1600. Throne Inheritance

Description

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.

Solutions

Solution 2: Explicit-Stack Preorder

Thinking

The given $\textit{Successor}$ walks to the oldest child not yet listed, then backtracks to the parent. Simulating that definition on every query rescans children and becomes quadratic once the number of births reaches $10^5$. The same recurrence is a preorder walk of a multi-way tree: write the person, then visit children in birth order. Death does not reshape the tree; it only omits a name. Recursion along a birth chain uses a call depth equal to the family size and overflows Python once the chain reaches length $1000$. The query therefore uses a stack. A popped person is appended when still alive, and that person’s children are pushed from last to first so the oldest child is popped next.

The inheritance order is a preorder traversal of a multi-way tree. A hash table $g$ stores each person’s children in birth order, and a set $dead$ stores the people who have died.

When calling birth(parentName, childName), append childName to the child list of parentName.
When calling death(name), add name to $dead$.
When calling getInheritanceOrder(), the stack starts with the king. After x is popped, append x when x is not in $dead$, then push the children of x from last to first so birth order is preserved.

In terms of time complexity, both birth and death have a time complexity of $O(1)$, and getInheritanceOrder has a time complexity of $O(n)$. The space complexity is $O(n)$, where $n$ is the number of nodes.

class ThroneInheritance {
    private Map<String, List<String>> g = new HashMap<>();
    private Set<String> dead = new HashSet<>();
    private List<String> ans;
    private String king;

    public ThroneInheritance(String kingName) {
        king = kingName;
    }

    public void birth(String parentName, String childName) {
        g.computeIfAbsent(parentName, k -> new ArrayList<>()).add(childName);
    }

    public void death(String name) {
        dead.add(name);
    }

    public List<String> getInheritanceOrder() {
        ans = new ArrayList<>();
        dfs(king);
        return ans;
    }

    private void dfs(String x) {
        if (!dead.contains(x)) {
            ans.add(x);
        }
        for (String y : g.getOrDefault(x, Collections.emptyList())) {
            dfs(y);
        }
    }
}

/**
 * Your ThroneInheritance object will be instantiated and called as such:
 * ThroneInheritance obj = new ThroneInheritance(kingName);
 * obj.birth(parentName,childName);
 * obj.death(name);
 * List<String> param_3 = obj.getInheritanceOrder();
 */


// Solution 2
class ThroneInheritance {
    private String king;
    private Set<String> dead = new HashSet<>();
    private Map<String, List<String>> g = new HashMap<>();

    public ThroneInheritance(String kingName) {
        king = kingName;
    }

    public void birth(String parentName, String childName) {
        g.computeIfAbsent(parentName, k -> new ArrayList<>()).add(childName);
    }

    public void death(String name) {
        dead.add(name);
    }

    public List<String> getInheritanceOrder() {
        List<String> ans = new ArrayList<>();
        Deque<String> stk = new ArrayDeque<>();
        stk.push(king);
        while (!stk.isEmpty()) {
            String x = stk.pop();
            if (!dead.contains(x)) {
                ans.add(x);
            }
            List<String> children = g.getOrDefault(x, List.of());
            for (int i = children.size() - 1; i >= 0; --i) {
                stk.push(children.get(i));
            }
        }
        return ans;
    }
}

/**
 * Your ThroneInheritance object will be instantiated and called as such:
 * ThroneInheritance obj = new ThroneInheritance(kingName);
 * obj.birth(parentName,childName);
 * obj.death(name);
 * List<String> param_3 = obj.getInheritanceOrder();
 */

class ThroneInheritance {
public:
    unordered_map<string, vector<string>> g;
    unordered_set<string> dead;
    string king;
    vector<string> ans;

    ThroneInheritance(string kingName) {
        king = kingName;
    }

    void birth(string parentName, string childName) {
        g[parentName].push_back(childName);
    }

    void death(string name) {
        dead.insert(name);
    }

    vector<string> getInheritanceOrder() {
        ans.resize(0);
        dfs(king);
        return ans;
    }

    void dfs(string& x) {
        if (!dead.count(x)) {
            ans.push_back(x);
        }
        for (auto& y : g[x]) {
            dfs(y);
        }
    }
};

