# Time:  O(n)
# Space: O(h)

# iterative dfs
class Solution(object):
    def mostProfitablePath(self, edges, bob, amount):
        """
        :type edges: List[List[int]]
        :type bob: int
        :type amount: List[int]
        :rtype: int
        """
        def iter_dfs():
            lookup = [[float("-inf"), float("inf")] for _ in xrange(len(adj))]
            stk = [(1, (0, -1, 0))]
            while stk:
                step, (u, p, ah) = stk.pop()
                if step == 1:
                    stk.append((2, (u, p, ah)))
                    for v in adj[u]:
                        if v == p:
                            continue
                        stk.append((1, (v, u, ah+1)))
                elif step == 2:
                    if len(adj[u])+(u == 0) == 1:
                        lookup[u][0] = 0
                    if u == bob:
                        lookup[u][1] = 0
                    for v in adj[u]:
                        if v == p:
                            continue
                        lookup[u][0] = max(lookup[u][0], lookup[v][0])
                        lookup[u][1] = min(lookup[u][1], lookup[v][1])
                    if ah == lookup[u][1]:
                        lookup[u][0] += amount[u]//2
                    elif ah < lookup[u][1]:
                        lookup[u][0] += amount[u]
                    lookup[u][1] += 1
            return lookup[0][0]

        adj = [[] for _ in xrange(len(edges)+1)]
        lookup = [False]*len(adj)
        for u, v in edges:
            adj[u].append(v)
            adj[v].append(u)
        return iter_dfs()


# Time:  O(n)
# Space: O(h)
# dfs
class Solution2(object):
    def mostProfitablePath(self, edges, bob, amount):
        """
        :type edges: List[List[int]]
        :type bob: int
        :type amount: List[int]
        :rtype: int
        """
        def dfs(u, ah):
            lookup[u] = True
            result = 0 if len(adj[u])+(u == 0) == 1 else float("-inf")
            bh = 0 if u == bob else float("inf")
            for v in adj[u]:
                if lookup[v]:
                    continue
                r, h = dfs(v, ah+1)
                result = max(result, r)
                bh = min(bh, h)
            if ah == bh:
                result += amount[u]//2
            elif ah < bh:
                result += amount[u]
            return result, bh+1

        adj = [[] for _ in xrange(len(edges)+1)]
        lookup = [False]*len(adj)
        for u, v in edges:
            adj[u].append(v)
            adj[v].append(u)
        return dfs(0, 0)[0]