leetcode筆記：House Robber

一. 題目描述

You are a professional robber planning to rob houses along a street. Each house has a certain amount of money stashed, the only constraint stopping you from robbing each of them is that adjacent houses have security system connected andit will automatically contact the police if two adjacent houses were broken into on the same night.

Given a list of non-negative integers representing the amount of money of each house, determine the maximum amount of money you can rob tonightwithout alerting the police.

二. 題目分析

動態規劃，設置maxV[i]表示到第i個房子位置，最大收益。

遞推關系為maxV[i] = max(maxV[i-2]+num[i], maxV[i-1])

注：可能會對上述遞推關系產生疑問，是否存在如下可能性，maxV[i-1]並不含num[i-1]？

在這種情況下maxV[i-1]等同於maxV[i-2]，因此前者更大。

三. 示例代碼

class Solution {
public:
    int rob(vector &num) {
        int n = num.size();
        if(n == 0)
            return 0;
        else if(n == 1)
            return num[0];
        else
        {
            vector maxV(n, 0);
            maxV[0] = num[0];
            maxV[1] = max(num[0], num[1]);
            for(int i = 2; i < n; i ++)
                maxV[i] = max(maxV[i-2]+num[i], maxV[i-1]);
            return maxV[n-1];
        }
    }
};