/**
 * Your ThroneInheritance object will be instantiated and called as such:
 * ThroneInheritance* obj = new ThroneInheritance(kingName);
 * obj->birth(parentName,childName);
 * obj->death(name);
 * vector<string> param_3 = obj->getInheritanceOrder();
 */


// Solution 2
class ThroneInheritance {
public:
    ThroneInheritance(string kingName) {
        king = kingName;
    }

    void birth(string parentName, string childName) {
        g[parentName].emplace_back(childName);
    }

    void death(string name) {
        dead.insert(name);
    }

    vector<string> getInheritanceOrder() {
        vector<string> ans;
        vector<string> stk{king};
        while (!stk.empty()) {
            string x = stk.back();
            stk.pop_back();
            if (!dead.contains(x)) {
                ans.emplace_back(x);
            }
            auto it = g.find(x);
            if (it == g.end()) {
                continue;
            }
            auto& children = it->second;
            for (int i = (int) children.size() - 1; i >= 0; --i) {
                stk.push_back(children[i]);
            }
        }
        return ans;
    }

private:
    string king;
    unordered_set<string> dead;
    unordered_map<string, vector<string>> g;
};

/**
 * Your ThroneInheritance object will be instantiated and called as such:
 * ThroneInheritance* obj = new ThroneInheritance(kingName);
 * obj->birth(parentName,childName);
 * obj->death(name);
 * vector<string> param_3 = obj->getInheritanceOrder();
 */

class ThroneInheritance:
    def __init__(self, kingName: str):
        self.g = defaultdict(list)
        self.dead = set()
        self.king = kingName

    def birth(self, parentName: str, childName: str) -> None:
        self.g[parentName].append(childName)

    def death(self, name: str) -> None:
        self.dead.add(name)

    def getInheritanceOrder(self) -> List[str]:
        def dfs(x):
            if x not in self.dead:
                ans.append(x)
            for y in self.g[x]:
                dfs(y)

        ans = []
        dfs(self.king)
        return ans


# Your ThroneInheritance object will be instantiated and called as such:
# obj = ThroneInheritance(kingName)
# obj.birth(parentName,childName)
# obj.death(name)
# param_3 = obj.getInheritanceOrder()



# Solution 2
class ThroneInheritance:

    def __init__(self, kingName: str):
        self.king = kingName
        self.dead = set()
        self.g = defaultdict(list)

    def birth(self, parentName: str, childName: str) -> None:
        self.g[parentName].append(childName)

    def death(self, name: str) -> None:
        self.dead.add(name)

    def getInheritanceOrder(self) -> List[str]:
        ans = []
        stk = [self.king]
        while stk:
            x = stk.pop()
            if x not in self.dead:
                ans.append(x)
            for y in reversed(self.g[x]):
                stk.append(y)
        return ans


# Your ThroneInheritance object will be instantiated and called as such:
# obj = ThroneInheritance(kingName)
# obj.birth(parentName,childName)
# obj.death(name)
# param_3 = obj.getInheritanceOrder()

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

func Constructor(kingName string) ThroneInheritance {
	g := map[string][]string{}
	dead := map[string]bool{}
	return ThroneInheritance{g, dead, kingName}
}

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

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

func (this *ThroneInheritance) GetInheritanceOrder() []string {
	var dfs func(x string)
	ans := []string{}

	dfs = func(x string) {
		if !this.dead[x] {
			ans = append(ans, x)
		}
		for _, y := range this.g[x] {
			dfs(y)
		}
	}
	dfs(this.king)
	return ans
}

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


// Solution 2
type ThroneInheritance struct {
	king string
	dead map[string]bool
	g    map[string][]string
}

