Posts tagged as “heap”

花花酱 LeetCode 1488. Avoid Flood in The City

By zxi on June 20, 2020

Your country has an infinite number of lakes. Initially, all the lakes are empty, but when it rains over the nth lake, the nth lake becomes full of water. If it rains over a lake which is full of water, there will be a flood. Your goal is to avoid the flood in any lake.

Given an integer array rains where:

rains[i] > 0 means there will be rains over the rains[i] lake.
rains[i] == 0 means there are no rains this day and you can choose one lake this day and dry it.

Return an array ans where:

ans.length == rains.length
ans[i] == -1 if rains[i] > 0.
ans[i] is the lake you choose to dry in the ith day if rains[i] == 0.

If there are multiple valid answers return any of them. If it is impossible to avoid flood return an empty array.

Notice that if you chose to dry a full lake, it becomes empty, but if you chose to dry an empty lake, nothing changes. (see example 4)

Example 1:

Input: rains = [1,2,3,4]
Output: [-1,-1,-1,-1]
Explanation: After the first day full lakes are [1]
After the second day full lakes are [1,2]
After the third day full lakes are [1,2,3]
After the fourth day full lakes are [1,2,3,4]
There's no day to dry any lake and there is no flood in any lake.

Example 2:

Input: rains = [1,2,0,0,2,1]
Output: [-1,-1,2,1,-1,-1]
Explanation: After the first day full lakes are [1]
After the second day full lakes are [1,2]
After the third day, we dry lake 2. Full lakes are [1]
After the fourth day, we dry lake 1. There is no full lakes.
After the fifth day, full lakes are [2].
After the sixth day, full lakes are [1,2].
It is easy that this scenario is flood-free. [-1,-1,1,2,-1,-1] is another acceptable scenario.

Example 3:

Input: rains = [1,2,0,1,2]
Output: []
Explanation: After the second day, full lakes are  [1,2]. We have to dry one lake in the third day.
After that, it will rain over lakes [1,2]. It's easy to prove that no matter which lake you choose to dry in the 3rd day, the other one will flood.

Example 4:

Input: rains = [69,0,0,0,69]
Output: [-1,69,1,1,-1]
Explanation: Any solution on one of the forms [-1,69,x,y,-1], [-1,x,69,y,-1] or [-1,x,y,69,-1] is acceptable where 1 <= x,y <= 10^9

Example 5:

Input: rains = [10,20,20]
Output: []
Explanation: It will rain over lake 20 two consecutive days. There is no chance to dry any lake.

Constraints:

1 <= rains.length <= 10^5
0 <= rains[i] <= 10^9

Solution: Binary Search

Store the days we can dry a lake in a treeset.
Store the last day when a lake becomes full in a hashtable.
Whenever we encounter a full lake, try to find the first available day that we can dry it. If no such day, return no answer.

Time complexity: O(nlogn)
Space complexity: O(n)

C++

// Author: Huahua

class Solution {

public:

vector<int> avoidFlood(vector<int>& rains) {

const int n = rains.size();

vector<int> ans(n, -1);

unordered_map<int, int> full; // lake -> day

set<int> dry; // days we can dry lakes.

for (int i = 0; i < n; ++i) {

const int lake = rains[i];

if (lake > 0) {

if (full.count(lake)) {

// Find the first day we can dry it.

auto it = dry.upper_bound(full[lake]);

if (it == end(dry)) return {};

ans[*it] = lake;

dry.erase(it);

}

full[lake] = i;

} else {

dry.insert(i);

ans[i] = 1;

}

return ans;

}

};

花花酱 LeetCode 1094. Car Pooling

By zxi on June 22, 2019

You are driving a vehicle that has capacity empty seats initially available for passengers. The vehicle only drives east (ie. it cannot turn around and drive west.)

Given a list of trips, trip[i] = [num_passengers, start_location, end_location] contains information about the i-th trip: the number of passengers that must be picked up, and the locations to pick them up and drop them off. The locations are given as the number of kilometers due east from your vehicle’s initial location.

Return true if and only if it is possible to pick up and drop off all passengers for all the given trips.

Example 1:

Input: trips = [[2,1,5],[3,3,7]], capacity = 4
Output: false

Example 2:

Input: trips = [[2,1,5],[3,3,7]], capacity = 5
Output: true

Example 3:

Input: trips = [[2,1,5],[3,5,7]], capacity = 3
Output: true

Example 4:

Input: trips = [[3,2,7],[3,7,9],[8,3,9]], capacity = 11
Output: true

Solution1: Min heap

Sort events by location

Time complexity: O(nlogn)
Space complexity: O(n)

C++

// Author: Huahua

class Solution {

public:

bool carPooling(vector<vector<int>>& trips, int capacity) {

priority_queue<int> q;

for (const auto& trip : trips) {

int pick_up = -((trip[1] << 10) | (1 << 9) | trip[0]);

int drop_off = -((trip[2] << 10) | trip[0]);

q.push(pick_up);

q.push(drop_off);

}

while (q.size()) {

int key = -q.top(); q.pop();

int sign = ((key >> 9) & 1) ? 1: -1;

int num = key & 0xFF;

if ((capacity -= sign * num) < 0)

return false;

}

return true;

}

};

Solution 2: Preprocessing

Time complexity: O(n)
Space complexity: O(1000)

C++

// Author: Huahua

class Solution {

public:

bool carPooling(vector<vector<int>>& trips, int capacity) {

vector<int> d(1001);

for (const auto& trip : trips) {

d[trip[1]] -= trip[0];

d[trip[2]] += trip[0];

}

for (const int c : d)

if ((capacity += c) < 0) return false;

return true;

}

};

花花酱 LeetCode 628. Maximum Product of Three Numbers

By zxi on August 17, 2018

Problem

Given an integer array, find three numbers whose product is maximum and output the maximum product.

