3429 - Paint House IV.

Medium

You are given an even integer n representing the number of houses arranged in a straight line, and a 2D array cost of size n x 3, where cost[i][j] represents the cost of painting house i with color j + 1.

The houses will look beautiful if they satisfy the following conditions:

• No two adjacent houses are painted the same color.

• Houses equidistant from the ends of the row are not painted the same color. For example, if n = 6, houses at positions (0, 5), (1, 4), and (2, 3) are considered equidistant.

Return the minimum cost to paint the houses such that they look beautiful.

Example 1:

Input: n = 4, cost = [3,5,7,6,2,9,4,8,1,7,3,5]

Output: 9

Explanation:

The optimal painting sequence is [1, 2, 3, 2] with corresponding costs [3, 2, 1, 3]. This satisfies the following conditions:

• No adjacent houses have the same color.

• Houses at positions 0 and 3 (equidistant from the ends) are not painted the same color (1 != 2).

• Houses at positions 1 and 2 (equidistant from the ends) are not painted the same color (2 != 3).

The minimum cost to paint the houses so that they look beautiful is 3 + 2 + 1 + 3 = 9.

Example 2:

Input: n = 6, cost = [2,4,6,5,3,8,7,1,9,4,6,2,3,5,7,8,2,4]

Output: 18

Explanation:

The optimal painting sequence is [1, 3, 2, 3, 1, 2] with corresponding costs [2, 8, 1, 2, 3, 2]. This satisfies the following conditions:

• No adjacent houses have the same color.

• Houses at positions 0 and 5 (equidistant from the ends) are not painted the same color (1 != 2).

• Houses at positions 1 and 4 (equidistant from the ends) are not painted the same color (3 != 1).

• Houses at positions 2 and 3 (equidistant from the ends) are not painted the same color (2 != 3).

The minimum cost to paint the houses so that they look beautiful is 2 + 8 + 1 + 2 + 3 + 2 = 18.

Constraints:

• <code>2 <= n <= 10⁵</code>

• n is even.

• cost.length == n

• cost[i].length == 3

• <code>0 <= costi\[j] <= 10⁵</code>