Add Tim Sort (#125)

Author: whyvineet

sorting_algorithms/tim_sort.r

@@ -0,0 +1,90 @@
+# Insertion Sort: Sort small subarrays (runs)
+insertion_sort <- function(arr, left, right) {
+  for (i in (left + 1):right) {
+    key <- arr[i]
+    j <- i - 1
+    while (j >= left && arr[j] > key) {
+      arr[j + 1] <- arr[j]
+      j <- j - 1
+    }
+    arr[j + 1] <- key
+  }
+  return(arr)
+}
+
+# Merge two sorted subarrays
+merge <- function(arr, left, mid, right) {
+  n1 <- mid - left + 1
+  n2 <- right - mid
+
+  left_part <- arr[left:(mid)]
+  right_part <- arr[(mid + 1):right]
+
+  i <- 1
+  j <- 1
+  k <- left
+
+  # Merge left_part and right_part into arr
+  while (i <= n1 && j <= n2) {
+    if (left_part[i] <= right_part[j]) {
+      arr[k] <- left_part[i]
+      i <- i + 1
+    } else {
+      arr[k] <- right_part[j]
+      j <- j + 1
+    }
+    k <- k + 1
+  }
+
+  # Copy remaining elements of left_part, if any
+  while (i <= n1) {
+    arr[k] <- left_part[i]
+    i <- i + 1
+    k <- k + 1
+  }
+
+  # Copy remaining elements of right_part, if any
+  while (j <= n2) {
+    arr[k] <- right_part[j]
+    j <- j + 1
+    k <- k + 1
+  }
+
+  return(arr)
+}
+
+# TimSort function
+tim_sort <- function(arr) {
+  n <- length(arr)
+  min_run <- 32
+  
+  # Sort individual subarrays of size min_run using insertion sort
+  for (start in seq(1, n, by = min_run)) {
+    end <- min(start + min_run - 1, n)
+    arr <- insertion_sort(arr, start, end)
+  }
+  
+  # Merge sorted subarrays
+  size <- min_run
+  while (size < n) {
+    for (left in seq(1, n, by = 2 * size)) {
+      mid <- min(left + size - 1, n)
+      right <- min(left + 2 * size - 1, n)
+      if (mid < right) {
+        arr <- merge(arr, left, mid, right)
+      }
+    }
+    size <- 2 * size
+  }
+  
+  return(arr)
+}
+
+# Example usage:
+# -------------------
+# Input: c(5, 21, 7, 23, 19, 11, 16, 13)
+# Expected Output: c(5, 7, 11, 13, 16, 19, 21, 23)
+
+elements_vec <- c(5, 21, 7, 23, 19, 11, 16, 13)
+tim_sorted_vec <- tim_sort(elements_vec)
+print(tim_sorted_vec)