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POComparison of running times - similar code runs 4 times slower
 

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    <p>I am solving the palindrome partition problem which requires to return all palindrome partitions of a given string (<a href="http://oj.leetcode.com/problems/palindrome-partitioning/" rel="nofollow">http://oj.leetcode.com/problems/palindrome-partitioning/</a>). I found two solutions to this problem. I am having difficulty to understand why there is a huge difference in the running times of these two approaches:</p> <p>(Assume <code>bool isPal()</code> is a given function which tells whether given string is palindrome or not in O(length) time)</p> <p>1st Solution: (Uses backtracking):</p> <pre><code>void find(string s, int start, vector&lt;string&gt; &amp;r, vector&lt;vector&lt;string&gt; &gt; &amp;res){ if (start &gt;= s.size()){ res.push_back(r); }else{ for (int i=start;i&lt;s.size();i++){ if (isPal(s.substr(start, i-start+1))){ r.push_back(s.substr(start,i-start+1)); find(s,i+1,r,res); r.pop_back(); } } } } vector&lt;vector&lt;string&gt;&gt; partition(string s) { vector&lt;vector&lt;string&gt; &gt; res; vector&lt;string&gt; r; find(s,0,r,res); return res; } </code></pre> <p>2nd Solution:</p> <pre><code>vector&lt;vector&lt;string&gt; &gt; partition(string s) { vector&lt;vector&lt;string&gt; &gt; answer; if(s.size() == 0) return answer; // if s is Palindrome, push to answer if(isPal(s)) answer.push_back(vector&lt;string&gt;(1,s)); if(s.size() == 1) return answer; for(int i=1; i&lt;s.size(); ++i) { string s1 = s.substr(0, i); string s2 = s.substr(i, s.size()-i); if(isPal(s1)) { // get sub_answers of partition(s[i:]) vector&lt;vector&lt;string&gt; &gt; sub_answer = partition(s2); // add s1 to the begin of sub_answers for(int j=0; j&lt;sub_answer.size(); ++j) { sub_answer[j].insert(sub_answer[j].begin(), s1); answer.push_back(sub_answer[j]); } } } return answer; } </code></pre> <p>Even though both the solutions have the same underlying idea, the 1st solution runs in <strong>108ms</strong>, while the 2nd one takes <strong>472ms</strong> time. Is this because of theoretical inefficiency (maybe 2nd solution solves a single problem multiple times) or because of inefficient implementation (some C++ concepts)? Please point out the reason for inefficiency of 2nd solution.</p> <p><strong>Note</strong>: Both solutions are correct and give the same result.</p>
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