Codeforces 339B Xenia and Ringroad Solution & Explanation

Difficulty : 1300

Problem Description

Xenia lives in a city that has n houses built along the main ringroad. The ringroad houses are numbered 1 through n in the clockwise order. The ringroad traffic is one way and also is clockwise.

Xenia has recently moved into the ringroad house number 1. As a result, she’s got m things to do. In order to complete the i-th task, she needs to be in the house number a_i and complete all tasks with numbers less than i. Initially, Xenia is in the house number 1, find the minimum time she needs to complete all her tasks if moving from a house to a neighboring one along the ringroad takes one unit of time.

Input

The first line contains two integers n and m (2 ≤ n ≤ 10⁵, 1 ≤ m ≤ 10⁵). The second line contains m integers a₁, a₂, …, a_m (1 ≤ a_i ≤ n). Note that Xenia can have multiple consecutive tasks in one house.

Output

Print a single integer — the time Xenia needs to complete all tasks.

Please, do not use the %lld specifier to read or write 64-bit integers in С++. It is preferred to use the cin, cout streams or the %I64d specifier.

Examples

Note

In the first test example the sequence of Xenia’s moves along the ringroad looks as follows: 1 → 2 → 3 → 4 → 1 → 2 → 3. This is optimal sequence. So, she needs 6 time units.

Solution

In our solution, we use a variable to store the current position, and we calculate the distance using a Ternary operator.

C# Solution

Solution1

string[] first = Console.ReadLine().Split(' '); // split by space
int n = int.Parse(first[0]); // number of houses

long[] missions = Console.ReadLine().Split(' ').Select(long.Parse).ToArray();

long now = 1;
long res = 0;

foreach (var m in missions)
{
    res += m >= now ? m - now : n - now + m;
    now = m;
}

Console.WriteLine(res);

We use long to perform calculations, aiming to avoid issues related to exceeding the range of int, especially in some test cases.

Java Solution

Solution1

import java.util.Scanner;
import java.util.Arrays;

public class Main {
    public static void main(String[] args) {
        Scanner scanner = new Scanner(System.in);
        
        String[] first = scanner.nextLine().split(" "); // split by space
        int n = Integer.parseInt(first[0]); // number of houses
        
        String input = scanner.nextLine();

        long[] missions = Arrays.stream(input.split(" "))
                            .mapToLong(Long::parseLong)
                            .toArray();
        
        long now = 1;
        long res = 0;
        
        for(long m : missions)
        {
            res += m >= now ? m - now : n - now + m;
            now = m;
        }
        System.out.println(res);
    }
}

Conclusion

This problem came from codeforces contest – Dashboard – Codeforces Round 197 (Div. 2) – Codeforces

Here to see other problem of this contest:

• Codeforces 339A Helpful Maths Solution & Explanation

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The problem link : Problem – 339B – Codeforces

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