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社区首页 >专栏 >Baozi Training Leetcode solution 198. House Robber

Baozi Training Leetcode solution 198. House Robber

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发布2020-06-24 15:11:00
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发布2020-06-24 15:11:00
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文章被收录于专栏:包子铺里聊IT

Leetcode solution 198. House Robber

Problem Statement

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:

代码语言:javascript
复制
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:

代码语言:javascript
复制
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:

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

Problem link

Video Tutorial

You can find the detailed video tutorial here

  • Youtube
  • B站

Thought Process

Easy problem and Dynamic Programming(DP) should jump into mind given it's only asking for max values (Just think about different combo we have to do without using DP, a little less than 2^N)

The mathematical induction formula is below, for any current max money at index i, you either choose to use the i-1 or i-2 + current house's money to not trigger police.

代码语言:javascript
复制
max[i] = max(max[i - 2] + a[i], max[i-1])

Solutions

DP
代码语言:javascript
复制
 1 public int rob(int[] num) {
 2     if (num == null || num.length == 0) {
 3         return 0;
 4     }
 5 
 6     int n = num.length;
 7     int[] lookup = new int[n + 1]; // DP array size normally larger than 1
 8     lookup[0] = 0;
 9     lookup[1] = num[0];
10 
11     for (int i = 2; i <= n; i++) {
12         lookup[i] = Math.max(lookup[i - 1], lookup[i - 2] + num[i - 1]);
13     }
14 
15     return lookup[n];
16 }

Time Complexity: O(N) N is the array size Space Complexity: O(N) since we used an extra array

References
  • Leetcode official solution

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原始发表:2020-06-21,如有侵权请联系 cloudcommunity@tencent.com 删除

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目录
  • Problem Statement
  • Video Tutorial
  • Thought Process
  • Solutions
    • DP
    • References
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