Second Chance (or Clock) Page Replacement Policy

Prerequisite – Page Replacement Algorithms
Apart from LRU, OPT and FIFO page replacement policies, we also have the second chance/clock page replacement policy. In the Second Chance page replacement policy, the candidate pages for removal are considered in a round robin matter, and a page that has been accessed between consecutive considerations will not be replaced. The page replaced is the one that, when considered in a round robin matter, has not been accessed since its last consideration. 
It can be implemented by adding a “second chance” bit to each memory frame-every time the frame is considered (due to a reference made to the page inside it), this bit is set to 1, which gives the page a second chance, as when we consider the candidate page for replacement, we replace the first one with this bit set to 0 (while zeroing out bits of the other pages we see in the process). Thus, a page with the “second chance” bit set to 1 is never replaced during the first consideration and will only be replaced if all the other pages deserve a second chance too!

Traditionally Second Chance and Clock are believed to be less efficient than LRU (having a higher miss ratio). Recent research from Carnegie Mellon University finds that Second Chance and Clock are more efficient than LRU with a lower miss ratio. Because Second Chance and Clock is faster and more scalable than LRU, this means LRU has no advantage over Second Chance and Clock anymore.

Example –
Let’s say the reference string is 0 4 1 4 2 4 3 4 2 4 0 4 1 4 2 4 3 4 and we have 3 frames. Let’s see how the algorithm proceeds by tracking the second chance bit and the pointer. 

• Initially, all frames are empty so after first 3 passes they will be filled with {0, 4, 1} and the second chance array will be {0, 0, 0} as none has been referenced yet. Also, the pointer will cycle back to 0. 
  
• Pass-4: Frame={0, 4, 1}, second_chance = {0, 1, 0} [4 will get a second chance], pointer = 0 (No page needed to be updated so the candidate is still page in frame 0), pf = 3 (No increase in page fault number). 
  
• Pass-5: Frame={2, 4, 1}, second_chance= {0, 1, 0} [0 replaced; it’s second chance bit was 0, so it didn’t get a second chance], pointer=1 (updated), pf=4 
  
• Pass-6: Frame={2, 4, 1}, second_chance={0, 1, 0}, pointer=1, pf=4 (No change) 
  
• Pass-7: Frame={2, 4, 3}, second_chance= {0, 0, 0} [4 survived but it’s second chance bit became 0], pointer=0 (as element at index 2 was finally replaced), pf=5 
  
• Pass-8: Frame={2, 4, 3}, second_chance= {0, 1, 0} [4 referenced again], pointer=0, pf=5 
  
• Pass-9: Frame={2, 4, 3}, second_chance= {1, 1, 0} [2 referenced again], pointer=0, pf=5 
  
• Pass-10: Frame={2, 4, 3}, second_chance= {1, 1, 0}, pointer=0, pf=5 (no change) 
  
• Pass-11: Frame={2, 4, 0}, second_chance= {0, 0, 0}, pointer=0, pf=6 (2 and 4 got second chances) 
  
• Pass-12: Frame={2, 4, 0}, second_chance= {0, 1, 0}, pointer=0, pf=6 (4 will again get a second chance) 
  
• Pass-13: Frame={1, 4, 0}, second_chance= {0, 1, 0}, pointer=1, pf=7 (pointer updated, pf updated) 
  
• Page-14: Frame={1, 4, 0}, second_chance= {0, 1, 0}, pointer=1, pf=7 (No change) 
  
• Page-15: Frame={1, 4, 2}, second_chance= {0, 0, 0}, pointer=0, pf=8 (4 survived again due to 2nd chance!) 
  
