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PODetermining asymptotic complexity of program
 

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    <p>Hey guys I'm fairly new to c++ and am trying to determine the asymptotic complexity of my program which takes in an input and determines if it's a polynomial or not.</p> <p>"If the length of the input expression is m chars, what is the big-Oh complexity of your program with respect to m?"</p> <p>My guess is O(m*log m) in which the first m is the for loop that iterates m times and log m is the while loop that counts exponents greater than 1 digit.</p> <p>Also, I'm trying to save a "largest" value which holds the largest exponent in order to calculate the polynomials runtime complexity. However, I am having confusion with storing the exponent correctly. Can anyone recommend an easier way? </p> <p>example input: "n^23 + 4n^10 - 3" should have 23 as the largest exponent</p> <pre><code>#include &lt;iostream&gt; #include &lt;string&gt; using namespace std; int main() { string input; int pcount = 1; //count for # of variables( min 3 to be poly) int largest = 0; // used for complexity int temp=0; cout &lt;&lt; "Enter equation below. " &lt;&lt; endl; getline(cin,input); //to input polynomial cout &lt;&lt; endl &lt;&lt; input &lt;&lt; endl; if (input[0] == '-' || input[0] == '+') //to check for '-' as first char pcount--; bool pcheck = true; for (unsigned i = 0; i &lt; input.size(); i++) { temp = 0; cout &lt;&lt; input[i] &lt;&lt; endl; if ( input[i] == '+' || input[i] == '-' ) pcount++; if ( input[i] == 'n') //checks for integer { if ( input[i+1] &amp;&amp; input[i+1] == '^' ) { if (input[i+2] == 46 || input[i+2] == 43 || input[i+2] == 45) { cout &lt;&lt; "fail" &lt;&lt; endl; pcheck = false; } temp = input[i+2]-48; // to check for largest exp while ( input[i+2] != 43 &amp;&amp; input[i+2] != 45) { if ( i+3 == input.size()) { cout &lt;&lt; "break"; break; } if( input[i+2] &lt; 48 || input[i+2] &gt;57) // 48-57 is ascii { cout &lt;&lt; "fail" &lt;&lt; endl; pcheck = false; } i++; temp = temp * 10; temp = temp + (input[i+2]-48); if (temp &gt; largest) largest = temp; } } } } if ( pcheck == true &amp;&amp; pcount &gt;= 3) //valid ints and at least 3 variables { cout &lt;&lt; "polynomial detected!" &lt;&lt; endl &lt;&lt; "The big-Oh complexity is O(n^" &lt;&lt; largest &lt;&lt; ")." &lt;&lt; endl; } else cout &lt;&lt; "not a poly" &lt;&lt; endl; return 0; } </code></pre>
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