Maximum profit by selling N items at two markets

Difficulty Level : Easy
Last Updated : 04 Mar, 2021

Given two array A[] and B[] each of length N where A[i] and B[i] are the prices of the i^th item when sold in market A and market B respectively. The task is to maximize the profile of selling all the N items but there is a catch if you went to market B then you can not return back. For example, if you sell the first k items in market A then you have to sell the rest of the items in market B.
Examples:

Input: A[] = {2, 3, 2}, B[] = {10, 3, 40}
Output: 53
Sell all the items in market B in order to
maximize the profit i.e. (10 + 3 + 40) = 53.
Input: A[] = {7, 5, 3, 4}, B[] = {2, 3, 1, 3}
Output: 19

Approach:

Create a prefix sum array preA[] where preA[i] will store the profit when the items A[0…i] are sold in market A.
Create a suffix sum array suffB[] where suffB[i] will store the profit when the items B[i…n-1] are sold in market B.
Now the problem gets reduced to finding an index i such that (preA[i] + suffB[i + 1]) is maximum.

Below is the implementation of the above approach:

C++

// C++ implementation of the approach
#include <bits/stdc++.h>
using namespace std;
 
// Function to calculate max profit
int maxProfit(int profitA[], int profitB[], int n)
{
 
    // Prefix sum array for profitA[]
    int preSum[n];
    preSum[0] = profitA[0];
    for (int i = 1; i < n; i++) {
        preSum[i] = preSum[i - 1] + profitA[i];
    }
 
    // Suffix sum array for profitB[]
    int suffSum[n];
    suffSum[n - 1] = profitB[n - 1];
    for (int i = n - 2; i >= 0; i--) {
        suffSum[i] = suffSum[i + 1] + profitB[i];
    }
 
    // If all the items are sold in market A
    int res = preSum[n - 1];
 
    // Find the maximum profit when the first i
    // items are sold in market A and the
    // rest of the items are sold in market
    // B for all possible values of i
    for (int i = 1; i < n - 1; i++) {
        res = max(res, preSum[i] + suffSum[i + 1]);
    }
 
    // If all the items are sold in market B
    res = max(res, suffSum[0]);
 
    return res;
}
 
// Driver code
int main()
{
    int profitA[] = { 2, 3, 2 };
    int profitB[] = { 10, 30, 40 };
    int n = sizeof(profitA) / sizeof(int);
 
    // Function to calculate max profit
    cout << maxProfit(profitA, profitB, n);
 
    return 0;
}

Java

// Java implementation of the approach 
class GFG 
{
    // Function to calculate max profit 
    static int maxProfit(int profitA[], int profitB[], int n) 
    { 
     
        // Prefix sum array for profitA[] 
        int preSum[] = new int[n]; 
        preSum[0] = profitA[0]; 
        for (int i = 1; i < n; i++) 
        { 
            preSum[i] = preSum[i - 1] + profitA[i]; 
        } 
     
        // Suffix sum array for profitB[] 
        int suffSum[] = new int[n]; 
        suffSum[n - 1] = profitB[n - 1]; 
        for (int i = n - 2; i >= 0; i--)
        { 
            suffSum[i] = suffSum[i + 1] + profitB[i]; 
        } 
     
        // If all the items are sold in market A 
        int res = preSum[n - 1]; 
     
        // Find the maximum profit when the first i 
        // items are sold in market A and the 
        // rest of the items are sold in market 
        // B for all possible values of i 
        for (int i = 1; i < n - 1; i++) 
        { 
            res = Math.max(res, preSum[i] + suffSum[i + 1]); 
        } 
     
        // If all the items are sold in market B 
        res = Math.max(res, suffSum[0]); 
     
        return res; 
    } 
     
    // Driver code 
    public static void main (String[] args)
    { 
        int profitA[] = { 2, 3, 2 }; 
        int profitB[] = { 10, 30, 40 }; 
        int n = profitA.length; 
     
        // Function to calculate max profit 
        System.out.println(maxProfit(profitA, profitB, n)); 
    } 
}
 
