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:
Example 1:
Input: n = 7, cost = [1,5,2,2,3,3,1]
Output: 6
Explanation: We can do the following increments:
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
class Solution {
fun minIncrements(n: Int, cost: IntArray): Int {
val last = n / 2 - 1
var res = 0
for (i in last downTo 0) {
var abs = cost[2 * i + 1] - cost[2 * i + 2]
if (abs < 0) abs *= -1
cost[i] += maxOf(cost[2 * i + 1], cost[2 * i + 2])
res += abs
}
return res
}
}