- Problem description:
- You are given a sorted array (of numbers)
Example:
Problem:
- Locate the array element that has the
value x
- Return the index of the
array element that contains the
value x
- Or: return −1 to indicate that the value x is not in the array.
- Return the index of the
array element that contains the
value x
- Locate the array element that has the
value x
- You are given a sorted array (of numbers)
Example:
-
Example 1:
- Locate the array element that has the
value 27
Solution:
- Locate the array element that has the
value 27
-
Example 2:
- Locate the array element that has the
value 28
Solution:
- Locate the array element that has the
value 28
- The binary search algorithm
(general case):
- Find x in
array elements
A[low .. high]:
- Compare
x with the
middle element in the array.
There are 3 possible outcomes:
- If
x == A[middle] (value of the
middle element of array):
- return middle (= the index of the middle element)
- If
x < A[middle]:
- Find x in
array elements
A[low .. (middle−1)]
Note:
- This is a smaller problem of the same kind !
- Find x in
array elements
A[low .. (middle−1)]
- If
x > A[middle]:
- Find x in
array elements
A[(middle+1) .. high]
Note:
- This is a smaller problem of the same kind !
- Find x in
array elements
A[(middle+1) .. high]
- If
x == A[middle] (value of the
middle element of array):
- Find x in
array elements
A[low .. high]:
- Base case:
-
Find x in an
empty array
A[low .. high]
where low > high
Example:
We return −1 (not found) in this case.
-
Find x in an
empty array
A[low .. high]
where low > high
- Java program:
public static int BinSearch( int x, int[] A, int low, int high ) { int middle; int mySol; if ( low > high ) { /* ------------------------------------------------------ Solve the base case: ------------------------------------------------------ */ return( -1 ); // Not found } else { /* ------------------------------------------------ Solve a non-trivial binary search ------------------------------------------------ */ middle = (low + high)/2; if ( x == A[middle] ) { mySol = middle; // Found x, return location in array } else if ( x < A[middle] ) { mySol = BinSearch( x, A, low, middle−1 ); // Solve smaller problem } else // x > A[middle] { mySol = BinSearch( x, A, middle+1, high ); // Solve smaller problem } return ( mySol ); } }
- Example Program:
(Demo above code)
- Prog file: click here
How to run the program:
- Right click on link and
save in a scratch directory
- To compile: javac Recurse4.java
- To run: java Recurse4