DP O(N) time, O(1) space with easy to understand explanation

  • 53

    For every house k, there are two options: either to rob it (include this house: i) or not rob it (exclude this house: e).

    1. Include this house:
      i = num[k] + e (money of this house + money robbed excluding the previous house)

    2. Exclude this house:
      e = max(i, e) (max of money robbed including the previous house or money robbed excluding the previous house)
      (note that i and e of the previous step, that's why we use tmp here to store the previous i when calculating e, to make O(1) space)

    Here is the code:

    public class Solution {
        public int rob(int[] num) {
            int i = 0;
            int e = 0;
            for (int k = 0; k<num.length; k++) {
                int tmp = i;
                i = num[k] + e;
                e = Math.max(tmp, e);
            return Math.max(i,e);

  • 0

    Good explanation. Thank you!

  • 0

    Very readable!!

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