[LeetCode] 265. Paint House II 粉刷房子之二

There are a row of n houses, each house can be painted with one of the k colors. 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 a n x k cost matrix. For example, costs[0][0] is the cost of painting house 0 with color 0; costs[1][2] is the cost of painting house 1 with color 2, and so on... Find the minimum cost to paint all houses.

Note:
All costs are positive integers.

Example:

Input: [[1,5,3],[2,9,4]]
Output: 5
Explanation: Paint house 0 into color 0, paint house 1 into color 2. Minimum cost: 1 + 4 = 5; 
             Or paint house 0 into color 2, paint house 1 into color 0. Minimum cost: 3 + 2 = 5.

Follow up:
Could you solve it in O(nk) runtime?

这道题是之前那道 Paint House 的拓展，那道题只让用红绿蓝三种颜色来粉刷房子，而这道题让用k种颜色，这道题不能用之前那题的解法，会 TLE。这题的解法的思路还是用 DP，但是在找不同颜色的最小值不是遍历所有不同颜色，而是用 min1 和 min2 来记录之前房子的最小和第二小的花费的颜色，如果当前房子颜色和 min1 相同，那么用 min2 对应的值计算，反之用 min1 对应的值，这种解法实际上也包含了求次小值的方法，感觉也是一种很棒的解题思路，参见代码如下：

解法一：

class Solution {
public:
    int minCostII(vector<vector<int>>& costs) {
        if (costs.empty() || costs[0].empty()) return 0;
        vector<vector<int>> dp = costs;
        int min1 = -1, min2 = -1;
        for (int i = 0; i < dp.size(); ++i) {
            int last1 = min1, last2 = min2;
            min1 = -1; min2 = -1;
            for (int j = 0; j < dp[i].size(); ++j) {
                if (j != last1) {
                    dp[i][j] += last1 < 0 ? 0 : dp[i - 1][last1];
                } else {
                    dp[i][j] += last2 < 0 ? 0 : dp[i - 1][last2];
                }
                if (min1 < 0 || dp[i][j] < dp[i][min1]) {
                    min2 = min1; min1 = j;
                } else if (min2 < 0 || dp[i][j] < dp[i][min2]) {
                    min2 = j;
                }
            }
        }
        return dp.back()[min1];
    }
};

下面这种解法不需要建立二维 dp 数组，直接用三个变量就可以保存需要的信息即可，参见代码如下：

解法二：

class Solution {
public:
    int minCostII(vector<vector<int>>& costs) {
        if (costs.empty() || costs[0].empty()) return 0;
        int min1 = 0, min2 = 0, idx1 = -1;
        for (int i = 0; i < costs.size(); ++i) {
            int m1 = INT_MAX, m2 = m1, id1 = -1;
            for (int j = 0; j < costs[i].size(); ++j) {
                int cost = costs[i][j] + (j == idx1 ? min2 : min1);
                if (cost < m1) {
                    m2 = m1; m1 = cost; id1 = j;
                } else if (cost < m2) {
                    m2 = cost;
                }
            }
            min1 = m1; min2 = m2; idx1 = id1;
        }
        return min1;
    }
};