House Thief Problem
Explore the House Thief problem that requires maximizing robbery amounts without hitting adjacent houses. Understand naive recursive methods and improve them via dynamic programming, using memoization and tabulation to optimize time and space complexity. Learn techniques to identify and implement efficient solutions to recursive number problems in programming interviews.
Statement
You are a professional robber, and after weeks of planning, you plan to rob some houses along a street. Each of these houses has a lot of money and valuables. Let’s say that you cannot rob houses adjacent to each other since they have security and burglar alarms installed.
Following the above-mentioned constraint and given an integer array, money, that represents the amount of money in each house, return the maximum amount of money you can steal tonight without alerting the police.
Let’s say you have an array of money as follows:
money: [1, 2, 3, 4, 5]
Considering we cannot rob the adjacent houses, we have six possible combinations that can possibly yield a substantial amount. Out of these combinations, we'll find one that yields the maximum money. The possible combinations are as under:
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