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If the value to find is less than the value being checked, then the search must continue in all values less than the current one. Likewise, if the value to find is greater than the checked value, the search must continue in all values greater than the current one.
The basic algorithm, then, can be described as:. This may be an over-simplification, but the basics are all there. Since a binary search can be performed on any ordered set of data, it makes sense that one can be performed on an array in which the items are sorted. To do this, you essentially treat the array as if it were a binary search tree, separating each step of the process into a current value, a path to the left, and a path to the right.
The search area of an array is defined by two values, a starting index and a stopping index sometimes called a min and a max. These represent the furthest left path and the furthest right path, respectively. The starting and stopping indices are used to calculate the middle index, which is equidistant between the two extremes.
At each step of the algorithm, the value in the middle index of the array is evaluated to determine what to do next. If the specified value is less than the current value, the stopping index is adjusted down to the middle minus one; if the specified value is greater than the current value, the starting index is adjusted up to be the middle plus one.
The search then continues by calculating a new middle and repeating the process. In the beginning, the starting index is 0, the stopping index is 9, and so the middle is 4 obtained by adding the starting index and the stopping index, then dividing by two and eliminating the decimal remainder.
You stop when the starting index and the stopping index are the same, therefore making the middle the same value as each. With all of that explanation out of the way, the actual code for a binary search of an array is pretty straightforward:. Each of the indices is calculated up front, then adjusted each time through the loop. The control condition on the loop ensures that the loop is exited if either the value is found or the starting and stopping indices have become equal.
The return statement needs to check to see if the value was actually found or not in order to return the correct location a missing value should return -1, as per array searching conventions. Doing a binary search on a sorted array is, on average, more efficient than a linear search traditional indexOf implementation because the maximum number of comparisons is kept small.
A binary search has an efficiency of O log n while a linear search has an efficiency of O n. As a point of comparison, a binary search on an array of , items performs a maximum of 16 comparisons while a linear search within the same array performs a maximum of , comparisons. Any viewpoints and opinions expressed in this article are those of Nicholas C.
Zakas and do not, in any way, reflect those of my employer, my colleagues, Wrox Publishing , O'Reilly Publishing , or anyone else. I speak only for myself, not for them. This site is reader-supported. You can support my work in a number of ways: Your support is greatly appreciated. All code examples on all pages, unless otherwise indicated, are BSD licensed.
The code With all of that explanation out of the way, the actual code for a binary search of an array is pretty straightforward: More complicated than you think Mimicking npm script in Node.
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