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Maximum profit after buying and selling stocks with transaction fees

  • Difficulty Level : Medium
  • Last Updated : 25 Jul, 2021

Given an array of positive integers containing the price of stocks and transaction fee, the task is to find the maximum profit and the difference of days on which you are getting the maximum profit. 
Examples: 
 

Input: arr[] = {6, 1, 7, 2, 8, 4}
      transactionFee = 2
Output: 8 1

Input: arr[] = {7, 1, 5, 3, 6, 4}
       transactionFee = 1
Output: 5 1

 

 

Explanation: Considering the first example: arr[] = {6, 1, 7, 2, 8, 4}, transactionFee = 2 
 



  1. If we buy and sell on the same day, we will not get any profit that’s why the difference between the buying and selling must be at least 1.
  2. With the difference of 1 day, if we buy a stock of rupees 1 and sell it rupees 7 with the difference of day 1 which mean purchase on day 2 and sell it next day,then after paying the transaction fee of rupees 2 i.e. 7-1-2=4, we will get profit of 4 rupees, same as if we purchase on day 4 and sell it on day 5 with the difference of day 1 then we get profit of 4 rupees. So the total profit is 8 rupees.
  3. With the difference of 2 days, we will not get any profit.
  4. With the difference of 3 days, if we buy stock of rupees 1 and sell it rupees 8 with the difference of 3 days which mean purchase on day 2 and sell it after 3 days then maximum profit after paying the transaction fee of rupees 2 i.e.8-1-2=5 we will get the profit of 5 rupees.
  5. With the difference of 4 days, if we buy stocks of rupees 1 and sell it rupees 4 with the difference of 4 days which mean purchase on day 2 and sell it after 4 days then after paying the transaction fee of rupees 2 i.e. 4-1-2=1, we will get profit of 1 rupees.
  6. With the difference of 5 days, we will not get any profit.

Approach: 
 

  1. Traverse the whole array with the difference of each day.
  2. Check the profit by subtracting the price of each day including transaction fee.
  3. Trace the maximum profit and store the diff_days on which we are getting the maximum profit.
  4. Repeat the above steps until the loop terminates.

Below is the implementation of above approach:
 

C++




// C++ implementation of above approach
#include <bits/stdc++.h>
using namespace std;
 
int max_profit(int a[],int b[],int n,int fee)
{
int i, j, profit;
 
int l, r, diff_day = 1, sum = 0;
 
//b[0] will contain the maximum profit
    b[0]=0;                
//b[1] will contain the day
//on which we are getting the maximum profit
    b[1]=diff_day;
for(i=1;i<n;i++)
{
    l=0;
    r=diff_day;
        sum=0;    
 
    for(j=n-1;j>=i;j--)
        {
        //here finding the max profit
            profit=(a[r]-a[l])-fee;
     
        //if we get less then or equal to zero
        // it means we are not getting the profit
            if(profit>0)    
                {
                sum=sum+profit;
                }
            l++;
     
            r++;
            }
//check if sum is greater then maximum then store the new maximum
    if(b[0] < sum)
{
    b[0] = sum;
     
    b[1] = diff_day;
 
    }
diff_day++;
}
 
return 0;
}
 
// Driver code
int main()
{
    int arr[] = { 6, 1, 7, 2, 8, 4 };
    int n = sizeof(arr) / sizeof(arr[0]);
    int b[2];
    int tranFee = 2;
 
    max_profit(arr, b, n, tranFee);
 
    cout << b[0] << ", " << b[1] << endl;
 
    return 0;
}

Java




// Java implementation of above approach
import java.util.*;
 
class solution
{
 
static int max_profit(int a[],int b[],int n,int fee)
{
int i, j, profit;
 
int l, r, diff_day = 1, sum = 0;
 
//b[0] will contain the maximum profit
    b[0]=0;                
//b[1] will contain the day
//on which we are getting the maximum profit
    b[1]=diff_day;
for(i=1;i<n;i++)
{
    l=0;
    r=diff_day;
        sum=0;    
 
    for(j=n-1;j>=i;j--)
        {
        //here finding the max profit
            profit=(a[r]-a[l])-fee;
     
        //if we get less then or equal to zero
        // it means we are not getting the profit
            if(profit>0)    
                {
                sum=sum+profit;
                }
            l++;
     
            r++;
            }
//check if sum is greater then maximum then store the new maximum
    if(b[0] < sum)
{
    b[0] = sum;
     
    b[1] = diff_day;
 
    }
diff_day++;
}
 
return 0;
}
 
// Driver code
public static void main(String args[])
{
    int arr[] = { 6, 1, 7, 2, 8, 4 };
    int n = arr.length;
    int[] b = new int[2];
    int tranFee = 2;
 
    max_profit(arr, b, n, tranFee);
 
    System.out.println(b[0]+", "+b[1]);
 
}
}
 
//This code is contributed by Surendra_Gangwar

Python3




# Python3 implementation of above approach
def max_profit(a, b, n, fee):
 
    i, j, profit = 1, n - 1, 0
     
    l, r, diff_day = 0, 0, 1
     
    # b[0] will contain the maximum profit
    b[0] = 0   
     
    # b[1] will contain the day on which
    # we are getting the maximum profit
    b[1] = diff_day
 
    for i in range(1, n):
        l = 0
        r = diff_day
        Sum = 0
     
        for j in range(n - 1, i - 1, -1):
             
