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# Min Height BST

![](/files/hJCqoEiFxaVC7B45PrSd)

* N, h

```jsx
function minHeightBst(arr) {
  return buildBst(arr, 0, arr.length - 1);
}

function buildBst(arr, s, e) {
  if (s > e) {
    return null;
  }
  
  const m = s + Math.floor((e - s) / 2);
  
  const bst = new BST(arr[m]);
  bst.left = buildBst(arr, s, m - 1);
  bst.right = buildBst(arr, m + 1, e);
  
  return bst;
}

class BST {
  constructor(value) {
    this.value = value;
    this.left = null;
    this.right = null;
  }

  insert(value) {
    if (value < this.value) {
      if (this.left === null) {
        this.left = new BST(value);
      } else {
        this.left.insert(value);
      }
    } else {
      if (this.right === null) {
        this.right = new BST(value);
      } else {
        this.right.insert(value);
      }
    }
  }
}

// Do not edit the line below.
exports.minHeightBst = minHeightBst;
```