Added recursive string length and interpolation search Algoritm

Algorithms/Recurssion/String_length_recursion.cpp

@@ -0,0 +1,22 @@
+// CPP program to calculate length of
+// a string using recursion
+#include <bits/stdc++.h>
+using namespace std;
+
+/* Function to calculate length */
+int recLen(char* str)
+{
+	// if we reach at the end of the string
+	if (*str == '\0')
+		return 0;
+	else
+		return 1 + recLen(str + 1);
+}
+
+/* Driver program to test above function */
+int main()
+{
+	char str[] = "GeeksforGeeks";
+	cout << recLen(str);
+	return 0;
+}

Algorithms/SearchingALgo/interpolation_search.cpp

@@ -0,0 +1,94 @@
+//Algoritm-----------------------------------------------
+// The idea of formula is to return higher value of pos
+// when element to be searched is closer to arr[hi]. And
+// smaller value when closer to arr[lo]
+//pos = lo + [ (x - arr[lo]) * (hi - lo) / (arr[hi] - arr[Lo]) ]
+/*
+arr[] ==> Array where elements need to be searched
+x     ==> Element to be searched
+lo    ==> Starting index in arr[]
+hi    ==> Ending index in arr[]
+
+
+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])
+
+
+*/
+
+// C++ program to implement interpolation
+// search with recursion
+#include <bits/stdc++.h>
+using namespace std;
+
+// If x is present in arr[0..n-1], then returns
+// index of it, else returns -1.
+int interpolationSearch(int arr[], int lo, int hi, int x)
+{
+	int pos;
+
+	// Since array is sorted, an element present
+	// in array must be in range defined by corner
+	if (lo <= hi && x >= arr[lo] && x <= arr[hi]) {
+
+		// Probing the position with keeping
+		// uniform distribution in mind.
+		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 right sub array
+		if (arr[pos] < x)
+			return interpolationSearch(arr, pos + 1, hi, x);
+
+		// If x is smaller, x is in left sub array
+		if (arr[pos] > x)
+			return interpolationSearch(arr, lo, pos - 1, x);
+	}
+	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]);
+
+	// Element to be searched
+	int x = 18;
+	int index = interpolationSearch(arr, 0, n - 1, x);
+
+	// If element was found
+	if (index != -1)
+		cout << "Element found at index " << index;
+	else
+		cout << "Element not found.";
+
+	return 0;
+}
+
+// This code is contributed by equbalzeeshan