2146 - K Highest Ranked Items Within a Price Range.

Medium

You are given a 0-indexed 2D integer array grid of size m x n that represents a map of the items in a shop. The integers in the grid represent the following:

• 0 represents a wall that you cannot pass through.

• 1 represents an empty cell that you can freely move to and from.

• All other positive integers represent the price of an item in that cell. You may also freely move to and from these item cells.

It takes 1 step to travel between adjacent grid cells.

You are also given integer arrays pricing and start where pricing = [low, high] and start = [row, col] indicates that you start at the position (row, col) and are interested only in items with a price in the range of [low, high] ( inclusive ). You are further given an integer k.

You are interested in the positions of the k highest-ranked items whose prices are within the given price range. The rank is determined by the first of these criteria that is different:

• Distance, defined as the length of the shortest path from the start ( shorter distance has a higher rank).

• Price ( lower price has a higher rank, but it must be in the price range ).

• The row number ( smaller row number has a higher rank).

• The column number ( smaller column number has a higher rank).

Return the k highest-ranked items within the price range sorted by their rank (highest to lowest). If there are fewer than k reachable items within the price range, return all of them.

Example 1:

Input: grid = \[\[1,2,0,1],1,3,0,1,0,2,5,1], pricing = 2,5, start = 0,0, k = 3

Output: [0,1,1,1,2,1]

Explanation: You start at (0,0).

With a price range of 2,5, we can take items from (0,1), (1,1), (2,1) and (2,2).

The ranks of these items are:

• (0,1) with distance 1

• (1,1) with distance 2

• (2,1) with distance 3

• (2,2) with distance 4

Thus, the 3 highest ranked items in the price range are (0,1), (1,1), and (2,1).

Example 2:

Input: grid = \[\[1,2,0,1],1,3,3,1,0,2,5,1], pricing = 2,3, start = 2,3, k = 2

Output: [2,1,1,2]

Explanation: You start at (2,3).

With a price range of 2,3, we can take items from (0,1), (1,1), (1,2) and (2,1).

The ranks of these items are:

• (2,1) with distance 2, price 2

• (1,2) with distance 2, price 3

• (1,1) with distance 3

• (0,1) with distance 4

Thus, the 2 highest ranked items in the price range are (2,1) and (1,2).

Example 3:

Input: grid = \[\[1,1,1],0,0,1,2,3,4], pricing = 2,3, start = 0,0, k = 3

Output: [2,1,2,0]

Explanation: You start at (0,0).

With a price range of 2,3, we can take items from (2,0) and (2,1).

The ranks of these items are:

• (2,1) with distance 5

• (2,0) with distance 6

Thus, the 2 highest ranked items in the price range are (2,1) and (2,0).

Note that k = 3 but there are only 2 reachable items within the price range.

Constraints:

• m == grid.length

• n == grid[i].length

• <code>1 <= m, n <= 10⁵</code>

• <code>1 <= m * n <= 10⁵</code>

• <code>0 <= gridj<= 10⁵</code>

• pricing.length == 2

• <code>2 <= low <= high <= 10⁵</code>

• start.length == 2

• 0 <= row <= m - 1

• 0 <= col <= n - 1

• grid[row][col] > 0

• 1 <= k <= m * n