add insertion_sort and bulk of timsort

utils.sh

@@ -1,5 +1,79 @@
 #!/usr/bin/env bash
 
+_int.insertion_sort() {
+  local -n _int_isort_arr="$1"
+  local left="$2" right="$3"
+
+  for (( i=left+1; i<=right; i+=1 )) do
+    local value="${_int_isort_arr["$i"]}" j=$((i-1))
+    while (( j>=left && "${_int_isort_arr["$j"]}" > value )); do
+      _int_isort_arr[$((j+1))]="${_int_isort_arr["$j"]}"
+      ((j-=1))
+    done
+    _int_isort_arr[$((j+1))]="$value"
+  done
+}
+
+_int.merge() {
+  local -n _int_merge_arr="$1"
+  local l="$2" m="$3" r="$4" left=() right=()
+  local left_len=$((m-l+1)) right_len=$((r-m))
+
+  for (( i=0; i < left_len; i+=1 )); do
+    left[$i]="${_int_merge_arr[$((l+i))]}"
+  done
+
+  for (( i=0; i < right_len; i+=1 )); do
+    right[$i]="${_int_merge_arr[$((m+1+i))]}"
+  done
+
+  local i=0 j=0 k="$l"
+
+  while (( i < left_len && j < right_len )); do
+    if (( left[i] <= right[i] )); then
+      _int_merge_arr[$k]="${left[$i]}"
+      ((i+=1))
+    else
+      _int_merge_arr[$k]="${right[$j]}"
+      ((j+=1))
+    fi
+    ((k+=1))
+  done
+
+  while (( i < left_len )); do
+    _int_merge_arr[$k]="${left[$i]}"
+    ((k+=1))
+    ((i+=1))
+  done
+
+  while (( j < right_len )); do
+    _int_merge_arr[$k]="${right[$j]}"
+    ((k+=1))
+    ((j+=1))
+  done
+}
+
+utils.timsort() {
+  local -n _utils_timsort_arr="$1"
+  local len="${#_utils_timsort_arr[@]}"
+
+  for (( i=0; i < len; i+=32 )); do
+    _int.insertion_sort _utils_timsort_arr "$i" "$(utils.min2 "$((i+32-1))" "$((len-1))")"
+    for (( size=32; size < len; size=2*size )); do
+      for (( left=0; left < len; left+=2*size )); do
+        local mid="$((left+size-1))"
+        local right="$(utils.min2 "$((left+2*size-1))" "$((len-1))")"
+        (( mid < right )) && _int.merge _utils_timsort_arr "$left" "$mid" "$right"
+      done
+    done
+  done
+}
+
+utils.insertion_sort() {
+  local -n _utils_isort_arr="$1"
+  _int.insertion_sort _utils_isort_arr 0 "$((${#_utils_isort_arr[@]}-1))"
+}
+
 utils.qsort() {
   read -ra arr <<< "$@"
   ((${#arr[@]} == 0)) && echo && return
@@ -27,3 +101,13 @@ utils.sum() {
   for i in "${input[@]}"; do ((result+=i)); done
   echo "$result"
 }
+
+utils.min() {
+  read -ra input <<< "$@"
+  echo "${input[0]}"
+}
+
+utils.min2() {
+  (( $1 < $2 )) && echo "$1" && return
+  echo "$2"
+}