Content

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 systems connected and it will automatically contact the police if two adjacent houses were broken into on the same night.

Given an integer array nums representing the amount of money of each house, return the maximum amount of money you can rob tonight without alerting the police.

Example 1:

Input: nums = [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: nums = [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.

Constraints:

1 <= nums.length <= 100
0 <= nums[i] <= 400

Solution

1. 动态规划

Java

class Solution {
    public int rob(int[] nums) {
        // 1 <= nums.length <= 100
        // 0 <= nums[i] <= 400
        int n = nums.length;
        // dp[i]表示最后抢劫编号（编号0是一个虚拟的房子，没有钱方便计算）为i的房子可以获得的最大金额
        int[] dp = new int[n + 1];
        dp[1] = nums[0];
        int max = nums[0];
        // max0表示房子编号在[0, i - 2]范围内所能抢到的最大金额
        int max0 = 0;
        for (int i = 2; i <= n; i++) {
            max0 = Math.max(max0, dp[i - 2]);
            dp[i] = max0 + nums[i - 1];
            max = Math.max(max, dp[i]);
        }
        return max;
    }
}