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% Document Info
\author{minhkhanh29}
\pdfinfo{
  /Title (data-structures-and-algorithms-with-c.pdf)
  /Creator (Cheatography)
  /Author (minhkhanh29)
  /Subject (Data Structures and Algorithms with C Cheat Sheet)
}

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    \vspace{-2pt}\large{\bf{\textcolor{DarkBackground}{\textrm{Data Structures and Algorithms with C Cheat Sheet}}}} \\
    \normalsize{by \textcolor{DarkBackground}{minhkhanh29} via \textcolor{DarkBackground}{\uline{cheatography.com/172691/cs/36297/}}}
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  \mymulticolumn{2}{p{5.377cm}}{\bf\textcolor{white}{Cheatographer}}  \\
  \vspace{-2pt}minhkhanh29 \\
  \uline{cheatography.com/minhkhanh29} \\
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  \mymulticolumn{1}{p{5.377cm}}{\bf\textcolor{white}{Cheat Sheet}}  \\
   \vspace{-2pt}Not Yet Published.\\
   Updated 28th December, 2022.\\
   Page {\thepage} of \pageref{LastPage}.
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  Measure your website readability!\\
  www.readability-score.com
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\begin{multicols*}{4}

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\mymulticolumn{1}{x{3.833cm}}{\bf\textcolor{white}{Searching Algorithms}}  \tn
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\mymulticolumn{1}{x{3.833cm}}{· Linear Search – Unsorted Input \newline % Row Count 1 (+ 1)
· Linear Search – Sorted Input \newline % Row Count 2 (+ 1)
· Binary Search (Sorted Input) \newline % Row Count 3 (+ 1)
· String Search: Tries, Suffix Trees, Ternary Search. \newline % Row Count 5 (+ 2)
· Hashing and Symbol Tables% Row Count 6 (+ 1)
} \tn 
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\mymulticolumn{1}{x{3.833cm}}{\bf\textcolor{white}{Linear Search – Unsorted Input}}  \tn
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\mymulticolumn{1}{x{3.833cm}}{int linearSearchUnsorted(int arr{[}{]}, int size, int value) \newline \{ \newline     int i = 0; \newline     for(i = 0 ; i \textless{} size ; i++)\{ \newline         if(value == arr{[}i{]}) return i; \newline     \} \newline     return -1; \newline \}} \tn 
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\mymulticolumn{1}{x{3.833cm}}{{\bf{Time Complexity: O(n)}}. As we need to traverse the complete array in worst case. Worst case is when \newline your desired element is at the last position of the array. Here, 'n' is the size of the array. \newline {\bf{Space Complexity: O(1)}}. No extra memory is used to allocate the array.}  \tn 
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\mymulticolumn{1}{x{3.833cm}}{int linearSearchSorted(int arr{[}{]}, int size, int value) \newline \{ \newline     int i = 0; \newline     for(i = 0 ; i \textless{} size ; i++)\{ \newline         if(value == arr{[}i{]}) return i; \newline         else if(value \textless{} arr{[}i{]}) return -1; \newline     \} \newline     return -1; \newline \}} \tn 
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\mymulticolumn{1}{x{3.833cm}}{{\bf{Time Complexity: O(n)}}. As we need to traverse the complete array in worst case. Worst case is when your desired element is at the last position of the sorted array. However, in the average case this \newline algorithm is more efficient even though the growth rate is same as unsorted. \newline {\bf{Space Complexity: O(1)}}. No extra memory is used to allocate the array.}  \tn 
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\mymulticolumn{1}{x{3.833cm}}{\bf\textcolor{white}{Binary Search}}  \tn
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\mymulticolumn{1}{x{3.833cm}}{/{\emph{ Binary Search Algorithm – Iterative Way }}/ \newline int Binarysearch(int arr{[}{]}, int size, int value) \newline \{ \newline     int low = 0; \newline     int high = size-1; \newline     int mid; \newline     while(low \textless{}= high)\{ \newline         mid = low + (high-low)/2; /{\emph{ To avoid the overflow }}/ \newline         if (arr{[}mid{]} == value) return mid; \newline         else if (arr{[}mid{]} \textless{} value) low = mid + 1; \newline         else high = mid - 1; \newline     \} \newline     return -1; \newline \}} \tn 
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\mymulticolumn{1}{x{3.833cm}}{{\bf{Time Complexity: O(logn)}}. We always take half input and throwing out the other half. So the recurrencerelation for binary search is T(n) = T(n/2) + c. Using master theorem (divide and conquer), we get T(n) =O(logn) \newline {\bf{Space Complexity: O(1)}}}  \tn 
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% That's all folks
\end{multicols*}

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