• Page-16: Frame={1, 4, 2}, second_chance= {0, 1, 0}, pointer=0, pf=8 (2nd chance updated) 
  
• Page-17: Frame={3, 4, 2}, second_chance= {0, 1, 0}, pointer=1, pf=9 (pointer, pf updated) 
  
• Page-18: Frame={3, 4, 2}, second_chance= {0, 1, 0}, pointer=1, pf=9 (No change) 
  

In this example, second chance algorithm does as well as the LRU method, which is much more expensive to implement in hardware.
More Examples –

Input: 2 5 10 1 2 2 6 9 1 2 10 2 6 1 2 1 6 9 5 1
3
Output: 14

Input: 2 5 10 1 2 2 6 9 1 2 10 2 6 1 2 1 6 9 5 1
4
Output: 11 

Algorithm –
Create an array frames to track the pages currently in memory and another Boolean array second_chance to track whether that page has been accessed since it’s last replacement (that is if it deserves a second chance or not) and a variable pointer to track the target for replacement. 

1. Start traversing the array arr. If the page already exists, simply set its corresponding element in second_chance to true and return. 
   
2. If the page doesn’t exist, check whether the space pointed to by pointer is empty (indicating cache isn’t full yet) – if so, we will put the element there and return, else we’ll traverse the array arr one by one (cyclically using the value of pointer), marking all corresponding second_chance elements as false, till we find a one that’s already false. That is the most suitable page for replacement, so we do so and return. 
   
3. Finally, we report the page fault count. 
   

C++

// CPP program to find largest in an array
// without conditional/bitwise/ternary/ operators
// and without library functions.
#include<iostream>
#include<cstring>
#include<sstream>
using namespace std;

// If page found, updates the second chance bit to true
static bool findAndUpdate(int x,int arr[],
                bool second_chance[],int frames)

{
    int i;

    for(i = 0; i < frames; i++)
    {

        if(arr[i] == x)
        {
            // Mark that the page deserves a second chance
            second_chance[i] = true;

            // Return 'true', that is there was a hit
            // and so there's no need to replace any page
            return true;
        }
    }

    // Return 'false' so that a page for replacement is selected
    // as he reuested page doesn't exist in memory
    return false;

}


// Updates the page in memory and returns the pointer
static int replaceAndUpdate(int x,int arr[],
            bool second_chance[],int frames,int pointer)
{
    while(true)
    {

        // We found the page to replace
        if(!second_chance[pointer])
        {
            // Replace with new page
            arr[pointer] = x;

            // Return updated pointer
            return (pointer + 1) % frames;
        }

        // Mark it 'false' as it got one chance
        // and will be replaced next time unless accessed again
        second_chance[pointer] = false;

        //Pointer is updated in round robin manner
        pointer = (pointer + 1) % frames;
    }
}

static void printHitsAndFaults(string reference_string,
                                            int frames)
{
    int pointer, i, l=0, x, pf;

    //initially we consider frame 0 is to be replaced
    pointer = 0;

    //number of page faults
    pf = 0;

    // Create a array to hold page numbers
    int arr[frames];

    // No pages initially in frame,
    // which is indicated by -1
    memset(arr, -1, sizeof(arr));

    // Create second chance array.
    // Can also be a byte array for optimizing memory
    bool second_chance[frames];

    // Split the string into tokens,
    // that is page numbers, based on space

    string str[100];
    string word = "";
    for (auto x : reference_string)
    {
        if (x == ' ')
        {
            str[l]=word;
            word = "";
            l++;
        }
        else
        {
            word = word + x;
        }
    }
    str[l] = word;
    l++;
    // l=the length of array

    for(i = 0; i < l; i++)
    {
        x = stoi(str[i]);

        // Finds if there exists a need to replace
        // any page at all
        if(!findAndUpdate(x,arr,second_chance,frames))
        {
            // Selects and updates a victim page
            pointer = replaceAndUpdate(x,arr,
                    second_chance,frames,pointer);

            // Update page faults
            pf++;
        }
    }
    cout << "Total page faults were " << pf << "\n";
}

// Driver code
int main()
{
    string reference_string = "";
    int frames = 0;

    // Test 1:
    reference_string = "0 4 1 4 2 4 3 4 2 4 0 4 1 4 2 4 3 4";
    frames = 3;

    // Output is 9
    printHitsAndFaults(reference_string,frames);

    // Test 2:
    reference_string = "2 5 10 1 2 2 6 9 1 2 10 2 6 1 2 1 6 9 5 1";
    frames = 4;