            # here finding the max profit
            profit = (a[r] - a[l]) - fee
         
            # if we get less then or equal to zero
            # it means we are not getting the profit
            if(profit > 0):
                Sum = Sum + profit
                     
            l += 1
            r += 1
                 
        # check if Sum is greater then maximum
        # then store the new maximum
        if(b[0] < Sum):
            b[0] = Sum
            b[1] = diff_day
     
    diff_day += 1
     
    return 0
     
# Driver code
arr = [6, 1, 7, 2, 8, 4]
n = len(arr)
b = [0 for i in range(2)]
tranFee = 2
 
max_profit(arr, b, n, tranFee)
 
print(b[0], ",", b[1])
 
# This code is contributed by
# Mohit kumar 29

C#




// C# implementation of above approach
using System;
 
class GFG
{
     
static int max_profit(int []a, int []b,
                      int n, int fee)
{
int i, j, profit;
 
int l, r, diff_day = 1, sum = 0;
 
// b[0] will contain the
// maximum profit
b[0] = 0;
 
// b[1] will contain the day on which
// we are getting the maximum profit
b[1] = diff_day;
for(i = 1; i < n; i++)
{
    l = 0; r = diff_day; sum = 0;
 
    for(j = n - 1; j >= i; j--)
        {
            // here finding the max profit
            profit = (a[r] - a[l]) - fee;
     
            // if we get less then or equal
            // to zero it means we are not
            // getting the profit
            if(profit > 0)
            {
                sum = sum + profit;
            }
            l++;
     
            r++;
        }
         
    // check if sum is greater then maximum
    // then store the new maximum
    if(b[0] < sum)
    {
        b[0] = sum;
         
        b[1] = diff_day;
     
    }
    diff_day++;
}
 
return 0;
}
 
// Driver code
static public void Main ()
{
    int []arr = { 6, 1, 7, 2, 8, 4 };
    int n = arr.Length;
    int[] b = new int[2];
    int tranFee = 2;
     
    max_profit(arr, b, n, tranFee);
     
    Console.WriteLine(b[0] + ", " + b[1]);
}
}
 
// This code is contributed by Sachin

PHP




<?php
// PHP implementation of above approach
 
function max_profit(&$a, &$b, $n, $fee)
{
    $diff_day = 1;
    $sum = 0;
     
    // b[0] will contain the maximum profit
    $b[0] = 0;
     
    // b[1] will contain the day on which we
    // are getting the maximum profit
    $b[1] = $diff_day;
     
    for($i = 1; $i < $n; $i++)
    {
        $l = 0;
        $r = $diff_day;
        $sum = 0;
     
        for($j = $n - 1; $j >= $i; $j--)
        {
            // here finding the max profit
            $profit = ($a[$r] - $a[$l]) - $fee;
     
            // if we get less then or equal to zero
            // it means we are not getting the profit
            if($profit > 0)    
            {
                $sum = $sum + $profit;
            }
            $l++;
     
            $r++;
        }
         
        // check if sum is greater then maximum
        // then store the new maximum
        if($b[0] < $sum)
        {
            $b[0] = $sum;
             
            $b[1] = $diff_day;
        }
        $diff_day++;
    }
 
}
 
// Driver code
$arr = array(6, 1, 7, 2, 8, 4 );
$n = sizeof($arr);
$b = array();
$tranFee = 2;
 
max_profit($arr, $b, $n, $tranFee);
echo($b[0]);
echo(", ");
echo($b[1]);
 
// This code is contributed
// by Shivi_Aggarwal
?>

Javascript




<script>
 
// Javascript implementation of above approach
 
    function max_profit(a , b , n , fee) {
        var i, j, profit;
 
        var l, r, diff_day = 1, sum = 0;
 
        // b[0] will contain the maximum profit
        b[0] = 0;
        // b[1] will contain the day
        // on which we are getting the maximum profit
        b[1] = diff_day;
        for (i = 1; i < n; i++) {
            l = 0;
            r = diff_day;
            sum = 0;
 
            for (j = n - 1; j >= i; j--) {
                // here finding the max profit
                profit = (a[r] - a[l]) - fee;
 
                // if we get less then or equal to zero
                // it means we are not getting the profit
                if (profit > 0) {
                    sum = sum + profit;
                }
                l++;
 
                r++;
            }
            // check if sum is greater then maximum
            // then store the new maximum
            if (b[0] < sum) {
                b[0] = sum;
 
                b[1] = diff_day;
 
            }
            diff_day++;
        }
 
        return 0;
    }
 
    // Driver code
     
        var arr = [ 6, 1, 7, 2, 8, 4 ];
        var n = arr.length;
        var b = Array(2).fill(0);
        var tranFee = 2;
 
        max_profit(arr, b, n, tranFee);
 
        document.write(b[0] + ", " + b[1]);
 
 
// This code contributed by Rajput-Ji
 
</script>
Output: 
8, 1

 

Time complexity: O(N2)

Better approach:

Same as https://www.geeksforgeeks.org/stock-buy-sell/ but adds diff days as well

Python3




from typing import List, Tuple
 
def max_profit(prices: List[int], transaction_fee:int = 0) -> Tuple[int, int]:
    n = len(prices)
    start = 0
    end = 1
    profit = 0
    max_profit_till_now = float('-inf')
    diff = 0
    while start < n - 1 and end < n:
        while start < n - 1 and prices[start] > prices[start + 1]:
            start += 1
        end = start + 1
        while end < n - 1 and prices[end] < prices[end + 1]:
            end += 1
            if end == n:
                continue
        cur_profit = prices[end] - prices[start] - transaction_fee
        if cur_profit > 0:
            profit += cur_profit
        if max_profit_till_now < cur_profit:
            max_profit_till_now = cur_profit
            diff = end - start
        start = end + 1
    return profit, diff
print(max_profit([6, 1, 7, 2, 8, 4], 2))

Output:

(8, 1)

Time complexity: O(N)

Auxiliary Space: O(1)
 

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