## Best Time to Buy and Sell Stock III

### 描述

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

Design an algorithm to find the maximum profit. You may complete at most two transactions.

Note: You may not engage in multiple transactions at the same time (ie, you must sell the stock before you buy again).

### 分析

### 代码

{% if book.java %}
{% codesnippet "./code/best-time-to-buy-and-sell-stock-iii."+book.suffix, language=book.suffix %}{% endcodesnippet %}
{% endif %}

{% if book.cpp %}
cpp
// Best Time to Buy and Sell Stock III
// 时间复杂度O(n)，空间复杂度O(n)
class Solution {
public:
int maxProfit(vector& prices) {
if (prices.size() < 2) return 0;

const int n = prices.size();
vector f(n, 0);
vector g(n, 0);

for (int i = 1, valley = prices[0]; i < n; ++i) {
valley = min(valley, prices[i]);
f[i] = max(f[i - 1], prices[i] - valley);
}

for (int i = n - 2, peak = prices[n - 1]; i >= 0; --i) {
peak = max(peak, prices[i]);
g[i] = max(g[i], peak - prices[i]);
}

int max_profit = 0;
for (int i = 0; i < n; ++i)
max_profit = max(max_profit, f[i] + g[i]);

return max_profit;
}
};

{% endif%}

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