Adding large numbers in C++

Just wrote a C++ snippet to add huge numbers using strings -

#include <iostream>
using namespace std;

string add (string &s1, string &s2){
int carry=0,sum,i;

string  min=s1,
 max=s2,
 result = "";

// Finds the bigger string
if (s1.length()>s2.length()){
 max = s1;
 min = s2;
} else {
 max = s2;
 min = s1;
}

// Fills the result for overlapping regions of sum
for (i = min.length()-1; i>=0; i--){
 sum = min[i] + max[i + max.length() - min.length()] + carry - 2*'0';

 carry = sum/10;
 sum %=10;

 result = (char)(sum + '0') + result;
}

// Summates the previous carry and the remaining digits of bigger string
i = max.length() - min.length()-1;

while (i>=0){
 sum = max[i] + carry - '0';
 carry = sum/10;
 sum%=10;

 result = (char)(sum + '0') + result;
 i--;
}

// Adds the carry if remaining to the last digit e.g 999+1=1000
if (carry!=0){
 result = (char)(carry + '0') + result;
}

return result;
}

int main (){
// implementation
string a,b;
cin >> a >> b;
cout << add (a,b)<<endl;
return 0;
}

Output :

32485689234981709712094710984091842358764876328746187648716462938589273589723895789237587238947189748917894718973891728937189478913277893257891749817984719287439812789473289475328975981723894718927489127894712894

9999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999

32485689234981709712094710984091842358764876328746187648716462938589273599723895789237587238947189748917894718973891728937189478913277893257891749817984719287439812789473289475328975981723894718927489127894712893

Optimization by Memoization ( not memorization )

To iterate is Human, to Recurse, to Recurse, Divine - unknown

Solving COINS at spoj was a great lesson in recursion. Beautiful may the recursive code seem, but in some cases it is slow as a snail in worst case scenario. Consider finding nth Fibonacci by recursion as an example! And in some cases as in finding p^q, recursion is truly divine god's gift ;P.
Same is the case with COINS, its pretty easy to figure out the function that gets the job done... but give it something like n = 1000000000, poof! it vanishes into a deep slumber!
So, how can we make it work faster... ?
Have you ever noticed that, kids are asked to remember multiplication tables from 2 to 10 when in primary mathematics classes! Ever wondered why to do this mugging up at such a tender age. The answer is in... how we multiply two big numbers (abcd * pqrs). Here every digit i & j is in range of 0 through 9. So, if you've memorized multiplication table for 2 to 9, it will be very easy to get through (abcd * pqrs).
Thats exactly what we will do here. Basically as the problem gets solved for bigger numbers, loads of steps trickle down to maxm() function for small numbers, just like end of roots of a tree. So, here again we will pre-calculate and store maxm(n) in an array for 1<n<9400. Why 9400? Have a look at http://www.spoj.pl/problems/COINS/, you can't write more that 50KB of code! So this weekend I decide to see the real consequence of memoization. Here's the allegro code I wrote to plot time against my COIN's solution. Memoization 9400 values works for the spoj judge. And it seems even memorizing 450 values works amazingly for my Athlon 64 :P

