# Posts tagged as “medium”

You are given an array points representing integer coordinates of some points on a 2D-plane, where points[i] = [xi, yi].

The cost of connecting two points [xi, yi] and [xj, yj] is the manhattan distance between them: |xi - xj| + |yi - yj|, where |val| denotes the absolute value of val.

Return the minimum cost to make all points connected. All points are connected if there is exactly one simple path between any two points.

Example 1:

Input: points = [[0,0],[2,2],[3,10],[5,2],[7,0]]
Output: 20
Explanation:

We can connect the points as shown above to get the minimum cost of 20.
Notice that there is a unique path between every pair of points.


Example 2:

Input: points = [[3,12],[-2,5],[-4,1]]
Output: 18


Example 3:

Input: points = [[0,0],[1,1],[1,0],[-1,1]]
Output: 4


Example 4:

Input: points = [[-1000000,-1000000],[1000000,1000000]]
Output: 4000000


Example 5:

Input: points = [[0,0]]
Output: 0


Constraints:

• 1 <= points.length <= 1000
• -106 <= xi, yi <= 106
• All pairs (xi, yi) are distinct.

## Solution: Minimum Spanning Tree

Kruskal’s algorithm
Time complexity: O(n^2logn)
Space complexity: O(n^2)
using vector of vector, array, pair of pair, or tuple might lead to TLE…

## C++

Prim’s Algorithm
ds[i] := min distance from i to ANY nodes in the tree.

Time complexity: O(n^2) Space complexity: O(n)

## C++

You are given a list of preferences for n friends, where n is always even.

For each person ipreferences[i] contains a list of friends sorted in the order of preference. In other words, a friend earlier in the list is more preferred than a friend later in the list. Friends in each list are denoted by integers from 0 to n-1.

All the friends are divided into pairs. The pairings are given in a list pairs, where pairs[i] = [xi, yi] denotes xi is paired with yi and yi is paired with xi.

However, this pairing may cause some of the friends to be unhappy. A friend x is unhappy if x is paired with y and there exists a friend u who is paired with v but:

• x prefers u over y, and
• u prefers x over v.

Return the number of unhappy friends.

Example 1:

Input: n = 4, preferences = [[1, 2, 3], [3, 2, 0], [3, 1, 0], [1, 2, 0]], pairs = [[0, 1], [2, 3]]
Output: 2
Explanation:
Friend 1 is unhappy because:
- 1 is paired with 0 but prefers 3 over 0, and
- 3 prefers 1 over 2.
Friend 3 is unhappy because:
- 3 is paired with 2 but prefers 1 over 2, and
- 1 prefers 3 over 0.
Friends 0 and 2 are happy.


Example 2:

Input: n = 2, preferences = [[1], [0]], pairs = [[1, 0]]
Output: 0
Explanation: Both friends 0 and 1 are happy.


Example 3:

Input: n = 4, preferences = [[1, 3, 2], [2, 3, 0], [1, 3, 0], [0, 2, 1]], pairs = [[1, 3], [0, 2]]
Output: 4


Constraints:

• 2 <= n <= 500
• n is even.
• preferences.length == n
• preferences[i].length == n - 1
• 0 <= preferences[i][j] <= n - 1
• preferences[i] does not contain i.
• All values in preferences[i] are unique.
• pairs.length == n/2
• pairs[i].length == 2
• xi != yi
• 0 <= xi, yi <= n - 1
• Each person is contained in exactly one pair.

## Solution: HashTable

Put the order in a map {x -> {y, order}}, since this is dense, we use can 2D array instead of hasthable which is much faster.

Then for each pair, we just need to check every other pair and compare their orders.

Time complexity: O(n^2)
Space complexity: O(n^2)

## C++

Given a string s and an array of integers cost where cost[i] is the cost of deleting the character i in s.

Return the minimum cost of deletions such that there are no two identical letters next to each other.

Notice that you will delete the chosen characters at the same time, in other words, after deleting a character, the costs of deleting other characters will not change.

Example 1:

Input: s = "abaac", cost = [1,2,3,4,5]
Output: 3
Explanation: Delete the letter "a" with cost 3 to get "abac" (String without two identical letters next to each other).


