实现一个数据结构支持以下操作:
- Inc(key) - 插入一个新的值为 1 的 key。或者使一个存在的 key 增加一,保证 key 不为空字符串。
- Dec(key) - 如果这个 key 的值是 1,那么把他从数据结构中移除掉。否者使一个存在的 key 值减一。如果这个 key 不存在,这个函数不做任何事情。key 保证不为空字符串。
- GetMaxKey() - 返回 key 中值最大的任意一个。如果没有元素存在,返回一个空字符串
""
。 - GetMinKey() - 返回 key 中值最小的任意一个。如果没有元素存在,返回一个空字符串
""
。
挑战:以 O(1) 的时间复杂度实现所有操作。
class AllOne {
public:
/** Initialize your data structure here. */
AllOne() {
}
/** Inserts a new key <Key> with value 1. Or increments an existing key by 1. */
void inc(string key) {
if (!m.count(key)) {
if (buckets.empty() || buckets.back().val != 1) {
auto newBucket = buckets.insert(buckets.end(), {1, {key}});
m[key] = newBucket;
} else {
auto newBucket = --buckets.end();
newBucket->keys.insert(key);
m[key] = newBucket;
}
} else {
auto curBucket = m[key], lastBucket = (--m[key]);
if (lastBucket == buckets.end() || lastBucket->val != curBucket->val + 1) {
auto newBucket = buckets.insert(curBucket, {curBucket->val + 1, {key}});
m[key] = newBucket;
} else {
lastBucket->keys.insert(key);
m[key] = lastBucket;
}
curBucket->keys.erase(key);
if (curBucket->keys.empty()) buckets.erase(curBucket);
}
}
/** Decrements an existing key by 1. If Key's value is 1, remove it from the data structure. */
void dec(string key) {
if (!m.count(key)) return;
auto curBucket = m[key];
if (curBucket->val == 1) {
curBucket->keys.erase(key);
if (curBucket->keys.empty()) buckets.erase(curBucket);
m.erase(key);
return;
}
auto nextBucket = ++m[key];
if (nextBucket == buckets.end() || nextBucket->val != curBucket->val - 1) {
auto newBucket = buckets.insert(nextBucket, {curBucket->val - 1, {key}});
m[key] = newBucket;
} else {
nextBucket->keys.insert(key);
m[key] = nextBucket;
}
curBucket->keys.erase(key);
if (curBucket->keys.empty()) buckets.erase(curBucket);
}
/** Returns one of the keys with maximal value. */
string getMaxKey() {
return buckets.empty() ? "" : *(buckets.begin()->keys.begin());
}
/** Returns one of the keys with Minimal value. */
string getMinKey() {
return buckets.empty() ? "" : *(buckets.rbegin()->keys.begin());
}
private:
struct Bucket { int val; unordered_set<string> keys; };
list<Bucket> buckets;
unordered_map<string, list<Bucket>::iterator> m;
};
/**
* Your AllOne object will be instantiated and called as such:
* AllOne obj = new AllOne();
* obj.inc(key);
* obj.dec(key);
* string param_3 = obj.getMaxKey();
* string param_4 = obj.getMinKey();
*/