剑指 Offer 63. 股票的最大利润

思路

方法一：暴力法

class Solution {
public:
    int maxProfit(vector<int>& prices) {
        int n = (int)prices.size(), ans = 0;
        for (int i = 0; i < n; ++i){
            for (int j = i + 1; j < n; ++j) {
                ans = max(ans, prices[j] - prices[i]);
            }
        }
        return ans;
    }
};

方法二：动态规划

class Solution {
public:
    int maxProfit(vector<int>& prices) {
        if(prices.size() < 2)    //这种情况无法交易
            return 0;
            
        vector<int> dp(prices.size(), 0);
        int minPrice = prices[0];
        dp[0] = 0;

        for(int i = 1; i < prices.size(); ++i) {
            if(prices[i] < minPrice)
                minPrice = prices[i];
            
            dp[i] = max(dp[i-1], prices[i] - minPrice);
        }

        return dp[prices.size()-1];
    }
}

复杂度分析

时间复杂度：O(n)

空间复杂度：O(n)

空间优化

class Solution {
public:
    int maxProfit(vector<int>& prices) {
        if(prices.size() < 2)
            return 0;

        int minPrice = prices[0];
        int profit = 0;

        for(int i = 1; i < prices.size(); ++i) {
            if(prices[i] < minPrice)
                minPrice = prices[i];
            
            profit = max(profit, prices[i] - minPrice);
        }

        return profit;
    }
};

复杂度分析

时间复杂度：O(n)

空间复杂度：O(1)