feat: Add Jump Search algorithm in C++

Jump_Search_Algo/JumpSearch.cpp

@@ -0,0 +1,73 @@
+/*
+* C++ program to implement Jump Search.
+*
+* Jump Search is a searching algorithm for sorted arrays.
+* The basic idea is to check fewer elements (than linear search)
+* by jumping ahead by fixed steps.
+*/
+
+#include <iostream>
+#include <vector>
+#include <cmath>
+#include <algorithm>
+
+int jumpSearch(const std::vector<int>& arr, int x) {
+    int n = arr.size();
+
+    // Finding block size to be jumped
+    int step = std::sqrt(n);
+
+    // Finding the block where element is
+    // present (if it is present)
+    int prev = 0;
+    while (arr[std::min(step, n) - 1] < x) {
+        prev = step;
+        step += std::sqrt(n);
+        if (prev >= n)
+            return -1;
+    }
+
+    // Doing a linear search for x in block
+    // beginning with prev.
+    while (arr[prev] < x) {
+        prev++;
+
+        // If we reached next block or end of
+        // array, element is not present.
+        if (prev == std::min(step, n))
+            return -1;
+    }
+
+    // If element is found
+    if (arr[prev] == x)
+        return prev;
+
+    return -1;
+}
+
+// Main function to test the algorithm
+int main() {
+    std::vector<int> arr = {0, 1, 1, 2, 3, 5, 8, 13, 21,
+                        34, 55, 89, 144, 233, 377, 610};
+    int x = 55;
+
+    // Find the index of 'x' using Jump Search
+    int index = jumpSearch(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 = 7;
+    index = jumpSearch(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;
+}