198，House Robber

一、题目

Given a list of non-negative integers representing the amount of money of each house, determine the maximum amount of money you can rob tonight without alerting the police.

二、分析

　　f(k): 抢劫到第k个房间时得到的最大钱数

　　则有以下的递推关系：　

f(0) = nums[0]
f(1) = max(num[0], num[1])
f(k) = max( f(k-2) + nums[k], f(k-1) )

三、代码

 1 class Solution {
 2 public:
 3     int rob(vector<int>& nums) {
 4         int length = nums.size();
 5         if (length == 0)
 6             return 0;
 7         vector<int> money(length, nums[0]);
 8         if (length == 1)
 9             return nums[0];
10         else {
11             money[1] = max(nums[0], nums[1]);
12             for (int i = 2; i < length; ++i) {
13                 money[i] = max(money[i-1], money[i-2] + nums[i]);
14             }
15         }
16         return money[length - 1];
17
18     }
19 };

2）对上面程序的优化

 1 class Solution {
 2 public:
 3     int rob(vector<int>& nums) {
 4         int n = nums.size(), pre = 0, cur = 0;
 5         for (int i = 0; i < n; i++) {
 6             int temp = max(pre + nums[i], cur);
 7             pre = cur;
 8             cur = temp;
 9         }
10         return cur;
11     }
12 };

3)python实现

1 class Solution:
2
3     def rob(self, nums):
4
5         last, now = 0, 0
6
7         for i in nums: last, now = now, max(last + i, now)
8
9         return now