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Posts tagged as “heap”

花花酱 LeetCode 23. Merge k Sorted Lists

Problem

Merge k sorted linked lists and return it as one sorted list. Analyze and describe its complexity.

Example:

Input:
[
  1->4->5,
  1->3->4,
  2->6
]
Output: 1->1->2->3->4->4->5->6

Solution 1: Brute Force

Time complexity: O(nk)

Space complexity: O(1)

C++

Solution 2: Heap / Priority Queue

Time complexity: O(nlogk)

Space complexity: O(k)

C++

花花酱 LeetCode 628. Maximum Product of Three Numbers

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:

  1. The length of the given array will be in range [3,104] and all elements are in the range [-1000, 1000].
  2. 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)

Solution 2: Sorting

Time complexity: O(nlogn)

Space complexity: O(1)

Solution 3: Two Heaps (Priority Queues)

Time complexity: O(nlog3)

Space complexity: O(2 + 3)

 

花花酱 LeetCode 703. Kth Largest Element in a Stream

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

C++ / Min Heap

 

 

花花酱 LeetCode 239. Sliding Window Maximum

题目大意:给你一个数组,让你输出移动窗口的最大值。

Problem:

https://leetcode.com/problems/sliding-window-maximum/

Given an array nums, there is a sliding window of size k which is moving from the very left of the array to the very right. You can only see the k numbers in the window. Each time the sliding window moves right by one position.

For example,
Given nums = [1,3,-1,-3,5,3,6,7], and k = 3.

Therefore, return the max sliding window as [3,3,5,5,6,7].

Note: 
You may assume k is always valid, ie: 1 ≤ k ≤ input array’s size for non-empty array.

Follow up:
Could you solve it in linear time?

 

Idea:

 

Solution 1: Brute Force

Time complexity: O((n – k + 1) * k)

Space complexity: O(1)

C++

Java

Python

Solution 2: BST

Time complexity: O((n – k + 1) * logk)

Space complexity: O(k)

C++

Solution 3: Monotonic Queue

Time complexity: O(n)

Space complexity: O(k)

C++

C++ V2

C++ V3

Java

Python3

Python3 V2

花花酱 LeetCode 692. Top K Frequent Words

Problem:

Given a non-empty list of words, return the k most frequent elements.

Your answer should be sorted by frequency from highest to lowest. If two words have the same frequency, then the word with the lower alphabetical order comes first.

Example 1:

Example 2:

Note:

  1. You may assume k is always valid, 1 ≤ k ≤ number of unique elements.
  2. Input words contain only lowercase letters.

Follow up:

  1. Try to solve it in O(n log k) time and O(n) extra space.



Idea:

Priority queue / min heap

Solution

C++ / priority_queue O(n log k) / O(n)

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