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House Robber LC #198 Medium DP
Problem

Rob houses on a street. Adjacent houses have connected alarms — can't rob two adjacent houses. Return the maximum money you can rob.

Example
[2,7,9,3,1] → 12 (rob 2, 9, 1)
Constraints: 1 ≤ nums.length ≤ 100, 0 ≤ nums[i] ≤ 400
Try Examples
Custom:
Approach
dp[i] = max money from houses 0..i
At each house: Rob = nums[i] + dp[i-2] or Skip = dp[i-1]. Take max.
Houses & DP Values
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Variables
house i
—
rob
—
skip
—
max loot
—
Step Logic
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Algorithm
1
prev2=0, prev1=0 (money from 0 houses ago, 1 house ago)
2
curr = max(prev1, prev2 + nums[i])
3
prev2=prev1, prev1=curr; return prev1
Time
O(n)
Space
O(1)
Why This Works

At each house, decide: Rob (get nums[i] + best from 2 houses ago) or Skip (keep best from previous). Two variables suffice since we only need the previous two dp values.