CODE & ALGO

Design Authentication Manager

Leetcode#1797

Problem Statement

There is an authentication system that works with authentication tokens. For each session, the user will receive a new authentication token that will expire timeToLive seconds after the currentTime. If the token is renewed, the expiry time will be extended to expire timeToLive seconds after the (potentially different) currentTime.

Implement the AuthenticationManager class:

  • AuthenticationManager(int timeToLive) constructs the AuthenticationManager and sets the timeToLive.
  • generate(string tokenId, int currentTime) generates a new token with the given tokenId at the given currentTime in seconds.
  • renew(string tokenId, int currentTime) renews the unexpired token with the given tokenId at the given currentTime in seconds. If there are no unexpired tokens with the given tokenId, the request is ignored, and nothing happens.
  • countUnexpiredTokens(int currentTime) returns the number of unexpired tokens at the given currentTime.

Note that if a token expires at time t, and another action happens on time t (renew or countUnexpiredTokens), the expiration takes place before the other actions.

Example 1:

Input
["AuthenticationManager", "renew", "generate", "countUnexpiredTokens", "generate", "renew", "renew", "countUnexpiredTokens"]
[[5], ["aaa", 1], ["aaa", 2], [6], ["bbb", 7], ["aaa", 8], ["bbb", 10], [15]]
Output
[null,null,null,1,null,null,null,0]

Explanation 

AuthenticationManager authenticationManager = new AuthenticationManager(5); // Constructs the AuthenticationManager with timeToLive = 5 seconds.
authenticationManager.renew("aaa", 1); // No token exists with tokenId "aaa" at time 1, so nothing happens.
authenticationManager.generate("aaa", 2); // Generates a new token with tokenId "aaa" at time 2.
authenticationManager.countUnexpiredTokens(6); // The token with tokenId "aaa" is the only unexpired one at time 6, so return 1.
authenticationManager.generate("bbb", 7); // Generates a new token with tokenId "bbb" at time 7.
authenticationManager.renew("aaa", 8); // The token with tokenId "aaa" expired at time 7, and 8 >= 7, so at time 8 the renew request is ignored, and nothing happens.
authenticationManager.renew("bbb", 10); // The token with tokenId "bbb" is unexpired at time 10, so the renew request is fulfilled and now the token will expire at time 15.
authenticationManager.countUnexpiredTokens(15); // The token with tokenId "bbb" expires at time 15, and the token with tokenId "aaa" expired at time 7, so currently no token is unexpired, so return 0.

Constraints:

  • 1 <= timeToLive <= 108
  • 1 <= currentTime <= 108
  • 1 <= tokenId.length <= 5
  • tokenId consists only of lowercase letters.
  • All calls to generate will contain unique values of tokenId.
  • The values of currentTime across all the function calls will be strictly increasing.
  • At most 2000 calls will be made to all functions combined.

Golang code

/**
 * Your AuthenticationManager object will be instantiated and called as such:
 * obj := Constructor(timeToLive);
 * obj.Generate(tokenId,currentTime);
 * obj.Renew(tokenId,currentTime);
 * param_3 := obj.CountUnexpiredTokens(currentTime);
 */

// Input
// ["AuthenticationManager",   [5],            null
// "renew",                    ["aaa", 1],     null
// "generate",                 ["aaa", 2],     null
// "countUnexpiredTokens",     [6],            1
// "generate",                 ["bbb", 7],     null
// "renew",                    ["aaa", 8],     null
// "renew",                    ["bbb", 10],    null
// "countUnexpiredTokens"]     [15]            0

type AuthenticationManager struct {
	timeToLive int
	// tokenID string
	// endTime int
	// map[tokenID]endTime
	tokenMap map[string]int
}

func Constructor(timeToLive int) AuthenticationManager {
	return AuthenticationManager{
		timeToLive: timeToLive,
		tokenMap:   make(map[string]int),
	}
}

func (this *AuthenticationManager) Generate(tokenId string, currentTime int) {
	this.tokenMap[tokenId] = currentTime + this.timeToLive
}

func (this *AuthenticationManager) Renew(tokenId string, currentTime int) {
	// unexpired token condition check
	if this.tokenMap[tokenId] > currentTime {
		this.tokenMap[tokenId] = currentTime + this.timeToLive
	}
}

func (this *AuthenticationManager) CountUnexpiredTokens(currentTime int) int {
	count := 0
	for _, v := range this.tokenMap {
		if v > currentTime {
			count++
		}
	}
	return count
}