// This code is contributed by AnkitRai01

Python3

# Python3 implementation of the approach 
 
# Function to calculate max profit 
def maxProfit(profitA, profitB, n) :
 
    # Prefix sum array for profitA[] 
    preSum = [0] * n; 
    preSum[0] = profitA[0]; 
     
    for i in range(1, n) :
        preSum[i] = preSum[i - 1] + profitA[i]; 
 
    # Suffix sum array for profitB[] 
    suffSum = [0] * n; 
    suffSum[n - 1] = profitB[n - 1]; 
     
    for i in range(n - 2, -1, -1) : 
        suffSum[i] = suffSum[i + 1] + profitB[i]; 
 
    # If all the items are sold in market A 
    res = preSum[n - 1]; 
 
    # Find the maximum profit when the first i 
    # items are sold in market A and the 
    # rest of the items are sold in market 
    # B for all possible values of i 
    for i in range(1 , n - 1) :
        res = max(res, preSum[i] + suffSum[i + 1]); 
 
    # If all the items are sold in market B 
    res = max(res, suffSum[0]); 
 
    return res; 
 
# Driver code 
if __name__ == "__main__" : 
 
    profitA = [ 2, 3, 2 ]; 
    profitB = [ 10, 30, 40 ]; 
    n = len(profitA); 
 
    # Function to calculate max profit 
    print(maxProfit(profitA, profitB, n)); 
 
# This code is contributed by AnkitRai01

C#

// C# implementation of the approach 
using System;
 
class GFG 
{
     
    // Function to calculate max profit 
    static int maxProfit(int []profitA, 
                        int []profitB, int n) 
    { 
     
        // Prefix sum array for profitA[] 
        int []preSum = new int[n]; 
        preSum[0] = profitA[0]; 
        for (int i = 1; i < n; i++) 
        { 
            preSum[i] = preSum[i - 1] + profitA[i]; 
        } 
     
        // Suffix sum array for profitB[] 
        int []suffSum = new int[n]; 
        suffSum[n - 1] = profitB[n - 1]; 
        for (int i = n - 2; i >= 0; i--)
        { 
            suffSum[i] = suffSum[i + 1] + profitB[i]; 
        } 
     
        // If all the items are sold in market A 
        int res = preSum[n - 1]; 
     
        // Find the maximum profit when the first i 
        // items are sold in market A and the 
        // rest of the items are sold in market 
        // B for all possible values of i 
        for (int i = 1; i < n - 1; i++) 
        { 
            res = Math.Max(res, preSum[i] + 
                            suffSum[i + 1]); 
        } 
     
        // If all the items are sold in market B 
        res = Math.Max(res, suffSum[0]); 
     
        return res; 
    } 
     
    // Driver code 
    public static void Main(String[] args)
    { 
        int []profitA = { 2, 3, 2 }; 
        int []profitB = { 10, 30, 40 }; 
        int n = profitA.Length; 
     
        // Function to calculate max profit 
        Console.WriteLine(maxProfit(profitA, profitB, n)); 
    } 
}
 
// This code is contributed by 29AjayKumar

Output:

Alternate Implementation in Python :

Python3

# Python3 implementation of the approach 
def maxProfit (a, b, n):
 
    # Max profit will be saved here
    maxP = -1
 
    # loop to check all possible combinations of sales 
    for i in range(0, n+1):
 
        # the sum of the profit after the sale
        # for products 0 to i in market A 
        sumA = sum(a[:i])
 
        # the sum of the profit after the sale 
        # for products i to n in market B
        sumB = sum(b[i:])
 
        # Replace the value of Max Profit with a
        # bigger value among maxP and sumA+sumB
        maxP = max(maxP, sumA+sumB)
 
    #  Return the value of Max Profit 
    return maxP
  
# Driver Program 
if __name__ == "__main__" :  
    a = [2, 3, 2]
    b = [10, 30, 40]
    print(maxProfit(a, b, 4))
      
# This code is contributed by aman_malhotra

Output:

Time Complexity : O(N)

Auxiliary Space : O(N)

My Personal Notes

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