Dynamic Programming总结 (持续更新)

DP可以说是面试中比较难得题型，代码本身不会太复杂，难在想清楚问题，如何转换状态。本文抛砖引玉，一起研究下DP专题常考的题目。

House Robber

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: 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.

public int rob(int[] nums) {
    int[] dp = new int[nums.length];
    int max = 0;
    for (int i = 0; i < nums.length; i++) {
        if (i == 0) {
            dp[0] = nums[0];
        } else if (i == 1) {
            dp[1] = Math.max(nums[0], nums[1]);
        } else {
            dp[i] = Math.max(dp[i - 1], dp[i - 2] + nums[i]);
        }
        max = Math.max(dp[i], max);
    }
    return max;
}

Reference: https://zxth93.github.io/2017/12/29/LeetCode-dp%E7%B1%BB%E6%80%BB%E7%BB%93/

House Robber#

House Robber