1600. Throne Inheritance #

Problem #

A kingdom consists of a king, his children, his grandchildren, and so on. Every once in a while, someone in the family dies or a child is born.

The kingdom has a well-defined order of inheritance that consists of the king as the first member. Let’s define the recursive function Successor(x, curOrder), which given a person x and the inheritance order so far, returns who should be the next person after x in the order of inheritance.

Successor(x, curOrder):
    if x has no children or all of x's children are in curOrder:
        if x is the king return null
        else return Successor(x's parent, curOrder)
    else return x's oldest child who's not in curOrder

For example, assume we have a kingdom that consists of the king, his children Alice and Bob (Alice is older than Bob), and finally Alice’s son Jack.

In the beginning, curOrder will be ["king"].
Calling Successor(king, curOrder) will return Alice, so we append to curOrder to get ["king", "Alice"].
Calling Successor(Alice, curOrder) will return Jack, so we append to curOrder to get ["king", "Alice", "Jack"].
Calling Successor(Jack, curOrder) will return Bob, so we append to curOrder to get ["king", "Alice", "Jack", "Bob"].
Calling Successor(Bob, curOrder) will return null. Thus the order of inheritance will be ["king", "Alice", "Jack", "Bob"].

Using the above function, we can always obtain a unique order of inheritance.

Implement the ThroneInheritance class:

ThroneInheritance(string kingName) Initializes an object of the ThroneInheritance class. The name of the king is given as part of the constructor.
void birth(string parentName, string childName) Indicates that parentName gave birth to childName.
void death(string name) Indicates the death of name. The death of the person doesn’t affect the Successor function nor the current inheritance order. You can treat it as just marking the person as dead.
string[] getInheritanceOrder() Returns a list representing the current order of inheritance excluding dead people.

Example 1:

Input
["ThroneInheritance", "birth", "birth", "birth", "birth", "birth", "birth", "getInheritanceOrder", "death", "getInheritanceOrder"]
[["king"], ["king", "andy"], ["king", "bob"], ["king", "catherine"], ["andy", "matthew"], ["bob", "alex"], ["bob", "asha"], [null], ["bob"], [null]]
Output
[null, null, null, null, null, null, null, ["king", "andy", "matthew", "bob", "alex", "asha", "catherine"], null, ["king", "andy", "matthew", "alex", "asha", "catherine"]]

Explanation
ThroneInheritance t= new ThroneInheritance("king"); // order:king
t.birth("king", "andy"); // order: king >andy
t.birth("king", "bob"); // order: king > andy >bob
t.birth("king", "catherine"); // order: king > andy > bob >catherine
t.birth("andy", "matthew"); // order: king > andy >matthew > bob > catherine
t.birth("bob", "alex"); // order: king > andy > matthew > bob >alex > catherine
t.birth("bob", "asha"); // order: king > andy > matthew > bob > alex >asha > catherine
t.getInheritanceOrder(); // return ["king", "andy", "matthew", "bob", "alex", "asha", "catherine"]
t.death("bob"); // order: king > andy > matthew >bob > alex > asha > catherine
t.getInheritanceOrder(); // return ["king", "andy", "matthew", "alex", "asha", "catherine"]

Constraints:

1 <= kingName.length, parentName.length, childName.length, name.length <= 15
kingName, parentName, childName, and name consist of lowercase English letters only.
All arguments childName and kingName are distinct.
All name arguments of death will be passed to either the constructor or as childName to birth first.
For each call to birth(parentName, childName), it is guaranteed that parentName is alive.
At most 105 calls will be made to birth and death.
At most 10 calls will be made to getInheritanceOrder.

Problem Summary #

A kingdom is inhabited by the king, his children, his grandchildren, and so on. At any given time, someone in this family may be born or die. The kingdom has a clearly defined order of succession to the throne, and the first successor is always the king himself. We define the recursive function Successor(x, curOrder) : given a person x and the current inheritance order, the function returns the next successor after x.

Solution Approach #

The idea for this problem is not difficult. First, store each child of the king in order in a map, and then each child of the king also has a parent-child relationship; similarly, store them in order in the map. When executing the GetInheritanceOrder() function, traverse the king’s children in order. If each child also has children, recursively traverse all the way down. If the inheritance relationships are viewed as a tree, this problem is a preorder traversal problem on an n-ary tree.

Code #

package leetcode

type ThroneInheritance struct {
	king  string
	edges map[string][]string
	dead  map[string]bool
}

func Constructor(kingName string) (t ThroneInheritance) {
	return ThroneInheritance{kingName, map[string][]string{}, map[string]bool{}}
}

func (t *ThroneInheritance) Birth(parentName, childName string) {
	t.edges[parentName] = append(t.edges[parentName], childName)
}

func (t *ThroneInheritance) Death(name string) {
	t.dead[name] = true
}

func (t *ThroneInheritance) GetInheritanceOrder() (res []string) {
	var preorder func(string)
	preorder = func(name string) {
		if !t.dead[name] {
			res = append(res, name)
		}
		for _, childName := range t.edges[name] {
			preorder(childName)
		}
	}
	preorder(t.king)
	return
}

/**
 * Your ThroneInheritance object will be instantiated and called as such:
 * obj := Constructor(kingName);
 * obj.Birth(parentName,childName);
 * obj.Death(name);
 * param_3 := obj.GetInheritanceOrder();
 */