CodingGyan

House Robber

medium Data Structures and Algorithms

Problem

A row of houses has money a[i]. You can not rob two neighbouring houses. Read the array and print the largest amount you can rob.

Constraints

  • 1 <= n <= 10^5
  • 0 <= a[i] <= 10^4

Examples

Input

4
1 2 3 1

Output

4

Solutions

Best approachTime O(n)Space O(1)

At each house there are two choices. The best answer for the first i houses is max(best for i - 1, best for i - 2 + a[i]). Two variables are enough.

Same code works in Java810172125Basic features only, so nothing changes between versions.
/*
 * Problem : Maximum robbery.
 * Input   : n, then n integers.
 * Output  : The largest sum.
 * Approach: Skip it or take it.
 * Time    : O(n)
 * Space   : O(1)
 * Java    : 8 or newer.
 */
import java.util.Scanner;

public class Main {
    // This method solves the task. It receives the input and returns the answer.
    static long solve(int[] a) {
        // Step 1: skipLast = best amount when the last house is not robbed. takeLast = best amount up to the last house.
        long skipLast = 0;
        long takeLast = 0;

        for (int money : a) {
            // Step 2: For this house we either skip it (keep the best so far), or rob it (add to the best before the last house).
            long best = Math.max(takeLast, skipLast + money);
            skipLast = takeLast;
            takeLast = best;
        }
        return takeLast;
    }

    public static void main(String[] args) {
        Scanner scanner = new Scanner(System.in);
        int size = scanner.nextInt();
        int[] a = new int[size];
        for (int i = 0; i < size; i++) {
            a[i] = scanner.nextInt();
        }
        System.out.println(solve(a));
    }
}
Hints (1)
  1. Which two earlier results does the answer for house i need?

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