How would I find the time complexity of the following recursive algorithm?

Question

Assuming that r is the root of a tree (may be non-binary), c is a child of r, and each node contains an integer.

Algorithm findMax(r)
if r = null return null
int maxValue = r.value
if r.isLeaf return maxValue;
for each child c of r do{
    if findMax(c) > maxValue
        maxValue = findMax(c)
}
return maxValue

What are your own thoughts on this? Also, did you mean maxValue = findMax(c) and if findMax(c) > maxValue? — meowgoesthedog
– meowgoesthedog, Commented Oct 22, 2018 at 16:24
I think that it would be O(n^2) however the part I am unsure of is that the number of children for each node could be different. — Ben Tilden
– Ben Tilden, Commented Oct 22, 2018 at 16:26

dWinder · Accepted Answer · 2018-10-22 17:12:54Z

1

Currently it does have O(n) complexity when consider n to be number of node in the tree.

For each child-node of the root you call recursive function to all sub-tree root in c. So basically, you preform DFS on this graph which make in O(V+E) -> in your case, when the graph is a tree, it equel to O(V).

Notice, that you call recursive function of findMax in the if-statement - if it true you calculate it again - which increase complexity to O(2*n). Calculate the findMax function once, assign its result to local var and check and update the maxValue with it will reduce complexity to O(n).

answered Oct 22, 2018 at 17:12

dWinder

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