Example 1:

Input: [1,2,3]
Output: 6

Example 2:

Input: [1,2,3,4]
Output: 24

Note:

The length of the given array will be in range [3,10⁴] and all elements are in the range [-1000, 1000].
Multiplication of any three numbers in the input won’t exceed the range of 32-bit signed integer.

Idea:

Find the top 3 numbers t1, t2, t3, and bottom 2 numbers, b1, b2.

If all numbers are positives, answer must be t1 * t2 * t3.

Since the number can go negative, the answer must be either t1*t2*t3 or b1 * b2 * t1, if b1 and b2 are both negatives.

ex. nums: [5, 1, -6, 3, -1]

t1, t2, t3: 5, 3, 1

b1, b2: -6, -1

t1 * t2 * t3 = 15

t1 * b1 * b2 = 30

Solution 1: Manual Tracking

Time complexity: O(n)

Space complexity: O(1)

// Author: Huahua

// Running time: 28 ms

class Solution {

public:

int maximumProduct(vector<int>& nums) {

int max1 = INT_MIN;

int max2 = INT_MIN;

int max3 = INT_MIN;

int min1 = INT_MAX;

int min2 = INT_MAX;

for (const int num: nums) {

if (num > max1) {

max3 = max2;

max2 = max1;

max1 = num;

} else if (num > max2) {

max3 = max2;

max2 = num;

} else if (num > max3) {

max3=num;

}

if (num < min1) {

min2 = min1;

min1 = num;

} else if (num < min2) {

min2=num;

}

return max(max1*max2*max3, max1*min1*min2);

}

};

Solution 2: Sorting

Time complexity: O(nlogn)

Space complexity: O(1)

// Author: Huahua

// Running time: 48 ms

class Solution {

public:

int maximumProduct(vector<int>& nums) {

int n = nums.size();

sort(nums.rbegin(), nums.rend());

return max(nums[0] * nums[1] * nums[2], nums[0] * nums[n - 1] * nums[n - 2]);

}

};

Solution 3: Two Heaps (Priority Queues)

Time complexity: O(nlog3)

Space complexity: O(2 + 3)

// Author: Huahua

// Running time: 40 ms

class Solution {

public:

int maximumProduct(vector<int>& nums) {

priority_queue<int, vector<int>, less<int>> min_q; // max_heap

priority_queue<int, vector<int>, greater<int>> max_q; // min_heap

for (int num : nums) {

max_q.push(num);

if (max_q.size() > 3) max_q.pop();

min_q.push(num);

if (min_q.size() > 2) min_q.pop();

}

int max3 = max_q.top(); max_q.pop();

int max2 = max_q.top(); max_q.pop();

int max1 = max_q.top(); max_q.pop();

int min2 = min_q.top(); min_q.pop();

int min1 = min_q.top(); min_q.pop();

return max(max1 * max2 * max3, max1 * min1 * min2);

}

};

花花酱 LeetCode 703. Kth Largest Element in a Stream

By zxi on July 12, 2018

Problem

Design a class to find the kth largest element in a stream. Note that it is the kth largest element in the sorted order, not the kth distinct element.

Your KthLargest class will have a constructor which accepts an integer k and an integer array nums, which contains initial elements from the stream. For each call to the method KthLargest.add, return the element representing the kth largest element in the stream.

Example:

int k = 3;
int[] arr = [4,5,8,2];
KthLargest kthLargest = new KthLargest(3, arr);
kthLargest.add(3);   // returns 4
kthLargest.add(5);   // returns 5
kthLargest.add(10);  // returns 5
kthLargest.add(9);   // returns 8
kthLargest.add(4);   // returns 8

Note:
You may assume that nums‘ length ≥ k-1 and k ≥ 1.

Solution: BST / Min Heap

Time complexity: O(nlogk)

Space complexity: O(k)

C++ / BST

// Author: Huahua

// Running time: 32 ms

class KthLargest {

public:

KthLargest(int k, vector<int> nums): k_(k) {

for (int num : nums)

add(num);

}

int add(int val) {

s_.insert(val);

if (s_.size() > k_)

s_.erase(s_.begin());

return *s_.begin();

}

private:

const int k_;

multiset<int> s_;

};

C++ / Min Heap

// Author: Huahua

// Running time: 28 ms

class KthLargest {

public:

KthLargest(int k, vector<int> nums): k_(k) {

for (int num : nums)

add(num);

}

int add(int val) {

s_.push(val);

if (s_.size() > k_)

s_.pop();

return s_.top();

}

private:

const int k_;

priority_queue<int, vector<int>, greater<int>> s_; // min heap

};

Posts tagged as “heap”

花花酱 LeetCode 1488. Avoid Flood in The City

Solution: Binary Search

C++

花花酱 LeetCode 1094. Car Pooling

Solution1: Min heap

C++

Solution 2: Preprocessing

C++

花花酱 LeetCode 23. Merge k Sorted Lists

Problem

Solution 1: Brute Force

C++

Solution 2: Heap / Priority Queue

C++

花花酱 LeetCode 628. Maximum Product of Three Numbers

Problem

Idea:

Solution 1: Manual Tracking

Solution 2: Sorting

Solution 3: Two Heaps (Priority Queues)

花花酱 LeetCode 703. Kth Largest Element in a Stream

Problem

Solution: BST / Min Heap