Databases
StackOverflow2013
Postsdbo
POSearching for an element in a circular sorted array
 

Note that there are some explanatory texts on larger screens.

plurals
  1. POSearching for an element in a circular sorted array
    primarykey
    data
    text
    <p>We want to search for a given element in a circular sorted array in complexity not greater than <code>O(log n)</code>.<br> Example: Search for <code>13</code> in <code>{5,9,13,1,3}</code>. </p> <p>My idea was to convert the circular array into a regular sorted array then do a binary search on the resulting array, but my problem was the algorithm I came up was stupid that it takes <code>O(n)</code> in the worst case:</p> <pre><code>for(i = 1; i &lt; a.length; i++){ if (a[i] &lt; a[i-1]){ minIndex = i; break; } } </code></pre> <p>then the corresponding index of ith element will be determined from the following relation:</p> <pre><code>(i + minInex - 1) % a.length </code></pre> <p>it is clear that my conversion (from circular to regular) algorithm may take O(n), so we need a better one.</p> <p>According to ire_and_curses idea, here is the solution in Java:</p> <pre class="lang-java prettyprint-override"><code>public int circularArraySearch(int[] a, int low, int high, int x){ //instead of using the division op. (which surprisingly fails on big numbers) //we will use the unsigned right shift to get the average int mid = (low + high) &gt;&gt;&gt; 1; if(a[mid] == x){ return mid; } //a variable to indicate which half is sorted //1 for left, 2 for right int sortedHalf = 0; if(a[low] &lt;= a[mid]){ //the left half is sorted sortedHalf = 1; if(x &lt;= a[mid] &amp;&amp; x &gt;= a[low]){ //the element is in this half return binarySearch(a, low, mid, x); } } if(a[mid] &lt;= a[high]){ //the right half is sorted sortedHalf = 2; if(x &gt;= a[mid] &amp;&amp; x&lt;= a[high] ){ return binarySearch(a, mid, high, x); } } // repeat the process on the unsorted half if(sortedHalf == 1){ //left is sorted, repeat the process on the right one return circularArraySearch(a, mid, high, x); }else{ //right is sorted, repeat the process on the left return circularArraySearch(a, low, mid, x); } } </code></pre> <p>Hopefully this will work.</p>
    singulars
    1. PO
      singulars
      1. PTAnswer
    1. This table or related slice is empty.
    1. PTQuestion
    1. USCœur
    1. USguirgis
    plurals
    1. PL
      singulars
      1. LTLinked
    1. PL
      singulars
      1. LTLinked
    2. PL
      singulars
      1. LTLinked
    3. PL
      singulars
      1. LTDuplicate
    1. This table or related slice is empty.
    1. PO
      singulars
      1. PTAnswer
    2. PO
      singulars
      1. PTAnswer
    3. PO
      singulars
      1. PTAnswer
    1. VO
      singulars
      1. POSearching for an element in a circular sorted array
      1. This table or related slice is empty.
      1. VTUpMod
    2. VO
      singulars
      1. POSearching for an element in a circular sorted array
      1. This table or related slice is empty.
      1. VTUpMod
    3. VO
      singulars
      1. POSearching for an element in a circular sorted array
      1. This table or related slice is empty.
      1. VTUpMod
    1. COYou should clarify whether or not you know in advance where the circular array begins. Typically in real-world applications you would know.
      singulars
      1. POSearching for an element in a circular sorted array
      1. USChristopher Barber
    2. CONo, i don't know where the cirular array begins, if i know then i won't need a conversion algorithm instead i'll apply the above relation directly and do a binary-search.
      singulars
      1. POSearching for an element in a circular sorted array
      1. USguirgis
    3. COYou need to know if elements are distinct. Otherwise worst case is Omega(n).
      singulars
      1. POSearching for an element in a circular sorted array
      1. This table or related slice is empty.
 

Querying!

 
Guidance
A row detail

Detail views are divided into sections. All the information in the data section comes from columns in the selected row. The other sections display data from other, related rows.

Related data can be related in a to-one or a to-many fashion. Captions of data related in a to-many fashion link to a list view showing a filtered view of the table.

Try moving around until you find a non-empty to-many entry and click on the label to get to one. You can move back to the root by clicking on the database name in the header.

SQuiL has stopped working due to an internal error.

If you are curious you may find further information in the browser console, which is accessible through the devtools (F12).

Reload