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POComputational complexity of a program
 

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  1. POComputational complexity of a program
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    <p>I wrote the following program which should answer this question</p> <blockquote> <p>Write an efficient function to find the first nonrepeated character in a string. For instance, the first nonrepeated character in “total” is 'o' and the first nonrepeated character in “teeter” is 'r'. Discuss the efficiency of your algorithm.</p> </blockquote> <p>This is what I did:</p> <pre><code>#include &lt;stdio.h&gt; #include &lt;iostream&gt; #include &lt;vector&gt; using namespace std; class Node { public: Node::Node(char ch) { c = ch; next = NULL; } char c; Node *next; }; Node* addNode(Node *tail, char ch) { if(tail == NULL) return new Node(ch); else { Node *newN = new Node(ch); tail-&gt;next = newN; return newN; } } void deleteNode(char ch, Node** head, Node**tail) { Node *prev = NULL; Node *cur = *head; while(cur!=NULL) { if(cur-&gt;c == ch) { // found cut it if(prev == NULL) { // head cut off if(*tail == *head) { // worst possible, just one element delete *head; *head = NULL; return; } else { // Head cut off but not just first element Node *tmp = *head; *head = (*head)-&gt;next; delete tmp; return; } } else { // delete normal node if(*tail == cur) { // delete tail Node *tmp = *tail; *tail = prev; delete tmp; return; } else { // Normal node not tail prev-&gt;next = cur-&gt;next; delete cur; return; } } } // no match keep searching prev = cur; cur = cur-&gt;next; } } int main() { char str[] = "total"; char htable[26]; memset(htable, 0, sizeof(char)*26); Node *head = NULL; Node *tail = head; for(unsigned int i=0;;i++) { if(str[i] == '\0') break; // check first match char m = htable[str[i]-'a']; switch(m) { case 0: { // first time, add it to linked list htable[str[i]-'a']++; tail = addNode(tail, str[i]); if(head == NULL) head = tail; }break; case 1: { // bam, cut it out htable[str[i]-'a']++; deleteNode(str[i], &amp;head, &amp;tail); }break; } } if(head != NULL) printf("First char without repetition: %c", head-&gt;c); else printf("No char matched"); return 0; } </code></pre> <p>and it works (although I didn't free the memory at the end of the program for the linked list). Basically I keep an hashtable with a 0 if a character hasn't been found yet, a 1 if it has been found once (and it's added to the linked list at the tail position) and 2 if there are at least two occurrences of it (and should be removed by the linked list).</p> <p><strong>What's this program's computational complexity with big-O notation?</strong></p> <p>Since this algorithm just passes once per each element I think it's O(n), although the removal of the values in the linked list (in the worst case possible) would require additional O(k^2) where k is the length of the alphabet used. Something like O(n+k^2) it's my pick and if the string is very long and the alphabet restricted the algorithm becomes very efficient.</p>
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    1. USLinus Kleen
    1. USJohnny Pauling
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    1. COBased on your current program have you thought about what would happen if you did str = "toTal"?
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      1. POComputational complexity of a program
      1. USJosh
    2. COI'm deliberately not using uppercase letters for simplicity's sake
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      1. POComputational complexity of a program
      1. USJohnny Pauling
 

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