Replace BST nodes with the sum of nodes greater than the node. O(n) https://jsfiddle.net/Lr3mh8op/1/

1-sum.js

/* Given a binary tree, replace all node values with the sum of all node values greater than or equal to its own.

Note, in a binary search tree, values to the left are less than the parent, while values to the right are greater than the parent.
*/

const sum = node => {
  // Returns the sum of all values in the tree.
  return !node ? 0 : node.value + sum(node.left) + sum(node.right);
};

const update = (node, total) => {
  if (node) {
    // Calculate the total for the left.
    const leftSum = sum(node.left);
    
    // Update the node value to be the total right tree minus its own value.
    node.value = total - leftSum - node.value;
    
    // Update the rest of the tree.
    update(node.left, total);
    update(node.right, node.value);
  }
  
  return node;
};

2-client.js

const tree1 = {
  value: 3,
  left: {
    value: 2,
  },
  right: {
    value: 5,
  }
};

const tree2 = {
  value: 3,
  left: {
    value: 2,
    left: {
      value: 1,
    },
    right: {
      value: 3,
    }
  },
  right: {
    value: 5,
    left: {
      value: 4,
    },
    right: {
      value: 10,
    }
  }
};

$(function() {
  update(tree1, sum(tree1));
  $('#output').append(JSON.stringify(tree1, null, 2));
  
  $('#output').append('\n\n------------\n\n');
  
  update(tree2, sum(tree2));
  $('#output').append(JSON.stringify(tree2, null, 2));
});

3-output.txt

{
  "value": 5,
  "left": {
    "value": 8
  },
  "right": {
    "value": 0
  }
}

------------

{
  "value": 19,
  "left": {
    "value": 25,
    "left": {
      "value": 27
    },
    "right": {
      "value": 22
    }
  },
  "right": {
    "value": 10,
    "left": {
      "value": 15
    },
    "right": {
      "value": 0
    }
  }
}