    // Output is 11
    printHitsAndFaults(reference_string,frames);
    return 0;
}

// This code is contributed by NikhilRathor

Java

// Java program to find largest in an array
// without conditional/bitwise/ternary/ operators
// and without library functions.
import java.util.*;
import java.io.*;
class secondChance
{
    public static void main(String args[])throws IOException
    {
        String reference_string = "";
        int frames = 0;

        //Test 1:
        reference_string = "0 4 1 4 2 4 3 4 2 4 0 4 1 4 2 4 3 4";
        frames = 3;

        //Output is 9
        printHitsAndFaults(reference_string,frames);

        //Test 2:
        reference_string = "2 5 10 1 2 2 6 9 1 2 10 2 6 1 2 1 6 9 5 1";
        frames = 4;

        //Output is 11
        printHitsAndFaults(reference_string,frames);

    }

    //If page found, updates the second chance bit to true
    static boolean findAndUpdate(int x,int arr[],
                       boolean second_chance[],int frames)

    {
        int i;

        for(i = 0; i < frames; i++)
        {

            if(arr[i] == x)
            {
                //Mark that the page deserves a second chance
                second_chance[i] = true;

                //Return 'true', that is there was a hit
                //and so there's no need to replace any page
                return true;
            }
        }

        //Return 'false' so that a page for replacement is selected
        //as he reuested page doesn't exist in memory
        return false;

    }


    //Updates the page in memory and returns the pointer
    static int replaceAndUpdate(int x,int arr[],
                 boolean second_chance[],int frames,int pointer)
    {
        while(true)
        {

            //We found the page to replace
            if(!second_chance[pointer])
            {
                //Replace with new page
                arr[pointer] = x;

                //Return updated pointer
                return (pointer+1)%frames;
            }

            //Mark it 'false' as it got one chance
            // and will be replaced next time unless accessed again
            second_chance[pointer] = false;

            //Pointer is updated in round robin manner
            pointer = (pointer+1)%frames;
        }
    }

    static void printHitsAndFaults(String reference_string,
                                                  int frames)
    {
        int pointer,i,l,x,pf;

        //initially we consider frame 0 is to be replaced
        pointer = 0;

        //number of page faults
        pf = 0;

        //Create a array to hold page numbers
        int arr[] = new int[frames];

        //No pages initially in frame,
        //which is indicated by -1
        Arrays.fill(arr,-1);

        //Create second chance array.
        //Can also be a byte array for optimizing memory
        boolean second_chance[] = new boolean[frames];

        //Split the string into tokens,
        //that is page numbers, based on space
        String str[] = reference_string.split(" ");

        //get the length of array
        l = str.length;

        for(i = 0; i<l; i++)
        {

            x = Integer.parseInt(str[i]);

            //Finds if there exists a need to replace
            //any page at all
            if(!findAndUpdate(x,arr,second_chance,frames))
            {
                //Selects and updates a victim page
                pointer = replaceAndUpdate(x,arr,
                          second_chance,frames,pointer);

                //Update page faults
                pf++;
            }
        }

        System.out.println("Total page faults were "+pf);
    }
}

Python3

# Python3 program to find largest in an array
# without conditional/bitwise/ternary/ operators
# and without library functions.

# If page found, updates the second chance bit to true
def findAndUpdate(x, arr, second_chance, frames):

    for i in range(frames):

        if arr[i] == x:
            # Mark that the page deserves a second chance
            second_chance[i] = True

            # Return 'true', that is there was a hit
            #and so there's no need to replace any page
            return True

    # Return 'false' so that a page
    # for replacement is selected
    # as he reuested page doesn't
    # exist in memory
    return False

# Updates the page in memory
# and returns the pointer
def replaceAndUpdate(x, arr, second_chance, frames, pointer):
    while(True):

        # We found the page to replace
        if not second_chance[pointer]:

            # Replace with new page
            arr[pointer] = x

            #Return updated pointer
            return (pointer+1)%frames

        # Mark it 'false' as it got one chance
        # and will be replaced next time unless accessed again
        second_chance[pointer] = False

