**Leetcode 123 Best Time to Buy and Sell Stock III

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

O(n^2)的做法就不解释了，枚举划分的位置即可。但是关键点在最多两次，所以可以考虑前缀后缀和。

先说O(n^2)的

class Solution {
public:
int maxProfitForOne(vector<int>& prices, int l, int r) {
if (r - l == 0) return 0;
int ret = 0, cur_min = prices[l];
for (int i = l+1; i < r; i++) {
ret = max(ret, prices[i] - cur_min);
if (prices[i] < cur_min) {
cur_min = min(prices[i], cur_min);
}
}
return ret;
}

bool needJudge(vector<int>& prices, int idx) {
idx -= 1;
if (idx == 0 || idx == prices.size()-1) return true;
if (prices[idx] >= prices[idx - 1] && prices[idx] > prices[idx + 1])
return true;
else
return false;
}

int maxProfit(vector<int>& prices) {
if (prices.size() <= 1) return 0;
int ret = 0, left = 0, right = 0;
for (int sp = 1; sp < prices.size() + 1; sp ++) {
if (!needJudge(prices, sp)) continue;
left = maxProfitForOne( prices, 0, sp );
right = maxProfitForOne( prices, sp, prices.size() );
ret = max( ret, left + right );
}

return ret;
}
};

O(n)的 维护前缀后缀，注意边界。。。当时我想到的一个O(4*n)的分情况比较多

class Solution {
public:

int maxProfit(vector<int>& prices) {

if (prices.size() <= 1) return 0;

int prefix[prices.size()+1], suffix[prices.size()+1];

prefix[0] = 0; suffix[prices.size()] = 0;
int cur_min = prices[0], cur_ans = 0;
for (int i = 1; i < prices.size(); i++) {
cur_ans = max(cur_ans, prices[i] - cur_min);
prefix[i] = cur_ans;
if (prices[i] < cur_min) cur_min = prices[i];
}

int cur_max = prices[prices.size()-1];
cur_ans = 0;
for (int i = prices.size() - 1; i >= 0; i--) {
cur_ans = max(cur_ans, cur_max - prices[i]);
suffix[i] = cur_ans;
if (prices[i] > cur_max) cur_max = prices[i];
}
int ret = 0;
for (int i = 0; i < prices.size(); i++) {
ret = max(ret, prefix[i] + suffix[i+1]);
}

return ret;
}
};

然后发现还有更好的解：空间O(1)时间O(n)
https://discuss.leetcode.com/topic/5934/is-it-best-solution-with-o-n-o-1 http://blog.csdn.net/u012501459/article/details/46514309