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花花酱 LeetCode 1292. Maximum Side Length of a Square with Sum Less than or Equal to Threshold

Given a m x n matrix mat and an integer threshold. Return the maximum side-length of a square with a sum less than or equal to threshold or return 0 if there is no such square.

Example 1:

Input: mat = [[1,1,3,2,4,3,2],[1,1,3,2,4,3,2],[1,1,3,2,4,3,2]], threshold = 4
Output: 2
Explanation: The maximum side length of square with sum less than 4 is 2 as shown.

Example 2:

Input: mat = [[2,2,2,2,2],[2,2,2,2,2],[2,2,2,2,2],[2,2,2,2,2],[2,2,2,2,2]], threshold = 1
Output: 0

Example 3:

Input: mat = [[1,1,1,1],[1,0,0,0],[1,0,0,0],[1,0,0,0]], threshold = 6
Output: 3

Example 4:

Input: mat = [[18,70],[61,1],[25,85],[14,40],[11,96],[97,96],[63,45]], threshold = 40184
Output: 2

Constraints:

  • 1 <= m, n <= 300
  • m == mat.length
  • n == mat[i].length
  • 0 <= mat[i][j] <= 10000
  • 0 <= threshold <= 10^5

Solution: DP + Brute Force

Precompute the sums of sub-matrixes whose left-top corner is at (0,0).

Try all possible left-top corner and sizes.

Time complexity: O(m*n*min(m,n))
Space complexity: O(m*n)

C++

Solution 2: Binary Search

Search for the smallest size k that is greater than the threshold, ans = k – 1.

C++

Solution 3: Bounded Search

Time complexity: O(m*n + min(m,n))

C++

花花酱 LeetCode 1287. Element Appearing More Than 25% In Sorted Array

Given an integer array sorted in non-decreasing order, there is exactly one integer in the array that occurs more than 25% of the time.

Return that integer.

Example 1:

Constraints:

  • 1 <= arr.length <= 10^4
  • 0 <= arr[i] <= 10^5

Solution 1: Linear Scan

if arr[i] == arr[i + len/4] => arr[i] is the special integer.

Time complexity: O(n)
Space complexity: O(1)

C++

Solution 2: Binary Search

The answer must be one of (s[0], s[l/4], s[l/2], s[l*3/4])
Using binary search to find the range of each number, the one has more than 1/4 of total elements is the answer.

Time complexity: O(logn)
Space complexity: O(1)

C++

花花酱 LeetCode 1283. Find the Smallest Divisor Given a Threshold

Given an array of integers nums and an integer threshold, we will choose a positive integer divisor and divide all the array by it and sum the result of the division. Find the smallest divisor such that the result mentioned above is less than or equal to threshold.

Each result of division is rounded to the nearest integer greater than or equal to that element. (For example: 7/3 = 3 and 10/2 = 5).

It is guaranteed that there will be an answer.

Example 1:

Input: nums = [1,2,5,9], threshold = 6
Output: 5
Explanation: We can get a sum to 17 (1+2+5+9) if the divisor is 1. 
If the divisor is 4 we can get a sum to 7 (1+1+2+3) and if the divisor is 5 the sum will be 5 (1+1+1+2). 

Example 2:

Input: nums = [2,3,5,7,11], threshold = 11
Output: 3

Example 3:

Input: nums = [19], threshold = 5
Output: 4

Solution: Binary Search

Time complexity: O(nlogk)
Space complexity: O(1)

C++

花花酱 LeetCode 1268. Search Suggestions System

Given an array of strings products and a string searchWord. We want to design a system that suggests at most three product names from products after each character of searchWord is typed. Suggested products should have common prefix with the searchWord. If there are more than three products with a common prefix return the three lexicographically minimums products.

Return list of lists of the suggested products after each character of searchWord is typed. 

Example 1:

Input: products = ["mobile","mouse","moneypot","monitor","mousepad"], searchWord = "mouse"
Output: [
["mobile","moneypot","monitor"],
["mobile","moneypot","monitor"],
["mouse","mousepad"],
["mouse","mousepad"],
["mouse","mousepad"]
]
Explanation: products sorted lexicographically = ["mobile","moneypot","monitor","mouse","mousepad"]
After typing m and mo all products match and we show user ["mobile","moneypot","monitor"]
After typing mou, mous and mouse the system suggests ["mouse","mousepad"]

Example 2:

Input: products = ["havana"], searchWord = "havana"
Output: [["havana"],["havana"],["havana"],["havana"],["havana"],["havana"]]

Example 3:

Input: products = ["bags","baggage","banner","box","cloths"], searchWord = "bags"
Output: [["baggage","bags","banner"],["baggage","bags","banner"],["baggage","bags"],["bags"]]

Example 4:

Input: products = ["havana"], searchWord = "tatiana"
Output: [[],[],[],[],[],[],[]]

Constraints:

  • 1 <= products.length <= 1000
  • 1 <= Σ products[i].length <= 2 * 10^4
  • All characters of products[i] are lower-case English letters.
  • 1 <= searchWord.length <= 1000
  • All characters of searchWord are lower-case English letters.

Solution 1: Binary Search

Sort the input array and do two binary searches.
One for prefix of the search word as lower bound, another for prefix + ‘~’ as upper bound.
‘~’ > ‘z’

Time complexity: O(nlogn + l * logn)
Space complexity: O(1)

C++

Solution 2: Trie

Initialization: Sum(len(products[i]))
Query: O(len(searchWord))

C++