> are separated by a single space.</li>
</ul>

<p>Your task is to rearrange the words in text such that&nbsp;all words are rearranged in an increasing order of their lengths. If two words have the same length, arrange them in their original order.</p>

<p>Return the new text&nbsp;following the format shown above.</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>

<pre>
<strong>Input:</strong> text = &quot;Leetcode is cool&quot;
<strong>Output:</strong> &quot;Is cool leetcode&quot;
<strong>Explanation: </strong>There are 3 words, &quot;Leetcode&quot; of length 8, &quot;is&quot; of length 2 and &quot;cool&quot; of length 4.
Output is ordered by length and the new first word starts with capital letter.
</pre>

<p><strong class="example">Example 2:</strong></p>

<pre>
<strong>Input:</strong> text = &quot;Keep calm and code on&quot;
<strong>Output:</strong> &quot;On and keep calm code&quot;
<strong>Explanation: </strong>Output is ordered as follows:
&quot;On&quot; 2 letters.
&quot;and&quot; 3 letters.
&quot;keep&quot; 4 letters in case of tie order by position in original text.
&quot;calm&quot; 4 letters.
&quot;code&quot; 4 letters.
</pre>

<p><strong class="example">Example 3:</strong></p>

<pre>
<strong>Input:</strong> text = &quot;To be or not to be&quot;
<strong>Output:</strong> &quot;To be or to be not&quot;
</pre>

<p>&nbsp;</p>
<p><strong>Constraints:</strong></p>

<ul>
	<li><code>text</code> begins with a capital letter and then contains lowercase letters and single space between words.</li>
	<li><code>1 &lt;= text.length &lt;= 10^5</code></li>
</ul>

class Solution {
public:
    string arrangeWords(string text) {
        // String processing, sorting
        // Time: O(n+wlogw) | n -> len(text), w -> # words in text
        // Space: O(w) | w -> # words in text
        
        string res;
        
        // convert string to vector of words
        int n = text.size();
        vector<pair<string, int>> words;
        int idx = 0;
        for (int i=0; i<n; i++) {
            if (text[i] == ' ') {
                words.push_back({text.substr(idx, i-idx), idx});
                if (idx == 0) 
                    words[0].first[0] = tolower(words[0].first[0]);
                idx = i+1;
            }
        }
        words.push_back({text.substr(idx, n-idx), idx});
        
        // Sort the words based on length of word
        sort(words.begin(), words.end(), [](const auto& a, const auto& b) {
            // Seen hint 1
            // Even stable sorting is not able to pass some tcs, but why??
            // Stable sort, will be the relative position of element same.
            if (a.first.size() == b.first.size())
                return a.second < b.second;
            return a.first.size() < b.first.size();
        });
        
        // Convert words to sentence
        for (auto& [w, _]: words)
            res += w + " ";
        res.pop_back();
        
        // Make first character captial
        res[0] = toupper(res[0]);
        
        return res;
    }
};
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