1600. Throne Inheritance

题目

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.

题目大意

一个王国里住着国王、他的孩子们、他的孙子们等等。每一个时间点，这个家庭里有人出生也有人死亡。这个王国有一个明确规定的皇位继承顺序，第一继承人总是国王自己。我们定义递归函数 Successor(x, curOrder) ，给定一个人 x 和当前的继承顺序，该函数返回 x 的下一继承人。

解题思路

这道题思路不难。先将国王每个孩子按照顺序存在一个 map 中，然后每个国王的孩子还存在父子关系，同理也按顺序存在 map 中。执行 GetInheritanceOrder() 函数时，将国王的孩子按顺序遍历，如果每个孩子还有孩子，递归遍历到底。如果把继承关系看成一棵树，此题便是多叉树的先根遍历的问题。

代码

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();
 */

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