        # Pointer is updated in round robin manner
        pointer = (pointer + 1) % frames

def printHitsAndFaults(reference_string, frames):

    # initially we consider
    # frame 0 is to be replaced
    pointer = 0

    # number of page faults
    pf = 0

    # Create a array to hold page numbers
    arr = [0]*frames

    # No pages initially in frame,
    # which is indicated by -1
    for s in range(frames):
        arr[s] = -1

    # Create second chance array.
    # Can also be a byte array for optimizing memory
    second_chance = [False]*frames

    # Split the string into tokens,
    # that is page numbers, based on space
    Str = reference_string.split(' ')

    # get the length of array
    l = len(Str)

    for i in range(l):
        x = Str[i]

        # Finds if there exists a need to replace
        # any page at all
        if not findAndUpdate(x,arr,second_chance,frames):

            # Selects and updates a victim page
            pointer = replaceAndUpdate(x,arr,second_chance,frames,pointer)

            # Update page faults
            pf += 1

    print("Total page faults were", pf)

reference_string = ""
frames = 0

# Test 1:
reference_string = "0 4 1 4 2 4 3 4 2 4 0 4 1 4 2 4 3 4"
frames = 3

# Output is 9
printHitsAndFaults(reference_string,frames)

# Test 2:
reference_string = "2 5 10 1 2 2 6 9 1 2 10 2 6 1 2 1 6 9 5 1"
frames = 4

# Output is 11
printHitsAndFaults(reference_string,frames)

# This code is contributed by mukesh07.

C#

// C# program to find largest in an array
// without conditional/bitwise/ternary/ operators
// and without library functions.
using System;

public class secondChance
{
    public static void Main()
    {
        String reference_string = "";
        int frames = 0;

        // Test 1:
        reference_string = "0 4 1 4 2 4 3 4 2 4 0 4 1 4 2 4 3 4";
        frames = 3;

        // Output is 9
        printHitsAndFaults(reference_string,frames);

        // Test 2:
        reference_string = "2 5 10 1 2 2 6 9 1 2 10 2 6 1 2 1 6 9 5 1";
        frames = 4;

        // Output is 11
        printHitsAndFaults(reference_string,frames);

    }

    // If page found, updates the second chance bit to true
    static bool findAndUpdate(int x,int []arr,
                    bool []second_chance,int frames)

    {
        int i;

        for(i = 0; i < frames; i++)
        {

            if(arr[i] == x)
            {
                //Mark that the page deserves a second chance
                second_chance[i] = true;

                //Return 'true', that is there was a hit
                //and so there's no need to replace any page
                return true;
            }
        }

        // Return 'false' so that a page
        // for replacement is selected
        // as he reuested page doesn't
        // exist in memory
        return false;

    }


    // Updates the page in memory
    // and returns the pointer
    static int replaceAndUpdate(int x,int []arr,
                bool []second_chance,int frames,int pointer)
    {
        while(true)
        {

            //We found the page to replace
            if(!second_chance[pointer])
            {
                //Replace with new page
                arr[pointer] = x;

                //Return updated pointer
                return (pointer+1)%frames;
            }

            //Mark it 'false' as it got one chance
            // and will be replaced next time unless accessed again
            second_chance[pointer] = false;

            //Pointer is updated in round robin manner
            pointer = (pointer + 1) % frames;
        }
    }

    static void printHitsAndFaults(String reference_string,
                                                int frames)
    {
        int pointer, i, l, x, pf;

        // initially we consider
        // frame 0 is to be replaced
        pointer = 0;

        // number of page faults
        pf = 0;

        // Create a array to hold page numbers
        int []arr = new int[frames];

        // No pages initially in frame,
        // which is indicated by -1
        for(int s = 0;s<frames;s++)
            arr[s]=-1;


        //Create second chance array.
        //Can also be a byte array for optimizing memory
        bool []second_chance = new bool[frames];

