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rod_cutting_problem.cpp
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rod_cutting_problem.cpp
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#include <bits/stdc++.h>
using namespace std;
// recursion only approch
int rc(int i,int len[],int profit[],int tot)
{
int ans = 0;
if(i<=0)
return 0;
if(len[i]<=tot)
ans = max(ans,max(profit[i]+ rc(i, len, profit, tot - len[i]), rc(i - 1, len, profit, tot) ));
else
ans = max(ans,rc(i - 1, len, profit, tot));
return ans;
}
//recursion with momoization
int rcmem(int i,int len[],int profit[],int tot,vector<vector<int>>&dp)
{
int ans = 0;
if(i<=0)
return 0;
if(dp[i][tot]!=-1)
return dp[i][tot];
if(len[i]<=tot)
ans = max(ans,max(profit[i]+ rcmem(i, len, profit, tot - len[i],dp), rcmem(i - 1, len, profit, tot,dp) ));
else
ans = max(ans,rcmem(i - 1, len, profit, tot,dp));
return dp[i][tot]=ans;
}
int main()
{
int tc;
cin >> tc;
while(tc--)
{
int n;
cin >> n;
int profit[n];
int len[n];
vector<vector<int>> dp(n+1,vector<int>(n+1,-1));
for (int i = 0; i < n; i++)
{
cin >> profit[i];
len[i] = i + 1;
}
int ans = rcmem(n-1, len, profit, n,dp);
cout << ans << endl;
}
return 0;
}