Given an array representing prices of the stock on different days, find the maximum profit that can be earned by performing maximum of one transaction. A transaction consists of activity of buying and selling the stock on different or same days. For example in this array - {100, 80, 120, 130, 70, 60, 100, 125} the price of the stock on day-1 is 100, on day-2 is 80 and so on. The maximum profit that could be earned in this window is 65 (buy at 60 and sell at 125).

For price array - {100, 80, 70, 65, 60, 55, 50}, maximum profit that could be earned is 0.

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Algorithm/Insights

For the stock price array - {100, 80, 120, 130, 70, 60, 100, 125}, maximum profit obtainable at the end of each day is shown below.

If you observe above chart carefully, you should be able to notice that: for any given day, maximum profit obtainable is maximum of 1.Maximum profit obtained till previous day, 2.Stock price on that day - minimum stock price so far.

Therefore, to find out the maximum profit obtainable for a given window, all we need to is to keep track of minimum stock price seen so far (starting from day-1) and maximum profit obtained so far. Maximum profit obtained so far can be computed using above observation. Maximum profit obtained so far is initialized to 0 and minimum stock price seen so far is initialized to MAX_VALUE.

Please checkout function maximumProfit(int[] stockPrices) in code snippet for implementation details.

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Algorithm Visualization

Code Snippet

package com.ideserve.virendra.questions;
public class BuyAndSellStocks
{
public static int maximumProfit(int[] stockPrices)
{
int profit = 0;
int minimumPrice = Integer.MAX_VALUE;
/*
* for any given day, maximum profit obtainable is -
* maximum of(maximum profit obtained till previous day, stock price on that day - minimum stock price so far)
*/
for(int i = 0; i < stockPrices.length; i++)
{
profit = Math.max(profit, stockPrices[i] - minimumPrice);
minimumPrice = Math.min(stockPrices[i], minimumPrice);
}
return profit;
}
public static void main(String args[])
{
int[] stockPrices = {100, 80, 120, 130, 70, 60, 100, 125};
System.out.println("maximum profit that could be obtained is: " + maximumProfit(stockPrices));
}
}

Order of the Algorithm

Time Complexity is O(n) Space Complexity is O(1)

Contribution

Sincere thanks from IDeserve community to Virendra Karappa for compiling current post.

Virendra Karappa

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