# 121 Buy and Sell Stock

input是一個int array，記錄連續n天的股票價格，

題目說可以買進再賣出，問最大淨利是多少。

Concept:

所以關鍵就是要在最低點買進，最高點賣出，且最低點index要比最高點index小。

用一個int min記錄目前最低點，一個int[] dp記錄當天最大淨利，一個int profit記錄最大淨利。

Pseudocode:

dp[0] = prices[0]
min = prices[0]
for each element in prices
    dp[i] = prices[i]-min
    min = price[i] < min ? price[i] : min
    profit = dp[i] > profit ? dp[i] : profit

return profit

完整程式碼：

public class Solution {
    public int maxProfit(int[] prices) {
        if(prices.length == 0) return 0;
        int[] dp = new int[prices.length];
        dp[0] = prices[0];
        int min = prices[0];
        int profit = 0;
        for(int i=1; i<prices.length; i++){
            dp[i] = prices[i] - min;
            min = prices[i] < min ? prices[i] : min;
            profit = dp[i] > profit ? dp[i] : profit;
        }

        return profit;
    }
}

Optimize: 其實可以不用dp陣列來記，用一個變數來記profit就可以了

public class Solution {
    public int maxProfit(int[] prices) {
        int ans=0;
        if(prices.length==0)    return ans;

        int bought=prices[0];
        for(int i=1;i<prices.length;i++){
            if(prices[i]>bought){
                if(ans<(prices[i]-bought))
                    ans=prices[i]-bought;
            }
            else
                bought=prices[i];
        }
     return ans;
    }
}