Question

Compatible Warehouses HackerLand has a network of warehouses which can be represented as an undirected rooted weighted tree consisting of warehouse_nodes number of nodes, rooted at warehouse 1. There are (warehouse_nodes - 1) roads connecting they and warehouse_weight[i] denotes the distance covered by the ith road. Moreover, each warehouse has a value assigned to it denoted by the array val. A pair of warehouses (u, v) is said to be compatible if it satisfies the following conditions: • u is an ancestor of vin the tree network. distance(u, v) ≤ val[v], where distance(u, v) represents the sum of distances of roads that belong to the simple path connecting u and v. Expert Answer

Answer 1

The compatible warehouses problem in HackerLand involves finding pairs of warehouses where the path distance is within assigned warehouse values, highlighting the efficiency and transportation capability of the warehouse network.

Step-by-step explanation:

Understanding Compatible Warehouses in HackerLand

The problem at hand pertains to a network of warehouses represented as an undirected rooted weighted tree. In this scenario, a pair of warehouses is deemed compatible if one warehouse is an ancestor of the other in the tree network, and the sum of the distances along the path connecting them is less than or equal to the value assigned to the descendant warehouse. This compatibility check foregrounds important attributes such as efficiency and transportation capability, implying a preference for warehouse networks that maintain these qualities.

When analyzing the re-normalized weightings given by students, it's revealed that attributes like abundance, efficiency, and transportation capability are given higher importance, while attributes like the backyard criterion, acceptance, and the ability to produce heat are given lower significance. This prioritization hints at a collective student perspective that values functionalities that enhance performance and preserve logistic viability over individualistic or less directly functional features.

Answer 2

To know the number of compatible pairs of warehouses in the given tree network, follow these steps:

1. Preprocessing: Calculate the shortest path distances from root (warehouse 1) to all other nodes using Dijkstra's algorithm or Floyd-Warshall algorithm.

2. Recursively traverse the tree from the root node. For each node u, keep track of the total number of compatible pairs (count).

a. Check Children: Recursively visit each child node v of u.

• Compatibility Check: If u is an ancestor of v and distance(u, v) ≤ val[v], then the pair (u, v) is compatible. Increment count by 1.

b. Add Ancestors: Add u to the list of ancestors for all its children. This will ensure that compatible pairs involving u are counted when traversing its descendants.

3. Lastly, Post-processing: After traversing the entire tree, the total count will represent the number of compatible pairs of warehouses.

See text structure:

Compatible Warehouses:

HackerLand has a network of warehouses which can be represented as an undirected rooted weighted tree consisting of warehouse_nodes number of nodes, rooted at warehouse 1. There are (warehouse_nodes - 1) roads connecting them, and warehouse_weight[i] denotes the distance covered by the ith road. Moreover, each warehouse has a value assigned to it denoted by the array val.

A pair of warehouses (u, v) is said to be compatible if it satisfies the following conditions:

• u is an ancestor of v in the tree network.

• distance(u, v) ≤ val[v], where distance(u, v) represents the sum of distances of roads that belong to the simple path connecting u and v.