From 5b6c49691c60fcc60453744ac764d47addcf6f4a Mon Sep 17 00:00:00 2001
From: Arpit Chaudhary <arpit.choudhary244@gmail.com>
Date: Sun, 7 Jun 2026 16:44:52 +0530
Subject: [PATCH] Add lower bound binary search implementation

---
 search/binary_search_lower_bound.cpp | 62 ++++++++++++++++++++++++++++
 1 file changed, 62 insertions(+)
 create mode 100644 search/binary_search_lower_bound.cpp

diff --git a/search/binary_search_lower_bound.cpp b/search/binary_search_lower_bound.cpp
new file mode 100644
index 00000000000..737256a76b3
--- /dev/null
+++ b/search/binary_search_lower_bound.cpp
@@ -0,0 +1,62 @@
+/**
+ * @file
+ * @brief Implementation of lower bound binary search algorithm.
+ * @details
+ * The lower bound algorithm finds the index of the first element in a sorted
+ * array that is greater than or equal to a target value.
+ * Time Complexity: O(log N)
+ * Space Complexity: O(1)
+ */
+
+#include <cassert>
+#include <iostream>
+#include <vector>
+
+/**
+ * @brief Finds the lower bound of a target in a sorted vector.
+ * @param arr The sorted vector.
+ * @param target The value to find the lower bound for.
+ * @return The index of the lower bound, or the size of the array if all
+ * elements are smaller.
+ */
+int binary_search_lower_bound(const std::vector<int>& arr, int target) {
+    int left = 0;
+    int right = arr.size();
+
+    while (left < right) {
+        int mid = left + (right - left) / 2;
+
+        if (arr[mid] >= target) {
+            right = mid;
+        } else {
+            left = mid + 1;
+        }
+    }
+    return left;
+}
+
+/**
+ * @brief Test function to verify the algorithm
+ */
+void test() {
+    std::vector<int> nums = {1, 3, 5, 5, 5, 7, 9, 11};
+
+    // Test 1: Target exists (should find the first occurrence)
+    assert(binary_search_lower_bound(nums, 5) == 2);
+
+    // Test 2: Target does not exist, falls between elements
+    assert(binary_search_lower_bound(nums, 6) == 5);
+
+    // Test 3: Target is smaller than all elements
+    assert(binary_search_lower_bound(nums, 0) == 0);
+
+    // Test 4: Target is greater than all elements
+    assert(binary_search_lower_bound(nums, 15) == 8);
+
+    std::cout << "All lower bound tests passed successfully!" << std::endl;
+}
+
+int main() {
+    test();
+    return 0;
+}
\ No newline at end of file