Q21 Rod Cutting | Practice | GeeksforGeeks

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Fri Mar 24 2023 07:14:52 GMT+0000 (Coordinated Universal Time)

Saved by @Ayush_dabas07

//{ Driver Code Starts
import java.io.*;
import java.util.*;

class RodCutting {

    public static void main(String args[]) {
        Scanner sc = new Scanner(System.in);
        int t = sc.nextInt();
        while (t-- > 0) {
            int n = sc.nextInt();
            int[] arr = new int[n];
            for (int i = 0; i < n; i++) arr[i] = sc.nextInt();

            Solution ob = new Solution();
            System.out.println(ob.cutRod(arr, n));
        }
    }
}

// } Driver Code Ends


class Solution{
    public int cutRod(int price[], int n) {
        /* storage and meaning - every cell denotes maximum profit if the rod had been of
        that length 
        */
        
        int dp[] = new int[n+1];
        int nprice[] = new int[n+1];  //for ease of indexing
        
        //copying all prices in 1 based indexing
        for(int i = 1 ; i < n+1 ; i++)
        nprice[i] = price[i-1];
        
        //dp of 0 is already 0 
        dp[1] = nprice[1];  //1 length of rod can only be sold for price of 1 length
        
        
        for(int i = 2 ; i < n+1 ; i++){
            
            //storing profit when rod is not cut at all and sold at full length of i only
            int maxProfit = nprice[i]; 
            
            //cutting rod in 1 to i-1 pieces and checking for max profit 
          //with optimized i-j 
            for(int j = 1 ;j < i ; j++ )
            maxProfit = Math.max(maxProfit , dp[i-j] + nprice[j]);
          
          //or 
          //this will be cutting in j and taking cartesian product of optimized j & 
         //optimized i-j , we only have to travel till half as then pairs will get repeated
			// for(int j = 1 ;j <= i/2 ; j++ )
            // maxProfit = Math.max(maxProfit , dp[i-j] + dp[j]);
                
            dp[i] = maxProfit;
            
        }
        
        // for(int i = 0 ; i < n+1 ; i ++)
        // System.out.print(dp[i] + " ");
        
        return dp[n];
    }
}

https://practice.geeksforgeeks.org/problems/rod-cutting0840/1

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