Trees

BST Insert

Insert values into a binary search tree by comparing at each node.

Algorithm

The canonical tree is 4(2(1,3),6(5,7)), so this Bash DSA implementation can be compared directly with the rest of the DSA track.

Basic Implementation

basic.sh 
#!/usr/bin/env bash
declare -A val left right
new_node() { local id=$1 value=$2 l=${3:-0} r=${4:-0}; val[$id]=$value; left[$id]=$l; right[$id]=$r; }
render() {
  local id=$1
  if [[ "$id" == "0" || -z "$id" ]]; then printf "_"; return; fi
  if [[ "${left[$id]}" == "0" && "${right[$id]}" == "0" ]]; then printf "%s" "${val[$id]}"; return; fi
  printf "%s(" "${val[$id]}"; render "${left[$id]}"; printf ","; render "${right[$id]}"; printf ")"
}
sample_tree() {
  new_node 1 1; new_node 3 3; new_node 2 2 1 3
  new_node 5 5; new_node 7 7; new_node 6 6 5 7
  new_node 4 4 2 6
}
list_string() {
  local joined=""
  for value in "$@"; do
    [[ -n "$joined" ]] && joined+=", "
    joined+="$value"
  done
  printf '[%s]' "$joined"
}
sample_tree
render 4
echo

Complexity

  • Time: O(h) per insert
  • Space: O(n)

Implementation notes

  • Render tree structure explicitly instead of printing node objects.
  • The replay highlights the node, traversal state, queue, path, or search cursor that changes at each step.
binary search tree Values smaller than a node go left; larger values go right.