198. House Robber

Leetcode Dynamic Programming

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 and it 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 tonight without alerting the police.

Example 1:

Input: [1,2,3,1]
Output: 4
Explanation: Rob house 1 (money = 1) and then rob house 3 (money = 3).
             Total amount you can rob = 1 + 3 = 4.

Example 2:

Input: [2,7,9,3,1]
Output: 12
Explanation: Rob house 1 (money = 2), rob house 3 (money = 9) and rob house 5 (money = 1).
             Total amount you can rob = 2 + 9 + 1 = 12.

分析

这道题目和Maximum weight independent set of path graph一摸一样！真是佩服出题人，能改编成这样。

题目中的不能抢相邻的房间，相当于构建一个独立集。要求抢的物品价值最高，相当于构建一个最大独立集。

public int rob(int[] nums) {
    int[] totals = new int[nums.length + 2];
    for (int i = 2; i < totals.length; i++)
        totals[i] = Math.max(nums[i - 2] + totals[i - 2], totals[i - 1]);

    return totals[totals.length - 1];   
}

可以舍去中间结果：

public int rob(int[] nums) {
    int last = 0, secondLast = 0, cur = 0;
    for (int i = 0; i < nums.length; i++) {
        cur = Math.max(nums[i] + secondLast, last);
        secondLast = last;
        last = cur;
    } 
    return cur;   
}