Trees

BST Search

Search a binary search tree for one present and one absent value.

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.

search path A comparison chooses one subtree at each step, so whole branches are skipped.

Visual walkthrough

A BST search follows one comparison path. The same pinned tree shows a found path for 5 and a missing path for 8.

Step 1 - Find 5

Search 5 takes right from 4, then left from 6, then matches 5.

Present search path: 4 -> 6 -> 5.4#126#2135match7

Step 2 - Miss 8

Search 8 takes right from 4, right from 6, right from 7, then reaches null.

Absent search path: 4 -> 6 -> 7 -> null.4#126#21357#3nullnot found

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
search() { local id=4 target=$1; while [[ "$id" != "0" ]]; do if (( target == val[$id] )); then return 0; elif (( target < val[$id] )); then id=${left[$id]}; else id=${right[$id]}; fi; done; return 1; }
search 5 && echo "5 found" || echo "5 not found"
search 8 && echo "8 found" || echo "8 not found"

Complexity

  • Time: O(h) per search
  • Space: O(1) iterative

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.