Best Time to Buy and Sell Stock

LeetCode 121 | Difficulty: Easy

Easy

Problem Description

You are given an array prices where prices[i] is the price of a given stock on the i^th day.

You want to maximize your profit by choosing a single day to buy one stock and choosing a different day in the future to sell that stock.

Return the maximum profit you can achieve from this transaction. If you cannot achieve any profit, return 0.

Example 1:

Input: prices = [7,1,5,3,6,4]
Output: 5
Explanation: Buy on day 2 (price = 1) and sell on day 5 (price = 6), profit = 6-1 = 5.
Note that buying on day 2 and selling on day 1 is not allowed because you must buy before you sell.

Example 2:

Input: prices = [7,6,4,3,1]
Output: 0
Explanation: In this case, no transactions are done and the max profit = 0.

Constraints:

- `1 <= prices.length <= 10^5`

- `0 <= prices[i] <= 10^4`

Topics: Array, Dynamic Programming

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Approach

Dynamic Programming

Break the problem into overlapping subproblems. Define a state (what information do you need?), a recurrence (how does state[i] depend on smaller states?), and a base case. Consider both top-down (memoization) and bottom-up (tabulation) approaches.

When to use

Optimal substructure + overlapping subproblems (counting ways, min/max cost, feasibility).

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Solutions

Solution 1: C# (Best: 112 ms)

Metric	Value
Runtime	112 ms
Memory	23.1 MB
Date	2019-02-20

Solution

public class Solution {
    public int MaxProfit(int[] prices) {
    if(prices.Length==0) return 0;
        int minSoFar = prices[0];
    int maxProfitSoFar = 0;
    
    for (int i = 1; i < prices.Length; i++)
    {
        maxProfitSoFar = Math.Max(maxProfitSoFar, prices[i] - minSoFar);
        minSoFar = Math.Min(prices[i], minSoFar);
    
    }
    
    return maxProfitSoFar;
    }
}

📜 2 more C# submission(s)

Submission (2019-02-20) — 180 ms, 26 MB

public class Solution {
    public int MaxProfit(int[] prices) {
    if(prices.Length==0) return 0;
        int minSoFar = prices[0];
    int maxProfitSoFar = 0;
    
    for (int i = 1; i < prices.Length; i++)
    {
        maxProfitSoFar = Math.Max(maxProfitSoFar, prices[i] - minSoFar);
        minSoFar = Math.Min(prices[i], minSoFar);
        Console.WriteLine($"{prices[i]} {maxProfitSoFar} {minSoFar}");
    }
    
    return maxProfitSoFar<0 ? 0 : maxProfitSoFar;
    }
}

Submission (2022-02-16) — 220 ms, 48.1 MB

public class Solution {
    public int MaxProfit(int[] prices) {
    if(prices.Length==0) return 0;
        int minSoFar = prices[0];
    int maxProfitSoFar = 0;
    
    for (int i = 1; i < prices.Length; i++)
    {
        maxProfitSoFar = Math.Max(maxProfitSoFar, prices[i] - minSoFar);
        minSoFar = Math.Min(prices[i], minSoFar);
    
    }
    
    return maxProfitSoFar;
    }
}

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Complexity Analysis

Approach	Time	Space
Dynamic Programming	$O(n)$	$O(n)$

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Interview Tips

Key Points

• Start by clarifying edge cases: empty input, single element, all duplicates.
• Define the DP state clearly. Ask: "What is the minimum information I need to make a decision at each step?"
• Consider if you can reduce space by only keeping the last row/few values.