Sticky Sticks Hexagon Game in C#

Problem Statement

Rajesh is playing a very interesting mathematical game. He has collection of sticks of length 1,2,3,....,N. He is making hexagon out of his collection by using 6 sticks for each hexagon. He considers a hexagon "good" if the biggest stick has length at least L and lengths of all the other sticks are not more than X.A "good" hexagon does not have sticks of the same length more than K times. 
How many ways he can make a "Good" hexagon?

Input/Output Specs

Input Specification:Input contains four integers-
N( 2 <= N <= 10^9)
L ( 2 <= L <= N and N-L<=100)
X( 1<=X< L )
K ( 1 <= K <= 5)

Output Specification:
Output the number of different ways to make a "Good" hexagon% 1000000007

Examples

Example:1 when N=8, L=7, X=5, K=3: { 1,2,2,5,5,7 } is a good hexagon but {1,2,2,2,2,7}, { 1,2,3,4,5,6},{1,2,3,4,6,7} are not.Two hexagons are considered different if their side length sets are different.

For example {1,2,3,4,5,6} , {1,1,1,2,2,3} and {1,1,2,2,2,3} are all different hexagons. But {1,2,3,4,5,6} and { 2,4,6,1,3,5} are not different.

Example:2 When N=10, L=8, X=6, K=2
Output:       Total hexagons= 374

Note: Please return -1 for invalid cases.

One point we need to understand, in irregular hexagon sum of all other sides must be greater than the bigger side stick length then only it is consider as Good Hexagon

using System.IO;

using System;

using LL = System.Int64;

usingSystem.Collections.Generic;

public class CandidateCode

{

    static LL MOD = 1000000007;

    static LL N, K, L, X;

    static LL gcd(LL a, LL b)

    {

        if (b == 0) return a;

        return gcd(b, a % b);

    }

    static LL[] arr = new LL[10];

    static LL nck(LL n, LL k)

    {

        LL i, j, d;

        LL ret = 1;

        if (k > n) return0;

        for (i = 0; i < k; i++) arr[i] = n - i;

        for (i = 2; i <= k; i++)

            for (d = i, j = 0; j < k; j++)

            {

                LL g = gcd(arr[j], d);

                arr[j] /= g; d /= g;

            }

        for (i = 0; i < k; i++) ret = (((LL)ret * arr[i]) % MOD);

        return ret;

    }

    static LL calcAll(LL n, LL x, LL k)

    {

        LL ret = 0;

        LL i;

        if (x == 0) returnnck(n, k);

        for (i = 1; i <= x && i <= K; i++)

            ret = ((ret + calcAll(n, x - i, k + 1)) % MOD);

        return ret;

    }

    static void gen(LL pos, LLcarry, LL pattern, LLc, LL sum, LLval, LL idx)

    {

        LL i;

        if (pos == 5)

        {

            if ((sum / 10) != carry) return;

            LL x = carry * total + pattern, y = c * total + ids[val], d = sum % 10;

            cnt1[(vals[0] % 10), d, x, y, 0]++;

            if ((vals[4] % 10) == 0) cnt1[(vals[0] % 10), d, x, y, 1]++;

            return;

        }

        for (i = 0; i <= 9; i++)

        {

            if ((sum + i) / 10 > carry) break;

            vals[pos] = pat[pos] * 10 + i;

            if ((pos != 0) && (vals[pos] > vals[pos - 1]))

                break;

            LL nidx = ((pos == 0) || (vals[pos] == vals[pos - 1])) ? idx : idx - 1;

            gen(pos + 1, carry, pattern, c, sum + i, (val * 10 + nidx), nidx);

        }

    }

    static List<Int64> now = newList<Int64>();

    static LL[][] states = new LL[20][];

    static LL[] ids = new LL[100000];

    static LL[] valid = new LL[80];

    static LL total;

    static LL[, ,] next = new LL[2, 85, 85];

    static LL[,] size = new LL[2, 85];

    static voidgenStates(LL pos, LLval, LL last) // generates all possible encodings

    {

        if (pos == 5)

