Problem
Solution
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House Robber
Certification: Intermediate Level
Accuracy: 0%
Submissions: 0
Points: 15
Write a C program to find the maximum sum of non-adjacent elements in an array. You are a professional robber planning to rob houses along a street. Each house has a certain amount of money stashed. The constraint is that adjacent houses have security systems connected, so you cannot rob two adjacent houses.
Example 1
- Input: arr[] = {2, 1, 4, 9}
- Output: 11
- Explanation: We can rob house 0 (amount = 2) and house 2 (amount = 4) and house 3 (amount = 9). But we cannot rob house 2 and 3 together as they are adjacent. Maximum sum = 2 + 9 = 11 (rob house 0 and house 3).
Example 2
- Input: arr[] = {5, 2, 3, 9, 8, 4}
- Output: 19
- Explanation: We can rob houses at indices 0, 2, and 5 (Sum = 5 + 3 + 4 = 12), or rob houses at indices 0, 3, 5 (Sum = 5 + 9 + 4 = 18), or rob houses at indices 1, 3, 5 (Sum = 2 + 9 + 8 = 19). Maximum sum is 19.
Constraints
- 1 ≤ n ≤ 100
- 0 ≤ arr[i] ≤ 1000
- Time Complexity: O(n)
- Space Complexity: O(1)
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Solution Hints
- Use dynamic programming approach to solve this problem
- For each house, decide whether to rob it or not
- If you rob current house, you cannot rob the previous house
- If you don't rob current house, take the maximum from previous calculations
- Keep track of maximum sum including and excluding current element
- Return the maximum of both values at the end