Added Interpolation Search Algorithm to Searching

Added the Interpolation Search Algorithm used for sorted Arrays to Searching.

Author: Enigma-52

CPP/searching/interpolation_search.cpp

@@ -0,0 +1,85 @@
+
+// Let's assume that the elements of the array are linearly distributed.
+
+// General equation of line : y = m*x + c.
+// y is the value in the array and x is its index.
+
+// Now putting value of lo,hi and x in the equation
+// arr[hi] = m*hi+c ----(1)
+// arr[lo] = m*lo+c ----(2)
+// x = m*pos + c     ----(3)
+
+// m = (arr[hi] - arr[lo] )/ (hi - lo)
+
+// subtracting eqxn (2) from (3)
+// x - arr[lo] = m * (pos - lo)
+// lo + (x - arr[lo])/m = pos
+// pos = lo + (x - arr[lo]) *(hi - lo)/(arr[hi] - arr[lo])
+
+/*************************************************/
+
+// Algorithm
+// The rest of the Interpolation algorithm is the same except for the above partition logic.
+// Step1: In a loop, calculate the value of “pos” using the probe position formula.
+// Step2: If it is a match, return the index of the item, and exit.
+// Step3: If the item is less than arr[pos], calculate the probe position of the left sub-array. Otherwise, calculate the same in the right sub-array.
+// Step4: Repeat until a match is found or the sub-array reduces to zero.
+
+// Below is the implementation of the algorithm.
+
+/*************************************************/
+
+#include <bits/stdc++.h>
+using namespace std;
+
+int interpolationSearch(int arr[], int n, int x)
+{
+    // Find indexes of two corners
+    int lo = 0, hi = (n - 1);
+
+    // Since array is sorted, an element present
+    // in array must be in range defined by corner
+    while (lo <= hi && x >= arr[lo] && x <= arr[hi])
+    {
+        if (lo == hi)
+        {
+            if (arr[lo] == x)
+                return lo;
+            return -1;
+        }
+        // Probing the position with keeping
+        // uniform distribution in mind.
+        int pos = lo + (((double)(hi - lo) / (arr[hi] - arr[lo])) * (x - arr[lo]));
+
+        // Condition of target found
+        if (arr[pos] == x)
+            return pos;
+
+        // If x is larger, x is in upper part
+        if (arr[pos] < x)
+            lo = pos + 1;
+
+        // If x is smaller, x is in the lower part
+        else
+            hi = pos - 1;
+    }
+    return -1;
+}
+
+// Driver Code
+int main()
+{
+    // Array of items on which search will
+    // be conducted.
+    int arr[] = {10, 12, 13, 16, 18, 19, 20, 21, 22, 23, 24, 33, 35, 42, 47};
+    int n = sizeof(arr) / sizeof(arr[0]);
+    int x = 18; // Element to be searched
+    int index = interpolationSearch(arr, n, x);
+
+    // If element was found
+    if (index != -1)
+        cout << "Element found at index " << index;
+    else
+        cout << "Element not found.";
+    return 0;
+}