Output

Case 1

Input
["AuthenticationManager","renew","generate","countUnexpiredTokens","generate","renew","renew","countUnexpiredTokens"]
[[5],["aaa",1],["aaa",2],[6],["bbb",7],["aaa",8],["bbb",10],[15]]

Output
[null,null,null,1,null,null,null,0]

Optimised code using Heap

Explanation of Optimisations

  1. Efficient Cleanup:
    • The priority queue ensures the smallest expiration time is handled first.
    • Expired tokens are removed lazily, avoiding redundant checks over all tokens.
  2. Fast Operations:
    • Generate: O(log⁡n), inserts into the heap and map.
    • Renew: O(log⁡n), updates the heap and map.
    • CountUnexpiredTokens: O(klog⁡n), where k is the number of expired tokens at the current time.
  3. Memory Usage:
    • Slightly higher due to the heap, but manageable given constraints (2000 calls).
/**
 * Your AuthenticationManager object will be instantiated and called as such:
 * obj := Constructor(timeToLive);
 * obj.Generate(tokenId,currentTime);
 * obj.Renew(tokenId,currentTime);
 * param_3 := obj.CountUnexpiredTokens(currentTime);
 */

// Input
// ["AuthenticationManager",   [5],            null
// "renew",                    ["aaa", 1],     null
// "generate",                 ["aaa", 2],     null
// "countUnexpiredTokens",     [6],            1
// "generate",                 ["bbb", 7],     null
// "renew",                    ["aaa", 8],     null
// "renew",                    ["bbb", 10],    null
// "countUnexpiredTokens"]     [15]            0

type Token struct {
	tokenID    string
	expiryTime int
}

type MinHeap []Token

func (h MinHeap) Less(i, j int) bool {
	return h[i].expiryTime < h[j].expiryTime
}

func (h MinHeap) Len() int {
	return len(h)
}

func (h MinHeap) Swap(i, j int) {
	h[i], h[j] = h[j], h[i]
}

func (h *MinHeap) Push(t interface{}) {
	*h = append(*h, t.(Token))
}

func (h *MinHeap) Pop() interface{} {
	old := *h

	n := len(old)
	item := old[n-1]
	*h = old[:n-1]
	return item
}

type AuthenticationManager struct {
	timeToLive int
	// tokenID string
	// endTime int
	// map[tokenID]endTime
	tokenMap   map[string]int
	expiryHeap *MinHeap
}

func Constructor(timeToLive int) AuthenticationManager {
	h := &MinHeap{}
	heap.Init(h)
	return AuthenticationManager{
		timeToLive: timeToLive,
		tokenMap:   make(map[string]int),
		expiryHeap: h,
	}
}

func (this *AuthenticationManager) Generate(tokenId string, currentTime int) {
	this.tokenMap[tokenId] = currentTime + this.timeToLive
	heap.Push(this.expiryHeap, Token{
		tokenID:    tokenId,
		expiryTime: this.tokenMap[tokenId],
	})
}

func (this *AuthenticationManager) Renew(tokenId string, currentTime int) {
	// unexpired token condition check
	if expiryTime, exist := this.tokenMap[tokenId]; exist && expiryTime > currentTime {
		this.tokenMap[tokenId] = currentTime + this.timeToLive
		heap.Push(this.expiryHeap, Token{
			tokenID:    tokenId,
			expiryTime: this.tokenMap[tokenId],
		})
	}
}

func (this *AuthenticationManager) CountUnexpiredTokens(currentTime int) int {
	for this.expiryHeap.Len() > 0 && (*this.expiryHeap)[0].expiryTime <= currentTime {
		expiredToken := heap.Pop(this.expiryHeap).(Token)

		if expiredToken.expiryTime == this.tokenMap[expiredToken.tokenID] {
			delete(this.tokenMap, expiredToken.tokenID)
		}
	}
	return len(this.tokenMap)

	// count := 0
	// for _, v := range this.tokenMap {
	// 	if v > currentTime {
	// 		count++
	// 	}
	// }
	// return count
}

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