123. Best Time to Buy and Sell Stock III

题目：

Say you have an array for which the ith 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).

链接： http://leetcode.com/problems/best-time-to-buy-and-sell-stock-iii/

题解：

一上来就没有头绪，查了一些资料以后发现大家都是用dp，可是怎么用dp才能又简洁又漂亮。不少朋友都是用类似Best Time to Buy and Sell Stock I的方法，正序来一次，逆序再来一次，然后求解，这样可以解决只能卖2次的情况。这个方法也跟Trap Rain Water很像。

Time Complexity - O(n)， Space Complexity - O(n)。

public class Solution {
public int maxProfit(int[] prices) {
if(prices == null || prices.length < 2)
return 0;
int len = prices.length;
int localMin = prices[0];
int[] maxProfit = new int[len];

for(int i = 1; i < len; i++) {
maxProfit[i] = Math.max(maxProfit[i - 1], prices[i] - localMin);
localMin = Math.min(localMin, prices[i]);
}

int localMax = prices[len - 1];
int res = 0;

for(int i = len - 2; i >= 0; i--) {
localMax = Math.max(localMax, prices[i]);
res = Math.max(res, localMax - prices[i] + maxProfit[i]);
}

return res;
}
}

还有更好的方法，我们可以用几个变量来代替辅助数组。 - 见discussion区weijiac。

Time Complexity - O(n)， Space Complexity - O(1)。

之后还有Best Time to Buy and Sell Stock IV， 看了discussion里面有一篇weijiac的很好很受启发。他说自己是从"Single Number II"里想到一些类似的思路。我想可不可以像climb stairs一样，从只能走1，2步推广到只能走1，2，3步，至k步， 来思考下道题目。 还要好好想一想。试了一下用weijiac的方法在 IV里会超时，需要特殊处理，再继续研究吧。

Reference：
https://leetcode.com/discuss/25627/dp-o-kn-time-o-n-space-cpp-solution https://leetcode.com/discuss/18159/sharing-my-simple-and-clear-c-solution https://leetcode.com/discuss/48151/my-c-solution-o-n-time-o-1-space-8ms https://leetcode.com/discuss/18330/is-it-best-solution-with-o-n-o-1 http://blog.csdn.net/linhuanmars/article/details/23236995 http://blog.csdn.net/fightforyourdream/article/details/14503469 http://www.programcreek.com/2014/02/leetcode-best-time-to-buy-and-sell-stock-iii-java/ https://leetcode.com/discuss/38150/simple-dp-8ms-solution-for-best-time-to-buy-and-sell-stock-iii https://leetcode.com/discuss/21098/java-solution-with-just-two-traverses https://leetcode.com/discuss/24330/a-clear-concise-dp-solution https://leetcode.com/discuss/31271/a-clear-o-n-time-and-space-java-solution https://leetcode.com/discuss/10427/share-my-simple-o-n-time-solution https://leetcode.com/discuss/14806/solution-sharing-commented-code-o-n-time-and-o-n-space https://leetcode.com/discuss/15290/a-o-n-time-and-o-1-space-greedy-algorithm https://leetcode.com/discuss/1381/any-solutions-better-than-o-n-2 https://leetcode.com/discuss/2619/dont-need-dp-to-solve-it-within-o-n http://www.cnblogs.com/springfor/p/3877068.html http://www.programcreek.com/2014/03/leetcode-best-time-to-buy-and-sell-stock-iv-java/ https://leetcode.com/discuss/25603/a-concise-dp-solution-in-java https://leetcode.com/discuss/15153/a-clean-dp-solution-which-generalizes-to-k-transactions