#### Approach Framework

Explanation

As we need to reach every node in the given tree, we will have to traverse the tree, either with a depth-first search, or with a breadth-first search.

The main idea in this question is to give each node a position value. If we go down the left neighbor, then position -> position * 2; and if we go down the right neighbor, then position -> position * 2 + 1. This makes it so that when we look at the position values L and R of two nodes with the same depth, the width will be R - L + 1.

#### Approach #1: Breadth-First Search [Accepted]

Intuition and Algorithm

Traverse each node in breadth-first order, keeping track of that node's position. For each depth, the first node reached is the left-most, while the last node reached is the right-most.

Complexity Analysis

• Time Complexity: where is the number of nodes in the input tree. We traverse every node.

• Space Complexity: , the size of our queue.

#### Approach #2: Depth-First Search [Accepted]

Intuition and Algorithm

Traverse each node in depth-first order, keeping track of that node's position. For each depth, the position of the first node reached of that depth will be kept in left[depth].

Then, for each node, a candidate width is pos - left[depth] + 1. We take the maximum of the candidate answers.

Complexity Analysis

• Time Complexity: where is the number of nodes in the input tree. We traverse every node.

• Space Complexity: , the size of the implicit call stack in our DFS.

Analysis written by: @awice.