Farmer John is decorating his Spring Equinox Tree . It can be modeled as a rooted mathematical tree with N (1
Farmer John is decorating his Spring Equinox Tree (like a Christmas tree but popular about three months later). It can be modeled as a rooted mathematical tree with N (1 <= N <= 100,000) elements, labeled 1...N, with element 1 as the root of the tree. Each tree element e > 1 has a parent, P_e P e (1 <= P_e P e <= N). Element 1 has no parent (denoted '-1' in the input), of course, because it is the root of the tree. Each element i has a corresponding subtree (potentially of size 1) rooted there. FJ would like to make sure that the subtree corresponding to element i has a total of at least C_i C i (0 <= C_i C i <= 10,000,000) ornaments scattered among its members. He would also like to minimize the total amount of time it takes him to place all the ornaments (it takes time K* T_i T i to place K ornaments at element i (1 <= T_i T i <= 100)). Help FJ determine the minimum amount of time it takes to place ornaments that satisfy the constraints. Note that this answer might not fit into a 32-bit integer, but it will fit into a signed 64-bit integer. For example, consider the tree below where nodes located higher on the display are parents of connected lower nodes (1 is the root): 1 | 2 | 5 / 4 3 Suppose that FJ has the following subtree constraints: Minimum ornaments the subtree requires | Time to install an ornament Subtree | | root | C_i | T_i --------+--------+------- 1 | 9 | 3 2 | 2 | 2 3 | 3 | 2 4 | 1 | 4 5 | 3 | 3 Then FJ can place all the ornaments as shown below, for a total cost of 20: 1 [0/9(0)] legend: element# [ornaments here/ | total ornaments in subtree(node install time)] 2 [3/9(6)] | 5 [0/6(0)] / [1/1(4)] 4 3 [5/5(10)]
