Add binary_insertion_sort.r (#95)

sorting_algorithms/binary_insertion_sort.r

@@ -0,0 +1,43 @@
+# Binary Insertion Sort Function
+# Sorts an input vector using the Binary Insertion Sort algorithm.
+# Parameters:
+# - arr: Input vector to be sorted.
+# Returns:
+# - Sorted vector.
+binary_insertion_sort <- function(arr) {
+  # Loop through the input vector starting from the second element.
+  for (i in 2:length(arr)) {
+    # Store the current element in a variable.
+    key <- arr[i]
+    # Initialize left and right pointers for binary search.
+    left <- 1
+    right <- i - 1
+
+    # Binary search to find the correct position to insert the key.
+    while (left <= right) {
+      mid <- left + (right - left) %/% 2
+
+      if (key < arr[mid]) {
+        right <- mid - 1
+      } else {
+        left <- mid + 1
+      }
+    }
+
+    # Shift elements to the right to make space for the key.
+    for (j in i: (left + 1)) {
+      arr[j] <- arr[j - 1]
+    }
+
+    # Insert the key into its correct position.
+    arr[left] <- key
+  }
+
+  # Return the sorted vector.
+  return(arr)
+}
+
+# Example usage:
+elements_vec <- c(64, 34, 25, 12, 22, 11, 90)
+sorted_vec <- binary_insertion_sort(elements_vec)
+print(sorted_vec)