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Multiple States V

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 (i.e., buy one and sell one share of the stock), design an algorithm to find the maximum profit. Note that you cannot sell a stock before you buy one.

https://leetcode.com/problems/best-time-to-buy-and-sell-stock/description/

Example I

Input: [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. Not 7-1 = 6, as selling price needs to be larger than buying price.

Example II:

Input: [7,6,4,3,1]
Output: 0
Explanation: In this case, no transaction is done, i.e. max profit = 0.

Questions

  • LeetCode - 121. Best Time to Buy and Sell Stock

Transform Function

dp[i] = prices[i] - min_prices

Template I

class Solution {
    public int maxProfit(int[] prices) {
        int n = prices.length;
        int[] dp = new int[n + 1];
        dp[0] = Integer.MAX_VALUE;
        int min = Integer.MAX_VALUE, res = 0;

        for(int i = 1; i <= n; i++) {
            min = Math.min(min, prices[i - 1]);
            dp[i] = min;
            res = Math.max(res, prices[i - 1] - dp[i - 1]);
        }
        return res;
    }
}

Optimized

min = min_price_before
res = Math.max(prices[i] - min)

Template II

class Solution {
    public int maxProfit(int[] prices) {
        int min = Integer.MAX_VALUE, res = 0;
        for(int p : prices) {
            min = Math.min(p, min);
            res = Math.max(p - min, res);
        }
        return res;
    }
}