Package g2601_2700.s2673_make_costs_of_paths_equal_in_a_binary_tree

Class Solution

java.lang.Object
g2601_2700.s2673_make_costs_of_paths_equal_in_a_binary_tree.Solution
public class Solution extends java.lang.Object
2673 - Make Costs of Paths Equal in a Binary Tree.

Medium

You are given an integer n representing the number of nodes in a perfect binary tree consisting of nodes numbered from 1 to n. The root of the tree is node 1 and each node i in the tree has two children where the left child is the node 2 * i and the right child is 2 * i + 1.

Each node in the tree also has a cost represented by a given 0-indexed integer array cost of size n where cost[i] is the cost of node i + 1. You are allowed to increment the cost of any node by 1 any number of times.

Return the minimum number of increments you need to make the cost of paths from the root to each leaf node equal.

Note:

  • A perfect binary tree is a tree where each node, except the leaf nodes, has exactly 2 children.
  • The cost of a path is the sum of costs of nodes in the path.

Example 1:

Input: n = 7, cost = [1,5,2,2,3,3,1]

Output: 6

Explanation: We can do the following increments:

  • Increase the cost of node 4 one time.
  • Increase the cost of node 3 three times.
  • Increase the cost of node 7 two times.

Each path from the root to a leaf will have a total cost of 9.

The total increments we did is 1 + 3 + 2 = 6. It can be shown that this is the minimum answer we can achieve.

Example 2:

Input: n = 3, cost = [5,3,3]

Output: 0

Explanation: The two paths already have equal total costs, so no increments are needed.

Constraints:

  • 3 <= n <= 105
  • n + 1 is a power of 2
  • cost.length == n
  • 1 <= cost[i] <= 104

  • Constructor Summary

    Constructors
    Constructor
    Description
    Solution()
     

  • Method Summary

    Modifier and Type
    Method
    Description
    int
    minIncrements(int n, int[] cost)
     

    Methods inherited from class java.lang.Object

    clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

  • Constructor Details

    • Solution

      public Solution()

  • Method Details

    • minIncrements

      public int minIncrements(int n, int[] cost)