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13. Path Sum

easyAsked at Electronic Arts

Determine if a binary tree has a root-to-leaf path that sums to a target value, a pattern used in EA game scene-graph traversals.

By Alex Chen, Founder, InterviewChamp.AI · Last verified

Problem

Given the root of a binary tree and an integer targetSum, return true if the tree has a root-to-leaf path such that adding up all the values along the path equals targetSum. A leaf is a node with no children.

Constraints

  • Number of nodes in the tree is in the range [0, 5000]
  • -1000 <= Node.val <= 1000
  • -1000 <= targetSum <= 1000

Examples

Example 1

Input
root = [5,4,8,11,null,13,4,7,2,null,null,null,1], targetSum = 22
Output
true

Example 2

Input
root = [1,2,3], targetSum = 5
Output
false

Approaches

1. Brute force DFS

Recursively explore every root-to-leaf path and check if any sums to target.

Time
O(n)
Space
O(h)
function hasPathSum(root, targetSum) {
  if (!root) return false;
  if (!root.left && !root.right) return root.val === targetSum;
  return hasPathSum(root.left, targetSum - root.val) ||
         hasPathSum(root.right, targetSum - root.val);
}

Tradeoff:

2. Iterative DFS with stack

Use an explicit stack storing [node, remainingSum] pairs to avoid recursion overhead. This mirrors how EA's scene-graph walkers handle deep tree traversals in engine code.

Time
O(n)
Space
O(h)
function hasPathSum(root, targetSum) {
  if (!root) return false;
  const stack = [[root, targetSum]];
  while (stack.length) {
    const [node, rem] = stack.pop();
    if (!node.left && !node.right && rem === node.val) return true;
    if (node.right) stack.push([node.right, rem - node.val]);
    if (node.left) stack.push([node.left, rem - node.val]);
  }
  return false;
}

Tradeoff:

Electronic Arts-specific tips

EA interviews cover game development data structures, pathfinding (A*, BFS on grids), spatial algorithms, and simulation problems. Grid/matrix manipulation and BFS on 2D arrays are very common.

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