1791. Find Center of Star Graph

There is an undirected star graph consisting of n nodes labeled from 1 to n. A star graph is a graph where there is one center node and exactly n - 1 edges that connect the center node with every other node.

You are given a 2D integer array edges where each edges[i] = [ui, vi] indicates that there is an edge between the nodes ui and vi. Return the center of the given star graph.

3189. Minimum Moves to Get a Peaceful Board

Given a 2D array rooks of length n, where rooks[i] = [xi, yi] indicates the position of a rook on an n x n chess board. Your task is to move the rooks 1 cell at a time vertically or horizontally (to an adjacent cell) such that the board becomes peaceful.

A board is peaceful if there is exactly one rook in each row and each column.

Return the minimum number of moves required to get a peaceful board.

Note that at no point can there be two rooks in the same cell.

3183. The Number of Ways to Make the Sum

You have an infinite number of coins with values 1, 2, and 6, and only 2 coins with value 4.

Given an integer n, return the number of ways to make the sum of n with the coins you have.

Since the answer may be very large, return it modulo 109 + 7.

Note that the order of the coins doesn’t matter and [2, 2, 3] is the same as [2, 3, 2].

3167. Better Compression of String

You are given a string compressed representing a compressed version of a string. The format is a character followed by its frequency. For example, "a3b1a1c2" is a compressed version of the string "aaabacc".

We seek a better compression with the following conditions:

1. Each character should appear only once in the compressed version.
2. The characters should be in alphabetical order.

Return the better compression of compressed.

Note: In the better version of compression, the order of letters may change, which is acceptable.

3157. Find the Level of Tree with Minimum Sum

Given the root of a binary tree root where each node has a value, return the level of the tree that has the minimum sum of values among all the levels (in case of a tie, return the lowest level).

Note that the root of the tree is at level 1 and the level of any other node is its distance from the root + 1.

3197. Find the Minimum Area to Cover All Ones II

You are given a 2D binary array grid. You need to find 3 non-overlapping rectangles having non-zero areas with horizontal and vertical sides such that all the 1’s in grid lie inside these rectangles.

Return the minimum possible sum of the area of these rectangles.

Note that the rectangles are allowed to touch.

3196. Maximize Total Cost of Alternating Subarrays

You are given an integer array nums with length n.

The cost of a subarray nums[l..r], where 0 <= l <= r < n, is defined as:

1	>cost(l, r) = nums[l] - nums[l + 1] + ... + nums[r] * (−1)r − l

Your task is to split nums into subarrays such that the total cost of the subarrays is maximized, ensuring each element belongs to exactly one subarray.

Formally, if nums is split into k subarrays, where k > 1, at indices i1, i2, ..., ik − 1, where 0 <= i1 < i2 < ... < ik - 1 < n - 1, then the total cost will be:

1	>cost(0, i1) + cost(i1 + 1, i2) + ... + cost(ik − 1 + 1, n − 1)

Return an integer denoting the maximum total cost of the subarrays after splitting the array optimally.

Note: If nums is not split into subarrays, i.e. k = 1, the total cost is simply cost(0, n - 1).

3195. Find the Minimum Area to Cover All Ones I

You are given a 2D binary array grid. Find a rectangle with horizontal and vertical sides with the smallest area, such that all the 1’s in grid lie inside this rectangle.

Return the minimum possible area of the rectangle.

3194. Minimum Average of Smallest and Largest Elements

You have an array of floating point numbers averages which is initially empty. You are given an array nums of n integers where n is even.

You repeat the following procedure n / 2 times:

• Remove the smallest element, minElement, and the largest element maxElement, from nums.
• Add (minElement + maxElement) / 2 to averages.

Return the minimum element in averages.

3193. Count the Number of Inversions

You are given an integer n and a 2D array requirements, where requirements[i] = [endi, cnti] represents the end index and the inversion count of each requirement.

A pair of indices (i, j) from an integer array nums is called an inversion if:

• i < j and nums[i] > nums[j]

Return the number of permutations perm of [0, 1, 2, ..., n - 1] such that for all requirements[i], perm[0..endi] has exactly cnti inversions.

Since the answer may be very large, return it modulo 109 + 7.