        {

            ids[val] = total;

            states[total++] = now.ToArray();

            return;

        }

        now[(int)pos] = last;

        genStates(pos + 1, val * 10 + last, last);

        if (pos != 0) { now[(int)pos] = last - 1; genStates(pos + 1, val * 10 + last - 1, last - 1); }

    }

    static LL[, , , ,] cnt1 = new LL[10, 10, 85, 85, 2];

    static LL[, , , ,] cnt2 = new LL[10, 10, 85, 85, 2];

    static LL[, , , ,] cnt3 = new LL[10, 10, 85, 85, 2];

    static LL[, , , ,] cnt4 = new LL[10, 10, 85, 85, 2];

    static LL[] vals = new LL[10];

    static LL[] pat = new LL[10];

    static LL preCalc(LL i, LL j, LL k, LL l, LL x)

    {

        LL cc = cnt1[k, l, i, j, x];

        LL cd = ((k != 0) && (l != 0)) ? cnt4[k - 1, l - 1, i, j, x] : 0;

        LL ca = (l != 0) ? cnt2[k, l - 1, i, j, x] : 0;

        LL cb = (k != 0) ? cnt3[k - 1, l, i, j, x] : 0;

        cnt2[k, l, i, j, x] = ca + cc;

        cnt3[k, l, i, j, x] = cb + cc;

        cnt4[k, l, i, j, x] = ca + cb + cc + cd;

        return ca + cb + cc + cd;

    }

    static void make(LL carry, LLpattern) // compute the edges

    {

        LL i, j, k, l, x = carry * total + pattern;

        for (i = 0; i < 5; i++)

        {

            pat[i] = states[pattern][i];

        }

        for (i = 0; i < 5; i++)

            gen(0, carry, pattern, i, i, 0, 9);

        for (i = x, j = 0; j < 80; j++)

        {

            LL ok1 = 0, ok2 = 0;

            for (k = 0; k <= 9; k++)

                for (l = 0; l <= 9; l++)

                {

                    if (preCalc(i, j, k, l, 0) != 0) ok1 = 1;

                    if (preCalc(i, j, k, l, 1) != 0) ok2 = 1;

                }

            if (ok1 != 0) next[0, x, (size[0, x]++)] = j;

            if (ok2 != 0) next[1, x, (size[1, x]++)] = j;

        }

    }

    static LL[, , ,] memo = new LL[12, 2, 2, 85];

    static LL[, , ,] seen = new LL[12, 2, 2, 85];

    static LL length, cnt;

    static LL[] MM = new LL[15];

    static LL[] XX = new LL[15];

    static LL solve(LL pos, LLprefixX, LL prefixM, LL x, LL z)

    {

        LL i, ret = 0;

        if (pos == length) returnvalid[x];

        if (seen[pos, prefixX, prefixM, x] == cnt) return memo[pos, prefixX, prefixM, x];

        LL a = XX[pos], b = MM[pos];

        for (i = 0; i < size[z, x]; i++)

        {

            LL y = next[z, x, i];

            if ((prefixX != 0) && (prefixM != 0))

            {

                if (cnt1[a, b, x, y, z] != 0)

                    ret = ((ret + (LL)cnt1[a, b, x, y, z] * solve(pos + 1, 1, 1, y, z)) % MOD);

                if ((b != 0) && (cnt2[a, b - 1, x, y, z] != 0))

                    ret = ((ret + (LL)cnt2[a, b - 1, x, y, z] * solve(pos + 1, 1, 0, y, z)) % MOD);

                if ((a != 0) && (cnt3[a - 1, b, x, y, z] != 0))

                    ret = ((ret + (LL)cnt3[a - 1, b, x, y, z] * solve(pos + 1, 0, 1, y, z)) % MOD);

                if ((a != 0) && (b != 0) && (cnt4[a - 1, b - 1, x, y, z] != 0))

                    ret = ((ret + (LL)cnt4[a - 1, b - 1, x, y, z] * solve(pos + 1, 0, 0, y, z)) % MOD);

