LeetCode Q265: Paint House II (hard)

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?

Solution:

DP, when painting each house, keep track the lowest two costs. Time complexity O(kn), space complexity O(k).

	class Solution {
	public:
	int minCostII(vector<vector<int>>& costs) {
	int cost=0;
	if(costs.empty())
	return cost;
	int k = costs[0].size();
	vector<int> preCosts(k, 0);
	int minIdx1=0, minIdx2=1;
	for(int i=0; i<costs.size(); i++){
	vector<int> tmp(k, 0);
	int minV1=INT_MAX, minV2=INT_MAX;
	int tmpMinIdx1, tmpMinIdx2;
	for(int j=0; j<k; j++){
	if(j!=minIdx1&&j!=minIdx2)
	tmp[j]=preCosts[minIdx1]+costs[i][j];
	tmp[j]=j==minIdx1? preCosts[minIdx2]+costs[i][j]:preCosts[minIdx1]+costs[i][j];
	if(tmp[j]<minV1){
	minV2=minV1;
	minV1=tmp[j];
	tmpMinIdx2=tmpMinIdx1;
	tmpMinIdx1=j;
	}else{
	if(tmp[j]<minV2){
	minV2=tmp[j];
	tmpMinIdx2=j;
	}
	}
	}
	preCosts=tmp;
	minIdx1=tmpMinIdx1;
	minIdx2=tmpMinIdx2;
	}
	return preCosts[minIdx1];
	}
	};

view raw Q265PaintHouseII.cpp hosted with ❤ by GitHub

Round 2 solution:

	class Solution {
	public:
	int minCostII(vector<vector<int>>& costs) {
	int res = 0;
	if(costs.empty())
	return res;
	vector<int> cost(costs[0].size(), 0);
	for(int i=0; i<costs.size(); i++){
	vector<int> tmp(costs[0].size(), INT_MAX);
	res = INT_MAX;
	for(int j=0; j<costs[0].size(); j++){
	if(i==0)
	tmp[j]=costs[i][j];
	for(int p=0; p<costs[0].size(); p++){
	if(j==p)
	continue;
	tmp[j]=min(tmp[j], cost[p]+costs[i][j]);
	}
	res = min(res, tmp[j]);
	}
	cost = tmp;
	}
	return res;
	}
	};

view raw Q265Rnd2.cpp hosted with ❤ by GitHub