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

Given [3, 8, 4], return 8.

Challenge

time and memory.

Think

• When Rob meet a house, he has two choices: taken or not taken, but if he had stolen the previous house, it cannnot taken.
• Set two variable: include and exclude
• include means it has taken the previous house, while the exclude means it didn't take in previous house.
• So each time we consider about the exclude + cur_value and include, the max of them should be new include while the new exclude come from the max value of original include (last taken, current not taken) and original exclude (not taken in both last and current house)

Solution

    /**
     * @param A: An array of non-negative integers.
     * return: The maximum amount of money you can rob tonight
     */
    public long houseRobber(int[] A) {
        if(A == null)
            return 0L;
        long exclude = 0L;
        long include = 0L;

        for(int i = 0; i < A.length; i++) {
            long tmp = include;
            include = Math.max(include, exclude + A[i]);
            exclude = Math.max(tmp, exclude);
        }

        return Math.max(include, exclude);
    }

Follow Up

After robbing those houses on that street, the thief has found himself a new place for his thievery so that he will not get too much attention. This time, all houses at this place are arranged in a circle. That means the first house is the neighbor of the last one. Meanwhile, the security system for these houses remain the same as for those in the previous street.

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.

Think

The houses are in a cycle,so that when pick up the first element we cannot pick the last element because they are adjacent. So just seperate two parts for calculating: 0 to last second element, and 1 to last element, find the maximum from them.

Solution

    public int rob(int[] nums) {
        if(nums==null||nums.length==0)
            return 0;
        if(nums.length==1)
            return nums[0];
        return Math.max(helper(0, nums.length-2, nums), helper(1,nums.length-1,nums));
    }

    private int helper(int l, int r, int[] nums){
        if(nums==null||nums.length==0)
            return 0;
        int incl = 0;
        int excl = 0;
        for(int i = l;i<=r;i++){
            int tmp = incl;
            incl = excl+nums[i];
            excl = Math.max(excl, tmp);
        }
        return Math.max(incl, excl);
    }