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0-1Knapsack.cpp
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// Q173 https://www.codingninjas.com/codestudio/problems/1072980?topList=striver-sde-sheet-problems&utm_source=striver&utm_medium=website&leftPanelTab=0
// Recursion
// Time: O(2^n)
// Space: O(n)
#include<bits/stdc++.h>
int ks(vector<int> &val, vector<int> &wt, int ind, int W){
if(ind==0) {
if(wt[0]<=W) return val[0];
return 0;
}
int nt=ks(val,wt,ind-1,W);
int t=INT_MIN;
if(wt[ind]<=W)
t=val[ind]+ks(val,wt,ind-1,W-wt[ind]);
return max(t,nt);
}
int maxProfit(vector<int> &val, vector<int> &wt, int n, int W)
{
return ks(val,wt,n-1,W);
}
// Memorisation
// Time: O(N*m)
// Space: O(N*M)+O(N) = auxiliary stack space+ dp
#include<bits/stdc++.h>
int ks(vector<int> &val, vector<int> &wt, int ind, int W,vector<vector<int>> &dp){
if(ind==0) {
if(wt[0]<=W) return val[0];
return 0;
}
if(dp[ind][W]!=-1) return dp[ind][W];
int nt=ks(val,wt,ind-1,W,dp);
int t=INT_MIN;
if(wt[ind]<=W)
t=val[ind]+ks(val,wt,ind-1,W-wt[ind],dp);
return dp[ind][W]=max(t,nt);
}
int maxProfit(vector<int> &val, vector<int> &wt, int n, int W)
{ vector<vector<int>> dp(n,vector<int>(W+1,-1));
return ks(val,wt,n-1,W,dp);
}
// DP
// Time: O(N*m)
// Space: O(N*M)
#include<bits/stdc++.h>
int maxProfit(vector<int> &val, vector<int> &wt, int n, int W)
{ vector<vector<int>> dp(n,vector<int>(W+1,0));
for(int cw=0;cw<W+1;cw++) dp[0][cw]=val[0];
for(int ind=1;ind<n;ind++){
for(int cw=0;cw<=W;cw++){
int nt=dp[ind-1][cw];
int t=INT_MIN;
if(wt[ind]<=cw)
t=val[ind]+dp[ind-1][cw-wt[ind]];
dp[ind][cw]=max(t,nt);
}
}
// for(int ind=0;ind<n;ind++){
// for(int cw=0;cw<=W;cw++){
// cout<<dp[ind][cw]<<" ";
// }
// cout<<endl;
// }
return dp[n-1][W];
}
// TABULATION
// Time: O(N*m)
// Space: O(2*M)
#include<bits/stdc++.h>
int maxProfit(vector<int> &val, vector<int> &wt, int n, int W){
vector<int> p(W+1,0);
vector<int> c(W+1,0);
for(int cw=wt[0];cw<W+1;cw++) p[cw]=val[0];
for(int ind=1;ind<n;ind++){
for(int cw=0;cw<=W;cw++){
int nt=p[cw];
int t=INT_MIN;
if(wt[ind]<=cw)
t=val[ind]+p[cw-wt[ind]];
c[cw]=max(t,nt);
}
p=c;
}
return p[W];
}
// SINGLE ARRAY TABULATION
// Time: O(N*m)
// Space: O(M)
#include<bits/stdc++.h>
int maxProfit(vector<int> &val, vector<int> &wt, int n, int W){
vector<int> p(W+1,0);
// vector<int> c(W+1,0);
for(int cw=wt[0];cw<W+1;cw++) p[cw]=val[0];
for(int ind=1;ind<n;ind++){
for(int cw=W;cw>=0;cw--){
int nt=p[cw];
int t=INT_MIN;
if(wt[ind]<=cw)
t=val[ind]+p[cw-wt[ind]];
p[cw]=max(t,nt);
}
// p=c;
}
return p[W];
}