#include <iostream>
#include <allegro.h>
#include <time.h>

using namespace std;
unsigned int a[]={0,1,2,3,4,5,6,7,8,9,10,11,13,13,14,15,17,17,19,19,21,22,23,23,27,27,27,28,30,30,32,32,35,36,36,36,41,41,41,41,44,44,46,46,48,49,49,49,57,57,57,57,57,57,60,60,63,63,63,63,68,68,68,69,74,74,76,76,76,76,76,76,87,87,87,87,87,87,87,87,92,93,93,93,98,98,98,98,101,101,104,104,104,104,104,104,119,119,119,120,120,120,120,120,120,120,120,120,129,129,129,129,134,134,134,134,134,134,134,134,144,144,144,144,144,144,147,147,155,155,155,155,160,160,160,161,161,161,161,161,161,161,161,161,185,185,185,185,185,185,185,185,185,185,185,185,185,185,185,185,193,193,197,197,197,197,197,197,207,207,207,207,207,207,207,207,212,212,212,212,221,221,221,221,221,221,221,221,221,222,222,222,250,250,250,250,250,250,253,253,253,253,253,253,253,253,253,253,253,253,253,253,253,253,253,253,276,276,276,276,276,276,276,276,284,284,284,284,284,284,284,284,284,284,284,284,284,284,284,284,304,304,304,305,305,305,305,305,305,305,305,305,314,314,314,314,327,327,327,327,327,327,327,327,337,337,337,337,337,337,341,341,341,341,341,341,341,341,341,341,341,341,341,341,341,341,341,341,391,391,391,391,391,391,391,391,391,392,392,392,392,392,392,392,392,392,392,392,392,392,392,392,392,392,392,392,392,392,392,392,405,405,405,405,419,419,419,419,419,419,419,419,419,419,419,419,439,439,439,439,439,439,439,439,439,439,439,439,439,439,439,439,447,447,447,447,447,447,447,447,469,469,469,469,469,469,469,469,469,469,469,469,469,469,469,469,469,469,473,473,473,473,473,473,524,524,524,524,524,524,524,524,524,524,524,524,533,533,533,533,533,533,533,533,533,534,534,534,534,534,534,534,534,534,534,534,534,534,534,534,534,534,534,534,534,534,534,534,534,534,534,534,590,590,590,590,590,590,590,590,590,590,590,590,590,590,590,590,603,603,603,603,603,603,603,603,603,603,603,603,603,603,603,603,603,603,603,603,603,603,603,603,603,603,603,603,603,603,603,603,641,641,641,641,641,641,646,646,646,646,646,646,646,646,646,646,646,646,646,646,646,646,646,646,668,668,668,668,668,668,668,668,689,689,689,689,689,689,689,689,689,689,689,689,689,689,689,689,709,709,709,709,709,709,709,709,709,709,709,709,723,723,723,723,723,723,723,723,723,723,723,723,723,723,723,723,723,723,723,723,723,723,723,723,723,723,723,724,724,724,724,724,724,724,724,724,826,826,826,826,826,826,826,826,826,826,826,826,826,826,826,826,826,826,830,830,830,830,830,830,830,830,830,830,830,830,830,830,830,830,830,830,830,830,830,830,830,830,830,830,830,830,830,830,830,830,830,830,830,830,830,830,830,830,830,830,830,830,830,830,851,851,851,851,851,851,851,851,892,892,892,892,892,892,892,892,892,892,892,892,892,892,892,892,892,892,892,892,892,892,892,892,930,930,930,930,930,930,930,930,930,930,930,930,930,930,930,930,930,930,930,930,930,930,930,930,930,930,930,930,930,930,930,930,943,943,943,943,943,943,943,943,943,943,943,943,943,943,943,943,994,994,994,994,994,994,994,994,994,995,995,995,995,995,995,995,995,995,995,995,995,995,995,995,995,995,995,995,995,995,995,995,995,995,995,995,1009,1009,1009,1009,1009,1009,1009,1009,1009,1009,1009,1009,1101,1101,1101,1101,1101,1101,1101,1101,1101,1101,1101,1101,1101,1101,1101,1101,1101,1101,1101,1101,1101,1101,1101,1101,1123,1123,1123,1123,1123,1123,1123,1123,1123,1123,1123,1123,1123,1123,1123,1123,1123,1123,1128,1128,1128,1128,1128,1128,1128,1128,1128,1128,1128,1128,1128,1128,1128,1128,1128,1128,1128,1128,1128,1128,1128,1128,1128,1128,1128,1128,1128,1128,1128,1128,1128,1128,1128,1128,1128,1128,1128,1128,1128,1128,1128,1128,1128,1128,1128,1128,1128,1128,1128,1128,1128,1128,1257,1257,1257,1257,1257,1257,1257,1257,1257,1257,1257,1257,1257,1257,1257,1257,1257,1257,1257,1257,1257,1257,1257,1257,1257,1257,1257,1258,1258,1258,1258,1258,1279,1279,1279,1279,1279,1279,1279,1279,1279,1279,1279,1279,1279,1279,1279,1279,1279,1279,1279,1279,1279,1279,1279,1279,1279,1279,1279,1279,1279,1279,1279,1279,1279,1279,1279,1279,1279,1279,1279,1279,1279,1279,1279,1279,1279,1279,1279,1279,1279,1279,1279,1279,1279,1279,1279,1279,1279,1279,1279,1279,1279,1279,1279,1279,1350,1350,1350,1350,1350,1350,1350,1350,1350,1350,1350,1350,1370,1370,1370,1370,1370,1370,1370,1370,1370,1370,1370,1370,1370,1370,1370,1370,1370,1370,1370,1370,1370,1370,1370,1370,1370,1370,1370,1370,1370,1370,1370,1370,1370,1370,1370,1370,1421,1421,1421,1421,1421,1421,1421,1421,1421,1421,1421,1421,1421,1421,1421,1421,1455,1455,1455,1455,1455,1455,1455,1455,1455,1455,1455,1455,1455,1455,1455,1455,1455,1455,1455,1455,1455,1455,1455,1455,1455,1455,1455,1455,1455,1455,1455,1455,1493,1493,1493,1493,1493,1493,1493,1493,1493,1493,1493,1493,1493,1493,1493,1493,1493,1493,1493,1493,1493,1493,1493,1493,1533,1533,1533,1533,1533,1533,1533,1533,1533,1533,1533,1533,1533,1533,1533,1533,1533,1533,1533,1533,1533,1533,1533,1533,1533,1533,1533,1533,1533,1533,1533,1533,1533,1533,1533,1533,1533,1533,1533,1533,1533,1533,1533,1533,1533,1533,1533,1533,1533,1533,1533,1533,1533,1533,1538,1538,1538,1538,1538,1538,1538,1538,1538,1538,1538,1538,1538,1538,1538,1538,1538,1538,1741,1741,1741,1741,1741,1741,1741,1741,1741,1741,1741,1741,1741,1741,1741,1741,1741,1741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double lim = 0;