Example 2:

Input: s = "abc", cost = [1,2,3]
Output: 0
Explanation: You don't need to delete any character because there are no identical letters next to each other.


Example 3:

Input: s = "aabaa", cost = [1,2,3,4,1]
Output: 2
Explanation: Delete the first and the last character, getting the string ("aba").


Constraints:

• s.length == cost.length
• 1 <= s.length, cost.length <= 10^5
• 1 <= cost[i] <= 10^4
• s contains only lowercase English letters.

## Solution: Group by group

For a group of same letters, delete all expect the one with the highest cost.

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

## python3

Given two arrays of integers nums1 and nums2, return the number of triplets formed (type 1 and type 2) under the following rules:

• Type 1: Triplet (i, j, k) if nums1[i]2 == nums2[j] * nums2[k] where 0 <= i < nums1.length and 0 <= j < k < nums2.length.
• Type 2: Triplet (i, j, k) if nums2[i]2 == nums1[j] * nums1[k] where 0 <= i < nums2.length and 0 <= j < k < nums1.length.

Example 1:

Input: nums1 = [7,4], nums2 = [5,2,8,9]
Output: 1
Explanation: Type 1: (1,1,2), nums1[1]^2 = nums2[1] * nums2[2]. (4^2 = 2 * 8).


Example 2:

Input: nums1 = [1,1], nums2 = [1,1,1]
Output: 9
Explanation: All Triplets are valid, because 1^2 = 1 * 1.
Type 1: (0,0,1), (0,0,2), (0,1,2), (1,0,1), (1,0,2), (1,1,2).  nums1[i]^2 = nums2[j] * nums2[k].
Type 2: (0,0,1), (1,0,1), (2,0,1). nums2[i]^2 = nums1[j] * nums1[k].


Example 3:

Input: nums1 = [7,7,8,3], nums2 = [1,2,9,7]
Output: 2
Explanation: There are 2 valid triplets.
Type 1: (3,0,2).  nums1[3]^2 = nums2[0] * nums2[2].
Type 2: (3,0,1).  nums2[3]^2 = nums1[0] * nums1[1].


Example 4:

Input: nums1 = [4,7,9,11,23], nums2 = [3,5,1024,12,18]
Output: 0
Explanation: There are no valid triplets.


Constraints:

• 1 <= nums1.length, nums2.length <= 1000
• 1 <= nums1[i], nums2[i] <= 10^5

## Solution: Hashtable

For each number y in the second array, count its frequency.

For each number x in the first, if x * x % y == 0, let r = x * x / y
if r == y: ans += f[y] * f[y-1]
else ans += f[y] * f[r]

Final ans /= 2

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

## C++

Given a 2D grid consisting of 1s (land) and 0s (water).  An island is a maximal 4-directionally (horizontal or vertical) connected group of 1s.

The grid is said to be connected if we have exactly one island, otherwise is said disconnected.

In one day, we are allowed to change any single land cell (1) into a water cell (0).

Return the minimum number of days to disconnect the grid.

Example 1:

Input: grid = [[0,1,1,0],[0,1,1,0],[0,0,0,0]]
Output: 2
Explanation: We need at least 2 days to get a disconnected grid.
Change land grid[1][1] and grid[0][2] to water and get 2 disconnected island.


Example 2:

Input: grid = [[1,1]]
Output: 2
Explanation: Grid of full water is also disconnected ([[1,1]] -> [[0,0]]), 0 islands.


Example 3:

Input: grid = [[1,0,1,0]]
Output: 0


Example 4:

Input: grid = [[1,1,0,1,1],
[1,1,1,1,1],
[1,1,0,1,1],
[1,1,0,1,1]]
Output: 1


Example 5:

Input: grid = [[1,1,0,1,1],
[1,1,1,1,1],
[1,1,0,1,1],
[1,1,1,1,1]]
Output: 2


Constraints:

• 1 <= grid.length, grid[i].length <= 30
• grid[i][j] is 0 or 1.

## Solution: Brute Force

We need at most two days to disconnect an island.
1. check if we have more than one islands. (0 days)
2. For each 1 cell, change it to 0 and check how many islands do we have. (1 days)
3. Otherwise, 2 days

Time complexity: O(m^2*n^2)
Space complexity: O(m*n)

## C++

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