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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.
Follow up:
Could you solve it in O(nk) runtime?
这里时间复杂度是O(nk)，说明要求我们用O(k)的时间计算每一层的新的cost。
cost‘[i] = costs[m][i] + min{cost[0], cost[1], ..., cost[i - 1], cost[i + 1], ..., cost[k - 1]}
原想法是对每一个i重新计算，时间复杂度是O(k2)。包含了大量的重复计算
其实我们只需求出cost[]序列的最小值和第二小的值。Time complexity O(k)
1 public class Solution { 2 public int minCostII(int[][] costs) { 3 if (costs == null || costs.length < 1) { 4 return 0; 5 } 6 int m = costs.length, k = costs[0].length; 7 int[] cost = new int[k]; 8 int[] tmp = new int[k]; 9 for (int i = 0; i < k; i++) { 10 cost[i] = costs[m - 1][i]; 11 } 12 for (int i = m - 2; i >= 0; i--) { 13 // calculate most and second minimum number 14 int[] min = calcMin(cost); 15 for (int j = 0; j < k; j++) { 16 // if cost[j] is minimum, then add second minimum with costs[i][j] 17 if (cost[j] == min[0]) { 18 cost[j] = min[1] + costs[i][j]; 19 } else { 20 // if cost[j] is not minimum, then add minimum with costs[i][j] 21 cost[j] = min[0] + costs[i][j]; 22 } 23 } 24 } 25 if (k < 2) { 26 return cost[0]; 27 } 28 int[] result = calcMin(cost); 29 return result[0]; 30 } 31 32 private int[] calcMin(int[] nums) { 33 if (nums == null || nums.length < 2) { 34 return new int[0]; 35 } 36 int[] mins = new int[2]; 37 mins[0] = Math.min(nums[0], nums[1]); 38 mins[1] = Math.max(nums[0], nums[1]); 39 for (int i = 2; i < nums.length; i++) { 40 if (nums[i] < mins[0]) { 41 mins[1] = mins[0]; 42 mins[0] = nums[i]; 43 } else if (nums[i] < mins[1]) { 44 mins[1] = nums[i]; 45 } 46 } 47 return mins; 48 } 49 }
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原文地址：http://www.cnblogs.com/ireneyanglan/p/4948901.html
