Distributing M items in a circle of size N starting from K-th position

M items are to be delivered in a circle of size N. Find the position where the M-th item will be delivered if we start from a given position K. Note that items are distributed at adjacent positions starting from K.

Examples :

Input : N = 5 // Size of circle
        M = 2 // Number of items
        K = 1 // Starting position
Output : 2
The first item will be given to 1st 
position. Second (or last) item will 
be delivered to 2nd position

Input : N = 5 
        M = 8 
        K = 2
Output : 4
The last item will be delivered to 
4th position

We check if the number of items to be distributed is greater than our remaining positions in current cycle of circle or not. If yes, then we simply return m + k – 1 (We distribute items in same cycle starting from k). Else we compute number of remaining items after completing current cycle and return mod of remaining items.

Below is the implementation of the above idea:

C++

// C++ program to find the position where
// last item is delivered.
#include <bits/stdc++.h>
using namespace std;

// n ==> Size of circle
// m ==> Number of items
// k ==> Initial position
int lastPosition(int n, int m, int k)
{
    // n - k + 1 is number of positions
    // before we reach beginning of circle
    // If m is less than this value, then
    // we can simply return (m-1)th position
    if (m <= n - k + 1)
        return m + k - 1;

    // Let us compute remaining items before
    // we reach beginning.
    m = m - (n - k + 1);

    // We compute m % n to skip all complete
    // rounds. If we reach end, we return n
    // else we return m % n
    return (m % n == 0) ? n : (m % n);
}

// Driver code
int main()
{
    int n = 5;
    int m = 8;
    int k = 2;
    cout << lastPosition(n, m, k);
    return 0;
}

Java

// Java program to find the position where
// last item is delivered.
class GFG {

    // n ==> Size of circle
    // m ==> Number of items
    // k ==> Initial position
    static int lastPosition(int n, int m, int k)
    {

        // n - k + 1 is number of positions
        // before we reach beginning of circle
        // If m is less than this value, then
        // we can simply return (m-1)th position
        if (m <= n - k + 1)
            return m + k - 1;

        // Let us compute remaining items before
        // we reach beginning.
        m = m - (n - k + 1);

        // We compute m % n to skip all complete
        // rounds. If we reach end, we return n
        // else we return m % n
        return (m % n == 0) ? n : (m % n);
    }

    // Driver Program to test above function
    public static void main(String arg[])
    {
        int n = 5;
        int m = 8;
        int k = 2;
        System.out.print(lastPosition(n, m, k));
    }
}

// This code is contributed by Anant Agarwal.

Python3

# Python program to find the position where
# last item is delivered.

# n ==> Size of circle
# m ==> Number of items
# k ==> Initial position
def lastPosition(n, m, k):

    # n - k + 1 is number of positions
    # before we reach beginning of circle
    # If m is less than this value, then
    # we can simply return (m-1)th position
    if (m <= n - k + 1):
       return m + k - 1

    # Let us compute remaining items before
    # we reach beginning.
    m = m - (n - k + 1)

    # We compute m % n to skip all complete
    # rounds. If we reach end, we return n
    # else we return m % n
    if(m % n == 0):
        return n
    else:
        return m % n

# Driver code
n = 5
m = 8
k = 2
print(lastPosition(n, m, k))

# This code is contributed by Sachin Bisht

C#

// C# program to find the position where
// last item is delivered.
using System;

class GFG {

    // n ==> Size of circle
    // m ==> Number of items
    // k ==> Initial position
    static int lastPosition(int n, int m, int k)
    {

        // n - k + 1 is number of positions
        // before we reach beginning of circle
        // If m is less than this value, then
        // we can simply return (m-1)th position
        if (m <= n - k + 1)
            return m + k - 1;

        // Let us compute remaining items before
        // we reach beginning.
        m = m - (n - k + 1);

        // We compute m % n to skip all complete
        // rounds. If we reach end, we return n
        // else we return m % n
        return (m % n == 0) ? n : (m % n);
    }

    // Driver Program to test above function
    public static void Main()
    {
        int n = 5;
        int m = 8;
        int k = 2;

        Console.WriteLine(lastPosition(n, m, k));
    }
}

// This code is contributed by vt_m.

PHP

<?php
// PHP program to find the
// position where last item
// is delivered.

// n ==> Size of circle
// m ==> Number of items
// k ==> Initial position

function lastPosition($n, $m, $k)
{
    // n - k + 1 is number of
    // positions before we reach
    // beginning of circle.
    // If m is less than this value,
    // then we can simply return
    // (m-1)th position
    if ($m <= $n - $k + 1)
    return $m + $k - 1;

    // Let us compute remaining items
    // before we reach beginning.
    $m = $m - ($n - $k + 1);

    // We compute m % n to skip
    // all complete rounds. If we
    // reach end, we return n
    // else we return m % n
    return ($m % $n == 0) ? $n : ($m % $n);
}

// Driver code
$n = 5;
$m = 8;
$k = 2;
echo lastPosition($n, $m, $k);

// This code is contributed by ajit
?>

Javascript

<script>
// Javascript program to find the
// position where last item
// is delivered.

// n ==> Size of circle
// m ==> Number of items
// k ==> Initial position

function lastPosition(n, m, k)
{

    // n - k + 1 is number of
    // positions before we reach
    // beginning of circle.
    // If m is less than this value,
    // then we can simply return
    // (m-1)th position
    if (m <= n - k + 1)
    return m + k - 1;

    // Let us compute remaining items
    // before we reach beginning.
    m = m - (n - k + 1);

    // We compute m % n to skip
    // all complete rounds. If we
    // reach end, we return n
    // else we return m % n
    return (m % n == 0) ? n : (m % n);
}

// Driver code
let n = 5;
let m = 8;
let k = 2;
document.write(lastPosition(n, m, k));

// This code is contributed by _saurabh_jaiswal
</script>

Output :

4

Time Complexity: O(1)
Auxiliary Space: O(1)

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