            }

            if ((prefixX != 0) && (prefixM == 0))

            {

                if (cnt2[a, 9, x, y, z] != 0)

                    ret = ((ret + (LL)cnt2[a, 9, x, y, z] * solve(pos + 1, 1, 0, y, z)) % MOD);

                if ((a != 0) && (cnt4[a - 1, 9, x, y, z] != 0))

                    ret = ((ret + (LL)cnt4[a - 1, 9, x, y, z] * solve(pos + 1, 0, 0, y, z)) % MOD);

            }

            if ((prefixX == 0) && (prefixM != 0))

            {

                if (cnt3[9, b, x, y, z] != 0)

                    ret = ((ret + (LL)cnt3[9, b, x, y, z] * solve(pos + 1, 0, 1, y, z)) % MOD);

                if ((b != 0) && cnt4[9, b - 1, x, y, z] != 0)

                    ret = ((ret + (LL)cnt4[9, b - 1, x, y, z] * solve(pos + 1, 0, 0, y, z)) % MOD);

            }

            if ((prefixX == 0) && (prefixM == 0))

            {

                if (cnt4[9, 9, x, y, z] != 0)

                    ret = ((ret + (LL)cnt4[9, 9, x, y, z] * solve(pos + 1, 0, 0, y, z)) % MOD);

            }

        }

        seen[pos, prefixX, prefixM, x] = cnt;

        return memo[pos, prefixX, prefixM, x] = ret;

    }

    static LL calc(LL X, LL M, LL z)

    {

        LL ret = 0;

        ++cnt;

        length = 0;

        while ((X != 0) || (M != 0))

        {

            XX[length] = X % 10;

            MM[length] = M % 10;

            X /= 10; M /= 10;

            length++;

        }

        if (length > 1)

        {

            for (LL i = 0; i < length / 2; i++)

            {

                LL temp = XX[i];

                XX[i] = XX[(length - 1) - i];

                XX[(length - 1) - i] = temp;

            }

            for (LL i = 0; i < length / 2; i++)

            {

                LL temp = MM[i];

                MM[i] = MM[(length - 1) - i];

                MM[(length - 1) - i] = temp;

            }   

        }

        ret = (solve(0, 1, 1, 0, z));

        return ret;

    }

    static LL calc()

    {

        LL ret = 0;

        LL i;

        LL p = ((calcAll(X, 5, 0)) % MOD);

        for (i = L; i <= N; i++)

        {

            LL q = ((calc(X, i, 0) - calc(X, i, 1)) % MOD);

            ret = (ret + (p - q) % MOD) % MOD;

        }

        if (ret < 0) ret += MOD;

        return ret;

    }

    public static int goodHexa(Int64input1, Int64 input2, Int64 input3, Int64input4)

    {

        N = input1; L = input2; X = input3; K = input4;

        LL ans;

        if (N >= 2 && N <= (Math.Pow(10, 9)) && (N - L <= 100) && L >= 2 && L <= N && X >= 1 && X < L && K >= 1 && K <= 5)

        {  

            now.Add(0); now.Add(0); now.Add(0); now.Add(0); now.Add(0);

            LL i, j, a;

            genStates(0, 0, 9);

            for (i = 0; i < 5; i++)

                for (j = 0; j < 16; j++)

                    make(i, j);

            for (i = 0; i < total; i++)

            {

                LL cnt = 0, ok = 1;

                for (j = 0; j < 5; j++)

                {

                    if (j == 0)

                    {

                        a = 0;

                    }

                    else

                        a = states[i][j - 1];

                    if ((j == 0) || (states[i][j] != a))

