# Posts published in “Algorithms”

Given an array arr, replace every element in that array with the greatest element among the elements to its right, and replace the last element with -1.

After doing so, return the array.

Example 1:

Input: arr = [17,18,5,4,6,1]
Output: [18,6,6,6,1,-1]

Constraints:

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

## Solution: Scan from right to left

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

## C++

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)

## 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++

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++

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"],
]
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)

## Solution 2: Trie

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

## C++

You are given a map of a server center, represented as a m * n integer matrix grid, where 1 means that on that cell there is a server and 0 means that it is no server. Two servers are said to communicate if they are on the same row or on the same column.

Return the number of servers that communicate with any other server.

Example 1:

Input: grid = [[1,0],[0,1]]
Output: 0
Explanation: No servers can communicate with others.

Example 2:

Input: grid = [[1,0],[1,1]]
Output: 3
Explanation: All three servers can communicate with at least one other server.


Example 3:

Input: grid = [[1,1,0,0],[0,0,1,0],[0,0,1,0],[0,0,0,1]]
Output: 4
Explanation: The two servers in the first row can communicate with each other. The two servers in the third column can communicate with each other. The server at right bottom corner can't communicate with any other server.


Constraints:

• m == grid.length
• n == grid[i].length
• 1 <= m <= 250
• 1 <= n <= 250
• grid[i][j] == 0 or 1

## Solution: Counting

Two passes:
First pass, count number of computers for each row and each column.
Second pass, count grid[i][j] if rows[i] or cols[j] has more than 1 computer.

Time complexity: O(m*n)
Space complexity: O(m + n)

## C++

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