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

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

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

func (this *ThroneInheritance) GetInheritanceOrder() (ans []string) {
	stk := []string{this.king}
	for len(stk) > 0 {
		x := stk[len(stk)-1]
		stk = stk[:len(stk)-1]
		if !this.dead[x] {
			ans = append(ans, x)
		}
		children := this.g[x]
		for i := len(children) - 1; i >= 0; i-- {
			stk = append(stk, children[i])
		}
	}
	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();
 */

class ThroneInheritance {
    private king: string;
    private dead: Set<string> = new Set();
    private g: Map<string, string[]> = new Map();

    constructor(kingName: string) {
        this.king = kingName;
    }

    birth(parentName: string, childName: string): void {
        this.g.set(parentName, this.g.get(parentName) || []);
        this.g.get(parentName)!.push(childName);
    }

    death(name: string): void {
        this.dead.add(name);
    }

    getInheritanceOrder(): string[] {
        const ans: string[] = [];
        const dfs = (x: string) => {
            if (!this.dead.has(x)) {
                ans.push(x);
            }
            for (const y of this.g.get(x) || []) {
                dfs(y);
            }
        };
        dfs(this.king);
        return ans;
    }
}

/**
 * Your ThroneInheritance object will be instantiated and called as such:
 * var obj = new ThroneInheritance(kingName)
 * obj.birth(parentName,childName)
 * obj.death(name)
 * var param_3 = obj.getInheritanceOrder()
 */



// Solution 2
class ThroneInheritance {
    private king: string;
    private dead: Set<string> = new Set();
    private g: Map<string, string[]> = new Map();

    constructor(kingName: string) {
        this.king = kingName;
    }

    birth(parentName: string, childName: string): void {
        this.g.set(parentName, this.g.get(parentName) || []);
        this.g.get(parentName)!.push(childName);
    }

    death(name: string): void {
        this.dead.add(name);
    }

    getInheritanceOrder(): string[] {
        const ans: string[] = [];
        const stk: string[] = [this.king];
        while (stk.length) {
            const x = stk.pop()!;
            if (!this.dead.has(x)) {
                ans.push(x);
            }
            const children = this.g.get(x) || [];
            for (let i = children.length - 1; i >= 0; --i) {
                stk.push(children[i]);
            }
        }
        return ans;
    }
}

/**
 * Your ThroneInheritance object will be instantiated and called as such:
 * var obj = new ThroneInheritance(kingName)
 * obj.birth(parentName,childName)
 * obj.death(name)
 * var param_3 = obj.getInheritanceOrder()
 */

public class ThroneInheritance {
    private string king;
    private HashSet<string> dead = new HashSet<string>();
    private Dictionary<string, List<string>> g = new Dictionary<string, List<string>>();
    private List<string> ans = new List<string>();

    public ThroneInheritance(string kingName) {
        king = kingName;
    }

    public void Birth(string parentName, string childName) {
        if (!g.ContainsKey(parentName)) {
            g[parentName] = new List<string>();
        }
        g[parentName].Add(childName);
    }

    public void Death(string name) {
        dead.Add(name);
    }

    public IList<string> GetInheritanceOrder() {
        ans.Clear();
        DFS(king);
        return ans;
    }

    private void DFS(string x) {
        if (!dead.Contains(x)) {
            ans.Add(x);
        }
        if (g.ContainsKey(x)) {
            foreach (string y in g[x]) {
                DFS(y);
            }
        }
    }
}

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


// Solution 2
public class ThroneInheritance {
    private string king;
    private HashSet<string> dead = new HashSet<string>();
    private Dictionary<string, List<string>> g = new Dictionary<string, List<string>>();

    public ThroneInheritance(string kingName) {
        king = kingName;
    }

    public void Birth(string parentName, string childName) {
        if (!g.ContainsKey(parentName)) {
            g[parentName] = new List<string>();
        }
        g[parentName].Add(childName);
    }

    public void Death(string name) {
        dead.Add(name);
    }

    public IList<string> GetInheritanceOrder() {
        List<string> ans = new List<string>();
        Stack<string> stk = new Stack<string>();
        stk.Push(king);
        while (stk.Count > 0) {
            string x = stk.Pop();
            if (!dead.Contains(x)) {
                ans.Add(x);
            }
            if (g.ContainsKey(x)) {
                List<string> children = g[x];
                for (int i = children.Count - 1; i >= 0; --i) {
                    stk.Push(children[i]);
                }
            }
        }
        return ans;
    }
}

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

1600 - Throne Inheritance

1600. Throne Inheritance

Description

Solutions

Solution 2: Explicit-Stack Preorder

All Problems

All Solutions

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1600. Throne Inheritance

Description

Solutions

Solution 2: Explicit-Stack Preorder

All Problems

All Solutions