[LeetCode] 1600. Throne Inheritance
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 tocurOrder
to get["king", "Alice"]
. - Calling
Successor(Alice, curOrder)
will return Jack, so we append tocurOrder
to get["king", "Alice", "Jack"]
. - Calling
Successor(Jack, curOrder)
will return Bob, so we append tocurOrder
to get["king", "Alice", "Jack", "Bob"]
. - Calling
Successor(Bob, curOrder)
will returnnull
. 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 theThroneInheritance
class. The name of the king is given as part of the constructor.void birth(string parentName, string childName)
Indicates thatparentName
gave birth tochildName
.void death(string name)
Indicates the death ofname
. The death of the person doesn't affect theSuccessor
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
, andname
consist of lowercase English letters only.- All arguments
childName
andkingName
are distinct. - All
name
arguments ofdeath
will be passed to either the constructor or aschildName
tobirth
first. - For each call to
birth(parentName, childName)
, it is guaranteed thatparentName
is alive. - At most
105
calls will be made tobirth
anddeath
. - At most
10
calls will be made togetInheritanceOrder
.
皇位继承顺序。
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。
Successor(x, curOrder):
如果 x 没有孩子或者所有 x 的孩子都在 curOrder 中:
如果 x 是国王,那么返回 null
否则,返回 Successor(x 的父亲, curOrder)
否则,返回 x 不在 curOrder 中最年长的孩子
比方说,假设王国由国王,他的孩子 Alice 和 Bob (Alice 比 Bob 年长)和 Alice 的孩子 Jack 组成。一开始, curOrder 为 ["king"].
调用 Successor(king, curOrder) ,返回 Alice ,所以我们将 Alice 放入 curOrder 中,得到 ["king", "Alice"] 。
调用 Successor(Alice, curOrder) ,返回 Jack ,所以我们将 Jack 放入 curOrder 中,得到 ["king", "Alice", "Jack"] 。
调用 Successor(Jack, curOrder) ,返回 Bob ,所以我们将 Bob 放入 curOrder 中,得到 ["king", "Alice", "Jack", "Bob"] 。
调用 Successor(Bob, curOrder) ,返回 null 。最终得到继承顺序为 ["king", "Alice", "Jack", "Bob"] 。
通过以上的函数,我们总是能得到一个唯一的继承顺序。请你实现 ThroneInheritance 类:
ThroneInheritance(string kingName) 初始化一个 ThroneInheritance 类的对象。国王的名字作为构造函数的参数传入。
void birth(string parentName, string childName) 表示 parentName 新拥有了一个名为 childName 的孩子。
void death(string name) 表示名为 name 的人死亡。一个人的死亡不会影响 Successor 函数,也不会影响当前的继承顺序。你可以只将这个人标记为死亡状态。
string[] getInheritanceOrder() 返回 除去 死亡人员的当前继承顺序列表。来源:力扣(LeetCode)
链接:https://leetcode-cn.com/problems/throne-inheritance
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这是一道关于树的设计题。我们需要一个hashmap记录每个人和他的所有第一继承人;一个hashset记录已经去世的人。
初始化的时候,把国王放入hashmap,并为他创建一个list记录他的继承人。
如果有人出生,则在hashmap里去找他的parent,把child加入parent背后的list里。
如果有人去世,把这个人的名字加入hashset。
getInheritanceOrder返回继承顺序的list,则是用DFS递归去hashmap里看,记得忽略已经去世的人。
时间O(n)
空间O(n)
Java实现
1 class ThroneInheritance { 2 // 记录每个人和他的后继 3 HashMap<String, List<String>> map; 4 // 记录死亡的人 5 Set<String> set; 6 String king; 7 8 public ThroneInheritance(String kingName) { 9 map = new HashMap<>(); 10 set = new HashSet<>(); 11 map.putIfAbsent(kingName, new ArrayList<>()); 12 king = kingName; 13 } 14 15 public void birth(String parentName, String childName) { 16 map.get(parentName).add(childName); 17 map.putIfAbsent(childName, new ArrayList<>()); 18 } 19 20 public void death(String name) { 21 set.add(name); 22 } 23 24 public List<String> getInheritanceOrder() { 25 List<String> res = new ArrayList<>(); 26 helper(king, res); 27 return res; 28 } 29 30 private void helper(String root, List<String> res) { 31 if (!set.contains(root)) { 32 res.add(root); 33 } 34 for (String child : map.get(root)) { 35 helper(child, res); 36 } 37 } 38 } 39 40 /** 41 * Your ThroneInheritance object will be instantiated and called as such: 42 * ThroneInheritance obj = new ThroneInheritance(kingName); 43 * obj.birth(parentName,childName); 44 * obj.death(name); 45 * List<String> param_3 = obj.getInheritanceOrder(); 46 */