Evolve from brute force to optimal

• This is similar to paint house.

1. O((k-1)^n) brute force
``````    int minCostII(vector<vector<int>>& costs) {
if(costs.empty()) return 0;
return minCost(-1,-1,costs);
}
int minCost(int i,int j, vector<vector<int>>& costs) { //minCost starting from house i with color j
if(i==costs.size()) return 0;
int mc = INT_MAX;
for(int k=0;k<costs[0].size();k++) if(k!=j) mc = min(mc, minCost(i+1,k,costs));
return i<0? mc : mc+costs[i][j];
}
``````
1. O(nk^2) Memoization
``````    int minCostII(vector<vector<int>>& costs) {
if(costs.empty()) return 0;
vector<vector<int>> mem(costs.size(),vector<int>(costs[0].size()));
return minCost(-1,-1,mem,costs);
}
int minCost(int i,int j, vector<vector<int>>& mem, vector<vector<int>>& costs) {
if(i==costs.size()) return 0;
if(i>0 && mem[i][j]) return mem[i][j];
int mc = INT_MAX;
for(int k=0;k<costs[0].size();k++) if(k!=j) mc = min(mc, minCost(i+1,k,mem,costs));
return i<0? mc : mem[i][j]=mc+costs[i][j];
}
``````
1. O(nk^2) dp
``````    int minCostII(vector<vector<int>>& costs) {
if(costs.empty()) return 0;
int n = costs.size(), k = costs[0].size();
vector<vector<int>> dp(n+1,vector<int>(k));
for(int i=n-1;i>=0;i--)
for(int j=0;j<k;j++)
dp[i][j]=getMin(j,dp[i+1]) + costs[i][j];
return getMin(-1, dp[0]);
}
int getMin(int j, vector<int> &pre) {
int mc = INT_MAX;
for(int i=0;i<pre.size();i++) if(i!=j) mc = min(mc,pre[i]);
return mc;
}
``````
1. O(nk) dp
``````    int minCostII(vector<vector<int>>& costs) {
int pre1=0,pre2=0,c1=-1;
for(auto &v:costs) {
int cur1=INT_MAX,cur2,co1;
for(int i=0;i<v.size();i++) {
int c = v[i]+ (i==c1?pre2:pre1);
if(c<cur1) {
cur2 = cur1;
co1 = i;
cur1 = c;
} else if (c<cur2) cur2 = c;
}
pre1 = cur1;
pre2 = cur2;
c1 = co1;
}
return pre1;
}
``````

• Your solution 1 and 2 doesnt seem to work in the tests..
theres a integer overflow issue..

• @henry19 I cannot access the problem. What is the test case that overflows? Changing mc from int to long may fix it.

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