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+# Intro sort in R:
+
+# IntroSort is a hybrid sorting algorithm that starts with Quick Sort,
+# switches to Heap Sort when recursion depth grows too large, and uses
+# Insertion Sort for small partitions. This provides robust O(n log n)
+# worst-case performance with excellent average-case behavior.
+
+intro.sort <- function(elements.vec) {
+  n <- length(elements.vec)
+  if (n <= 1) return(elements.vec)
+
+  SIZE_THRESHOLD <- 16
+  # Depth limit: 2 * floor(log2(n)) similar to the canonical definition
+  max.depth <- floor(2 * log(n, base = 2))
+
+  insertion.sort.range <- function(arr, low, high) {
+    if (low >= high) return(arr)
+    if ((low + 1) <= high) {
+      for (i in (low + 1):high) {
+        key <- arr[i]
+        j <- i - 1
+        while (j >= low && arr[j] > key) {
+          arr[j + 1] <- arr[j]
+          j <- j - 1
+        }
+        arr[j + 1] <- key
+      }
+    }
+    return(arr)
+  }
+
+  heap.sort.range <- function(arr, low, high) {
+    n <- high - low + 1
+    if (n <= 1) return(arr)
+
+    heapify <- function(a, heap.size, i, offset) {
+      # 0-based heap indices mapped into 'a' via 'offset'
+      repeat {
+        largest <- i
+        left <- 2 * i + 1
+        right <- 2 * i + 2
+
+        if (left < heap.size && a[offset + left] > a[offset + largest]) {
+          largest <- left
+        }
+        if (right < heap.size && a[offset + right] > a[offset + largest]) {
+          largest <- right
+        }
+
+        if (largest != i) {
+          tmp <- a[offset + i]
+          a[offset + i] <- a[offset + largest]
+          a[offset + largest] <- tmp
+          i <- largest
+        } else {
+          break
+        }
+      }
+      return(a)
+    }
+
+    # Build max heap
+    if ((floor(n / 2) - 1) >= 0) {
+      for (i in seq(floor(n / 2) - 1, 0, by = -1)) {
+        arr <- heapify(arr, n, i, low)
+      }
+    }
+
+    # Extract elements from heap
+    for (i in seq(n - 1, 1, by = -1)) {
+      tmp <- arr[low]
+      arr[low] <- arr[low + i]
+      arr[low + i] <- tmp
+      arr <- heapify(arr, i, 0, low)
+    }
+    return(arr)
+  }
+
+  partition.range <- function(arr, low, high) {
+    pivot <- arr[high]
+    i <- low - 1
+    if (low <= (high - 1)) {
+      for (j in low:(high - 1)) {
+        if (arr[j] <= pivot) {
+          i <- i + 1
+          tmp <- arr[i]
+          arr[i] <- arr[j]
+          arr[j] <- tmp
+        }
+      }
+    }
+    tmp <- arr[i + 1]
+    arr[i + 1] <- arr[high]
+    arr[high] <- tmp
+    return(list(arr = arr, p = i + 1))
+  }
+
+  util <- function(arr, low, high, depth.limit) {
+    if (low >= high) return(arr)
+    size <- high - low + 1
+    if (size <= SIZE_THRESHOLD) {
+      return(insertion.sort.range(arr, low, high))
+    }
+    if (depth.limit == 0) {
+      return(heap.sort.range(arr, low, high))
+    }
+    pr <- partition.range(arr, low, high)
+    arr <- pr$arr
+    p <- pr$p
+    arr <- util(arr, low, p - 1, depth.limit - 1)
+    arr <- util(arr, p + 1, high, depth.limit - 1)
+    return(arr)
+  }
+
+  elements.vec <- util(elements.vec, 1, n, max.depth)
+  return(elements.vec)
+}
+
+# Example:
+# intro.sort(c(10, 7, 8, 9, 1, 5, 3, 12))
+# [1] 1 3 5 7 8 9 10 12