121.md

121. Best Time to Buy and Sell Stock

Description

Say you have an array for which the ith element is the price of a given stock on day i.

If you were only permitted to complete at most one transaction (ie, buy one and sell one share of the stock), design an algorithm to find the maximum profit.

Example 1:

Input: [7, 1, 5, 3, 6, 4]
Output: 5

max. difference = 6-1 = 5 (not 7-1 = 6, as selling price needs to be larger than buying price)

Example 2:

Input: [7, 6, 4, 3, 1]
Output: 0

In this case, no transaction is done, i.e. max profit = 0.

Thinking Process

1. Iterate the array, keep track of the minimum value so far
2. Assume we are selling on day i, the max profits for selling on day i would be prices[i] - minSoFar

Code

public class Solution {
    public int maxProfit(int[] prices) {
        int n = prices.length;
        int minPrice = Integer.MAX_VALUE;
        int maxProfit = 0;
        
        for(int i = 0; i < n; i++){
            minPrice = Math.min(minPrice, prices[i]);
            maxProfit = Math.max(maxProfit, prices[i] - minPrice);
        }
        
        return maxProfit;
    }
}

Complexity

1. Time complexity is O(n)
2. Space complexity is O(1)