Knapsack problem time com' code example
Example: knapsack
using namespace std;
vector<pair<int,int> >a;
//dp table is full of zeros
int n,s,dp[1002][1002];
void ini(){
for(int i=0;i<1002;i++)
for(int j=0;j<1002;j++)
dp[i][j]=-1;
}
int f(int x,int b){
//base solution
if(x>=n or b<=0)return 0;
//if we calculate this before, we just return the answer (value diferente of 0)
if(dp[x][b]!=-1)return dp[x][b];
//calculate de answer for x (position) and b(empty space in knapsack)
//we get max between take it or not and element, this gonna calculate all the
//posible combinations, with dp we won't calculate what is already calculated.
return dp[x][b]=max(f(x+1,b),b-a[x].second>=0?f(x+1,b-a[x].second)+a[x].first:INT_MIN);
}
int main(){
//fast scan and print
ios_base::sync_with_stdio(0);cin.tie(0);
//we obtain quantity of elements and size of knapsack
cin>>n>>s;
a.resize(n);
//we get value of elements
for(int i=0;i<n;i++)
cin>>a[i].first;
//we get size of elements
for(int i=0;i<n;i++)
cin>>a[i].second;
//initialize dp table
ini();
//print answer
cout<<f(0,s);
return 0;
}