2673. Make Costs of Paths Equal in a Binary Tree
Explanation:
To make the cost of paths from the root to each leaf node equal, we need to balance the costs in the tree. We can achieve this by iteratively adjusting the costs of parent nodes based on the costs of their children. The idea is to propagate the excess costs from children to their parents such that the total cost of each path from the root to a leaf becomes equal. We will perform a depth-first traversal of the tree while keeping track of the excess cost at each node.
Algorithm:
- Perform a depth-first traversal of the tree from the root.
- Calculate the excess cost for each child node by subtracting the average cost of its children from its own cost.
- Propagate the excess cost to the parent node by adding the excess cost of its children.
- Recursively repeat steps 2 and 3 for each child node.
Time Complexity: The time complexity of this algorithm is O(n) where n is the number of nodes in the binary tree.
Space Complexity: The space complexity of this algorithm is O(n) for the recursive stack.
:
class Solution {
public int minCost(int n, int[] cost) {
return dfs(0, 0, cost);
}
private int dfs(int idx, int depth, int[] cost) {
if (idx >= cost.length) return 0;
int left = dfs(2 * idx + 1, depth + 1, cost);
int right = dfs(2 * idx + 2, depth + 1, cost);
int totalCost = left + right + cost[idx];
if (depth > 0) {
int excess = totalCost - cost[idx];
cost[idx] += excess;
return excess;
}
return totalCost;
}
}Code Editor (Testing phase)
Improve Your Solution
Use the editor below to refine the provided solution. Select a programming language and try the following:
- Add import statement if required.
- Optimize the code for better time or space complexity.
- Add test cases to validate edge cases and common scenarios.
- Handle error conditions or invalid inputs gracefully.
- Experiment with alternative approaches to deepen your understanding.
Click "Run Code" to execute your solution and view the output. If errors occur, check the line numbers and debug accordingly. Resize the editor by dragging its bottom edge.