unsigned int maxm(unsigned int n){
// 9400 - size of array
if (n<lim)
 return a[n];

unsigned int p;
p = n/2 + n/3 + n/4;

if (p>n)
 //sort of binary recursion which you should figure out to solve COINS
else
 return n;
}

int main (){
unsigned int n=10,col2,col;
double x=0,px=1,py=760,y;
clock_t start ,stop;

allegro_init();
set_color_depth(32);
set_gfx_mode (GFX_AUTODETECT_WINDOWED,1024,768,0,0);

clear_to_color (screen,makecol(0,0,0));

while (lim<450){
 col = makecol ((lim/450)*250+5,  (lim/450)*255, 100);
 col2=makecol (((lim/450)*250+5)/3,  (lim/450)*255/3, 100/3);
 while (n<310){
  n+=1;
  start = clock();
  maxm(n*20000);
  stop = clock();
  //  cout << stop <<" "<<start << endl;
  y=760-((stop-start)*5);
  rectfill (screen,px,760,px+3,y,col2);
  line (screen,px,py,px+3,y,col);
 
  px+=3;
  py=y;
 }
 lim=lim+5;
 x=0; px=1; py=760;
 n=10;
 cout << lim<<endl;
}
getchar();
}
END_OF_MAIN();

And here's the plot! amazing visible differences...

checkout the drastic improvement from lim=0 to lim=450!

That's all for the Friday research folks!

Recursive fractals

Off lately recursion has become much more fascinating than ever it was to me. And the obvious catalyst in this has been computer graphics. Without visualization its impossible to appreciate the beauty of recursion, trees, sorting algorithms, etc!
Having admired the Sierpinski triangles I wondered how such an experimentation would look upon squares. And I came up with the following written in devCPP & Allegro graphics library-

#include <allegro.h>

BITMAP *work;

void draw (int x,int y,int w){
int i,j,c,r,g,b;
if (x<0 || y<0 || x>639 || y>479 || w<5)
return;

int nw=w/2;
draw(x-w/2-1,y-w/2-1,nw);
draw(x+w/2+1,y+w/2+1,nw);
draw(x-w/2-1,y+w/2+1,nw);
draw(x+w/2+1,y-w/2-1,nw);

c=w;
for (w=c;w>=1;w--){
r=((float)(sin(w)*sin(w)*c/3)/(float)c)*(float)255;
g=((float)(c-w/2)/(float)c)*(float)255;
b=((float)(w/2)/(float)c)*(float)255;
if (w<1){
r=g=b=0;
}
rect(work,x-w/2,y-w/2,x+w/2,y+w/2, makecol (r,g,b));
}
w=c;
r=((float)(c-w)/(float)c)*(float)255;
g=((float)(c-w)/(float)c)*(float)255;
b=((float)w/(float)c)*(float)255;
rect(work,x-w/2-1,y-w/2-1,x+w/2+1,y+w/2+1, makecol (r/2,g/2,b/2));
}

int main (){
allegro_init();
install_keyboard();
set_color_depth(32);
set_gfx_mode (GFX_AUTODETECT_WINDOWED,640,480,0,0);

work = create_bitmap(640,480);
clear_to_color(work,makecol(255,255,255));

draw(320,240,200);
while (!key[KEY_ESC]){
vsync();
blit (work,screen,0,0,0,0,640,480);
}

allegro_exit();
return 0;
}
END_OF_MAIN();

