# DSA using Java - Interpolation Search

## Overview

Interpolation search is an improved variant of binary search. This search algorithm works on the probing position of required value. For this algorithm to work properly the data collection should be in sorted form.

Interpolation search search a particular item by computing the probe position.Initially probe position is the position of the middle most item of the collection. If match occurs then index of item is returned. If middle item is greater than item then probe position is again calculated in the sub-array to the right of the middle item other wise item is search in sub-array to the left of the middle item. This process continues on sub-array as well until the size of subarray reduces to zero.

Example of interpolation search is dictionary search, where to search a word starting from say, X we searches near the end of the dictionary thus by interpolating the probe position and so on.

## Algorithm

```Interpolation Search ( A: array of item, n: total no. of items
,x: item to be searched)
Step 1: Set lowerBound = 0
Step 2: Set upperBound = n - 1
Step 3: if lowerBound  = upperBound or A[lowerBound] = A[upperBound]
go to step 12
Step 4: set midPoint = lowerBound +
((upperBound -lowerBound) / (A[upperBound] - A[lowerBound]))
* (x - A[lowerBound])
Step 5: if A[midPoint] < x
Step 6: set from = midPoint + 1
Step 7: if A[midPoint] > x
Step 8: set to = midPoint - 1
Step 9  if A[midPoint] = x go to step 11
Step 10: Go to Step 3
Step 11: Print Element x Found at index midPoint and go to step 13
Step 13: Exit
```

## Demo Program

```package com.tutorialspoint.simplesearch;

import java.util.Arrays;

public class InterpolationSearchDemo {

public static void main(String args[]){
int[] sourceArray = {1,2,3,4,6,7,9,11,12,14,15,
16,17,19,33,34,43,45,55,66,76,88};
System.out.println("Input Array: " +Arrays.toString(sourceArray));
printline(50);
// find location of 55 //
int location = find(sourceArray, 55);
if(location != -1){
System.out.println("Element found at location: " +(location+1));
}else {
}
}

public static int find(int[] intArray, int data){
int lowerBound = 0;
int upperBound = intArray.length -1;
int midPoint = -1;
int comparisons = 0;
int index = -1;
while(lowerBound <= upperBound){
System.out.println("Comparison " + (comparisons +1) ) ;
System.out.println("lowerBound : "+lowerBound
+ " , intArray[" + lowerBound+"] = "
+ intArray[lowerBound]) ;
System.out.println("upperBound : "+upperBound
+ " , intArray[" + upperBound+"] = "
+ intArray[upperBound]) ;
comparisons++;
// probe the mid point
midPoint = lowerBound +
Math.round((float)(upperBound - lowerBound)
/ (intArray[upperBound] - intArray[lowerBound])
*  (data - intArray[lowerBound]));
System.out.println("midPoint = "+midPoint);
// data found
if(intArray[midPoint] == data){
index = midPoint;
break;
}
else {
// if data is larger
if(intArray[midPoint] < data){
// data is in upper half
lowerBound = midPoint + 1;
}
// data is smaller
else{
// data is in lower half
upperBound = midPoint -1;
}
}
}
System.out.println("Total comparisons made: " + comparisons);
return index;
}

public static void printline(int count){
for(int i=0;i <count-1;i++){
System.out.print("=");
}
System.out.println("=");
}
}
```

If we compile and run the above program then it would produce following result −

```Input Array: [1 2 3 4 6 7 9 11 12 14 15 16 17 19 33 34 43 45 55 66 ]
==================================================
Comparison 1
lowerBound : 0, intArray[0] = 1
upperBound : 19, intArray[19] = 66
midPoint = 16
Comparison 2
lowerBound : 17, intArray[17] = 45
upperBound : 19, intArray[19] = 66
midPoint = 18