feat: Add Interpolation Search algorithm in C++

Search_algo/Interpolation_Search.cpp

@@ -0,0 +1,69 @@
+/*
+* C++ program to implement Interpolation Search.
+*
+* Interpolation Search is an improvement over Binary Search for instances
+* where the values in a sorted array are uniformly distributed.
+*/
+
+#include <iostream>
+#include <vector>
+
+int interpolationSearch(const std::vector<int>& arr, int x) {
+    int n = arr.size();
+    if (n == 0) return -1;
+
+    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.
+        // pos = lo + [ (x-arr[lo])*(hi-lo) / (arr[hi]-arr[lo]) ]
+        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 lower part
+        else
+            hi = pos - 1;
+    }
+    return -1;
+}
+
+// Main function to test the algorithm
+int main() {
+    std::vector<int> arr = {10, 12, 13, 16, 18, 19, 20, 21,
+                        22, 23, 24, 33, 35, 42, 47};
+    int x = 18;
+
+    int index = interpolationSearch(arr, x);
+
+    if (index != -1) {
+        std::cout << "Number " << x << " is at index " << index << std::endl;
+    } else {
+        std::cout << "Number " << x << " is not in the array" << std::endl;
+    }
+
+    x = 30;
+    index = interpolationSearch(arr, x);
+
+    if (index != -1) {
+        std::cout << "Number " << x << " is at index " << index << std::endl;
+    } else {
+        std::cout << "Number " << x << " is not in the array" << std::endl;
+    }
+
+    return 0;
+}