713138. Maximum Value
Maximum Value
Slug: maximum-value--170645 Difficulty: Medium Id: 713138 Topic Tags: DFS, Tree, implementation, Data Structures, Algorithms Company Tags: Amazon
Summary
The problem is about finding the maximum value in a tree data structure. The given tree is represented as an adjacency list, where each node has a unique value. The goal is to find the maximum value in the tree.
Detailed Explanation
To solve this problem, we can use Depth-First Search (DFS) algorithm. We will start from the root of the tree and recursively explore all its child nodes until we reach a leaf node or the end of the traversal. At each step, we keep track of the maximum value seen so far.
Here is a step-by-step breakdown of the solution:
- Start from the root node of the tree.
- Initialize a variable
max_valueto store the maximum value seen so far. - Traverse the tree using DFS:
- For each node, check if it's a leaf node or not.
- If it's a leaf node, compare its value with
max_value. Updatemax_valueif the current node's value is greater. - If it's not a leaf node, recursively traverse its child nodes and update
max_valueaccordingly.
- Return the maximum value found in the tree.
Time complexity: O(N), where N is the number of nodes in the tree. This is because we visit each node exactly once.
Space complexity: O(H), where H is the height of the tree. This is because we need to store the recursive call stack, which can go up to the height of the tree.
Optimized Solutions
Java
public class MaximumValue {
public static int findMaxValue(int[][] tree) {
int max_value = Integer.MIN_VALUE;
dfs(tree, 0, max_value);
return max_value;
}
private static void dfs(int[][] tree, int node, int max_value) {
if (tree[node] == null) {
// Leaf node
max_value = Math.max(max_value, tree[node - 1]);
} else {
for (int child : tree[node]) {
dfs(tree, child, max_value);
}
}
}
}