Problem description:

There is a row of n houses, where each house can be painted one of three colors: red, blue, or green. The cost of painting each house with a certain color is different. You have to paint all the houses such that no two adjacent houses have the same color.

The cost of painting each house with a certain color is represented by an n x 3 cost matrix costs.

  • For example, costs[0][0] is the cost of painting house 0 with the color red; costs[1][2] is the cost of painting house 1 with color green, and so on…

Return the minimum cost to paint all houses.

Example 1:

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2
3
4
Input: costs = [[17,2,17],[16,16,5],[14,3,19]]
Output: 10
Explanation: Paint house 0 into blue, paint house 1 into green, paint house 2 into blue.
Minimum cost: 2 + 5 + 3 = 10.

Example 2:

1
2
Input: costs = [[7,6,2]]
Output: 2

Constraints:

  • costs.length == n
  • costs[i].length == 3
  • 1 <= n <= 100
  • 1 <= costs[i][j] <= 20

Solution:

There is a row of n houses, where each house can be painted one of three colors: red, blue, or green. The cost of painting each house with a certain color is different. You have to paint all the houses such that no two adjacent houses have the same color.

The cost of painting each house with a certain color is represented by an n x 3 cost matrix costs.

  • For example, costs[0][0] is the cost of painting house 0 with the color red; costs[1][2] is the cost of painting house 1 with color green, and so on…

Return the minimum cost to paint all houses.

Example 1:

1
2
3
4
Input: costs = [[17,2,17],[16,16,5],[14,3,19]]
Output: 10
Explanation: Paint house 0 into blue, paint house 1 into green, paint house 2 into blue.
Minimum cost: 2 + 5 + 3 = 10.

Example 2:

1
2
Input: costs = [[7,6,2]]
Output: 2

Constraints:

  • costs.length == n
  • costs[i].length == 3
  • 1 <= n <= 100
  • 1 <= costs[i][j] <= 20

time complexity: $O()$
space complexity: $O()$
reference:
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