        //Split the string into tokens,
        //that is page numbers, based on space
        String []str = reference_string.Split();

        //get the length of array
        l = str.Length;

        for(i = 0; i < l; i++)
        {

            x = int.Parse(str[i]);

            //Finds if there exists a need to replace
            //any page at all
            if(!findAndUpdate(x,arr,second_chance,frames))
            {
                //Selects and updates a victim page
                pointer = replaceAndUpdate(x,arr,
                        second_chance,frames,pointer);

                //Update page faults
                pf++;
            }
        }

        Console.WriteLine("Total page faults were "+pf);
    }
}

// This code has been contributed by 29AjayKumar

Javascript

<script>
    // Javascript program to find largest in an array
    // without conditional/bitwise/ternary/ operators
    // and without library functions.

    // If page found, updates the second chance bit to true
    function findAndUpdate(x, arr, second_chance, frames)

    {
        let i;

        for(i = 0; i < frames; i++)
        {

            if(arr[i] == x)
            {
                //Mark that the page deserves a second chance
                second_chance[i] = true;

                //Return 'true', that is there was a hit
                //and so there's no need to replace any page
                return true;
            }
        }

        // Return 'false' so that a page
        // for replacement is selected
        // as he reuested page doesn't
        // exist in memory
        return false;

    }


    // Updates the page in memory
    // and returns the pointer
    function replaceAndUpdate(x, arr, second_chance, frames, pointer)
    {
        while(true)
        {

            //We found the page to replace
            if(!second_chance[pointer])
            {
                //Replace with new page
                arr[pointer] = x;

                //Return updated pointer
                return (pointer+1)%frames;
            }

            //Mark it 'false' as it got one chance
            // and will be replaced next time unless accessed again
            second_chance[pointer] = false;

            //Pointer is updated in round robin manner
            pointer = (pointer + 1) % frames;
        }
    }

    function printHitsAndFaults(reference_string, frames)
    {
        let pointer, i, l, x, pf;

        // initially we consider
        // frame 0 is to be replaced
        pointer = 0;

        // number of page faults
        pf = 0;

        // Create a array to hold page numbers
        let arr = new Array(frames);
        arr.fill(0);

        // No pages initially in frame,
        // which is indicated by -1
        for(let s = 0;s<frames;s++)
            arr[s]=-1;


        //Create second chance array.
        //Can also be a byte array for optimizing memory
        let second_chance = new Array(frames);
        second_chance.fill(false);

        //Split the string into tokens,
        //that is page numbers, based on space
        let str = reference_string.split(' ');

        //get the length of array
        l = str.length;

        for(i = 0; i < l; i++)
        {
            x = str[i];

            //Finds if there exists a need to replace
            //any page at all
            if(!findAndUpdate(x,arr,second_chance,frames))
            {
                //Selects and updates a victim page
                pointer = replaceAndUpdate(x,arr,
                        second_chance,frames,pointer);

                //Update page faults
                pf++;
            }
        }

        document.write("Total page faults were " + pf + "</br>");
    }

    let reference_string = "";
    let frames = 0;

    // Test 1:
    reference_string = "0 4 1 4 2 4 3 4 2 4 0 4 1 4 2 4 3 4";
    frames = 3;

    // Output is 9
    printHitsAndFaults(reference_string,frames);

    // Test 2:
    reference_string = "2 5 10 1 2 2 6 9 1 2 10 2 6 1 2 1 6 9 5 1";
    frames = 4;

    // Output is 11
    printHitsAndFaults(reference_string,frames);

    // This code is contributed by divyesh072019.
</script>

Output:

Total page faults were 9
Total page faults were 11

Note:

1. The arrays arr and second_chance can be replaced and combined together via a hashmap (with element as key, true/false as value) to speed up search.
2. Time complexity of this method is O(Number_of_frames*reference_string_length) or O(mn) but since number of frames will be a constant in an Operating System (as main memory size is fixed), it is simply O(n) [Same as hashmap approach, but that will have lower constants]
3. Second chance algorithm may suffer from Belady’s Anomaly.