Paint House Problem Statement

You have been given a set of 'N' houses, each house can be painted using one of three colors: green, red, or yellow. A cost matrix is provided with dimensions 'N' * 3, where each element cost[i][j] represents the cost of painting the i-th house (using 0-based indexing) with the j-th color. The color codes are: green - 0, red - 1, and yellow - 2. Your task is to find the minimum total cost to paint all houses such that no two adjacent houses have the same color.

Example:

Input:

T = 1
N = 3
Cost Matrix = [[17, 2, 17], [16, 16, 5], [14, 3, 19]]

Output:

10

Explanation:

The minimum cost is achieved by painting house 0 with color 1 (cost = 2), house 1 with color 2 (cost = 5), and house 2 with color 1 (cost = 3).

Constraints:

1

Question

Paint House Problem Statement

You have been given a set of 'N' houses, each house can be painted using one of three colors: green, red, or yellow. A cost matrix is provided with dimensions 'N' * 3, where each element cost[i][j] represents the cost of painting the i-th house (using 0-based indexing) with the j-th color. The color codes are: green - 0, red - 1, and yellow - 2. Your task is to find the minimum total cost to paint all houses such that no two adjacent houses have the same color.

Example:

Input:

T = 1
N = 3
Cost Matrix = [[17, 2, 17], [16, 16, 5], [14, 3, 19]]

Output:

Explanation:

The minimum cost is achieved by painting house 0 with color 1 (cost = 2), house 1 with color 2 (cost = 5), and house 2 with color 1 (cost = 3).

Constraints:

1 <= T <= 50
1 <= N <= 10000
0 <= cost[i][j] <= 100

Where cost[i][j] represents the cost of painting the i-th house with j-th color.

Time limit: 1 second

Accepted Answer

Find the minimum total cost to paint all houses such that no two adjacent houses have the same color.

Use dynamic programming to keep track of the minimum cost of painting each house with each color while ensuring no two adjacent houses have the same color.
At each house, calculate the minimum cost of painting it with each color based on the previous house's colors.
Keep updating the minimum cost for each color at each house until reaching the last house.
Return the minimum cost of painting the last house with any color as the final result.

Asked in Springworks