                        cnt = 1;

                    else

                        cnt++;

                    if (cnt > K) ok = 0;

                }

                if (ok != 0)

                    valid[i] = 1;

            }

            ans = calc();

        }

        else

        {

            ans = -1;

        }

        return (int)ans; 

    }

}

Create a Bootable CD from Floppy image or from files

In this article we are going to see how to create a our own bootable CD. First thing we need following items

• mkisofs
• Source Floppy image to write to CD

For Windows user you can download it here ftp://ftp.berlios.de/pub/cdrecord/alpha/win32/ 

• Go to the location where floppy image is located

         cd  ~/myos

• Create a directory to store the contents of the CD

         mkdir  cddir

• Copy the contents that are need to be added in the CD

         cp bootfiles/* cddir

• Copy the floppy image inside the directory         

         cp  floppy.img cddir

          Here  

               -o        indicates output file

               -v        indicates label of the CD

               -b        floppy image

              cddir   where all files should be taken from.

• Create a CD image from Floppy image

         mkisofs -o  osboot.iso -v myos -b floppy.img cddir

our_kernel  is the name of your kernel 

Command line to create a Bootable cd with out floppy image

   mkdir  -p  $ISO_DIR/boot/grub

   cp  $GRUB_BIN/stage2_eltorito $ISO_DIR/boot/grub

   cp menu.lst $ISO_DIR/boot/grub

   cp  our_kernel $ISO_DIR

         mkisofs -R -b boot/grub/stage2_eltorito -no-emul-boot-boot-load-size 4 -boot-info-table -o          bootcd.iso  $ISO_DIR

I Hope from this article you can learn how to create a bootable CD , by having the source as floppy image or files.

Add Row Dynamically in Table Using JQuery

Below code is used to add the row dynamically to table using JQuery.

How to find the row in tbody inside the Table using Jquery : 

$(‘#Search_table’).find("tbody").find("tr");

<table id="Search_table">

<thead>

<tr><td>USER ID</td>

<td>USER NAME</td>

<td>CURRENT POINT</td>

<td>ADD POINT</td>

<td>ADD DESCRIPTION</td>

<td>ACTION</td>

</tr>

 </thead>

<tbody> </tbody>

</table>

<script>

$(document).ready(function ()

{      

var table_tr="<tr><td>RajeshG</td><td>Rajesh

</td><td>100</td><td>100</td><td>

point added </td><td>ACTION </td></tr>";

$('#Search_table').find("tbody").append(table_tr);

//to append the tr in the tbody tag                  

});

</script>

Add a FACEBOOK like button in your website using JQuery

  Sometime we had wonder how the like button is integrated with corresponding Social Networking, if we gave like then the corresponding website like information is posted in the social network.

Now let we see how to add the like button in our website?

Get the Jquery SDK from the Facebook then add the element in DIV tag.

<html xmlns="http://www.w3.org/1999/xhtml">

<title>jQuery Implement on facebook Like button </title>

 <div id="fb-root"></div>

<script>(function (d, s, id)

{

    var js, fjs = d.getElementsByTagName(s)[0];

    if (d.getElementById(id))

      return;

    js = d.createElement(s);

    js.id = id;

    js.src = "//connect.facebook.net/en_US/all.js#xfbml=1&appId=497727420302756";

    fjs.parentNode.insertBefore(js, fjs);

}

(document, 'script', 'facebook-jssdk'));

window.onload = function ()

{

  var url = window.location.protocol + "//" + window.location.hostname +

 window.location.pathname;

  document.getElementsByClassName ("fb-like")[0].attributes[4].nodeValue =url;

};

</script>

   

<body>

    <form id="form1" runat="server">

 <div class="fb-like" data-href="" data-send="true" data-width="250"

data-show-faces="true"></div>

    </form>

</body>

</html>

Click Here to see the output

From this article you can see the how to add the Facebook like button in your own website.