Some circular modifications -

#include <allegro.h>

BITMAP *work;

void draw (int x,int y,int w){
int i,j,c,r,g,b;
if (x<0 || y<0 || x>SCREEN_W || y>SCREEN_H || w<5)
return;

int nw=(float)w*(float)(.5);
draw(x-w/2-1,y-w/2-1,nw);
draw(x+w/2+1,y+w/2+1,nw);
draw(x-w/2-1,y+w/2+1,nw);
draw(x+w/2+1,y-w/2-1,nw);

c=w;
for (w=c;w>=1;w--){
r=((float)(w/2)/(float)c)*(float)255;
g=((float)(c-w/2)/(float)c)*(float)255;
b=((float)(c-w/2)/(float)c)*(float)255;
if (w<1){
r=g=b=0;
}
circlefill (work,x,y,w/2,makecol (r,g,b));
}
}

int main (){
allegro_init();
install_keyboard();
set_color_depth(32);
set_gfx_mode (GFX_AUTODETECT_WINDOWED,800,600,0,0);

work = create_bitmap(SCREEN_W,SCREEN_H);
clear_to_color(work,makecol(255,255,255));

draw(SCREEN_W/2,SCREEN_H/2,300);
while (!key[KEY_ESC]){
vsync();
blit (work,screen,0,0,0,0,SCREEN_W,SCREEN_H);
}

allegro_exit();
return 0;
}
END_OF_MAIN();

beautiful! what more can I say.

SPOJ PALIN

#include <iostream>
#include <vector>
using namespace std;

bool compare(vector<int> n1,vector<int> n2,int half){
 // if n1>n2 for problem size(n1) == size(n2)
 for (int i=n1.size()-1;i>=half;i--){
  if (n1[i]!=n2[i])
   return n1[i]>n2[i];
 }
 return false;
}

void work(vector<int>& num, int pos1, int pos2) {
 if (pos1 < 0) {
  num[num.size()-1] = 1;
  num.insert(num.begin(), 1);
  return;
  } else 
 if (num[pos1] < 9) {
        num[pos1] = num[pos2] = num[pos1] + 1;
        return;
    } else {
       num[pos1] = num[pos2] = 0;
        work(num, pos1-1, pos2+1);
        return;
   }
}

main (){
 char n;
 vector<int> num,old;
 int half,ssize;
 
 n=getc(stdin);
 while (n!='\n'){
  num.push_back(n-'0');
  n=getc(stdin);
 }
 while (num.size()>=1 && num[0]!=0){
  old = num;
  ssize=num.size();
  if (ssize%2==0){
   //even
   half=ssize/2;
   //mirror into vector
   for (int i=0;i<half;i++){
    num[ssize-1-i]=num[i];
   }
   if (compare(num,old,half)){
    for (int i=0;i<ssize;i++){
     printf ("%d",num[i]);
    }
    printf ("\n");
   } else {
    work (num,half-1,half);
    ssize=num.size();
    for (int i=0;i<ssize;i++){
     printf ("%d",num[i]);
    }
    printf ("\n");
   }
  } else {
   //odd
   half=ssize/2 ;
   //mirror into vector
   for (int i=0;i<half;i++){
    num[ssize-1-i]=num[i];
   }
   if (compare(num,old,half)){
    for (int i=0;i<ssize;i++){
     printf ("%d",num[i]);
    }
    printf ("\n");
   } else {
    work (num,half,half);
    ssize=num.size();
    for (int i=0;i<ssize;i++){
     printf ("%d",num[i]);
    }
    printf ("\n");
   }
  }
  num.clear();
  n=getc(stdin);
  while (n!='\n'){
   num.push_back(n-'0');
   n=getc(stdin);
  }
 }
}

Don't start smiling at the code above, thinking that you've got the solution!
The problem with the above is that its a TLE for SPOJ. If you can spot or fix the problem with the code, the points are free for you to grab. And if you are a little benevolent then do consider hinting me too on the shortcomings of this problem.
Adios

Going to ICPC finally

Went to ACM - ICPC 2007 Asia Region, Amritapuri this time. Amazing experience, and really tough problems for my level at this time! Still my team clean_sweep managed to rank 32nd in all 60+ competitors. Had pretty bad experience with mooshack. They should implement something like spoj.pl. I don't find those presentation problems in spoj!

team.each {|name| print name+","}

output
Bhuvanesh, Rijesh, Shaabi, Navdeep, Me!

at ICPC for each problem you solve... you get a baloon.. wonderful to see

after coming back I started on CodeFire with Shaabi, a programming contest platform for my own college. So, after struggling in the labs we finally had {PHP + MySQL + VB + DevCPP} => CodeFire!

My first linux ASM code

SECTION .data
 msg db "hello world",10
 len dw 12

SECTION .text
   global start
start:
 mov eax,4 ; the 'write' syscall
 mov ebx,1 ; on stdout
 mov ecx,msg ; the string
 mov edx,len ; its length
 int 0x80 ; interrupt
 mov eax,1 ; exit syscall
 mov ebx,0
 int 0x80 ;

Wooh!!! soon i will be reversing apps. nhahahaaa