IdeaMonk

thoughts, ideas, code and other things...

Friday, October 31, 2008

Binary Search Tree in C++

Finally delete_node() is done!
// BST.cpp - ideamonk.blogspot.com
#include <iostream>

using namespace std;

class BSTnode{
public:
int data;
BSTnode *left, *right;

BSTnode(){
left=right=NULL;
}

BSTnode (int dat, BSTnode *lft=NULL, BSTnode *rgt=NULL){
data = dat;
left = lft;
right = rgt;
}
};

class BST{
public:
BSTnode *root;

BST(){
root = NULL;
}

bool isEmpty() { return root==NULL; }

void insert (int el, BSTnode* &myroot){
if (myroot==NULL){
myroot = new BSTnode (el,0,0);
cout << el << " inserted\n";
} else if (el<myroot->data){
insert (el,myroot->left);
} else if (el>myroot->data){
insert (el,myroot->right);
}
}

bool search(int el, BSTnode* &start){
if (start!=NULL){
if (el<start->data){
return search(el,start->left);
} else if (el>start->data){
return search (el,start->right);
} else {
return true;
}
}
return false;
}

void inorder(BSTnode* &myroot){
if (myroot->left!=NULL)
inorder(myroot->left);
if (myroot!=NULL){
visit (myroot);
}
if (myroot->right!=NULL){
inorder(myroot->right);
}
}

void preorder(BSTnode* &myroot){
if (myroot!=NULL){
visit (myroot);
}
if (myroot->left!=NULL)
inorder(myroot->left);
if (myroot->right!=NULL){
inorder(myroot->right);
}
}

void postorder(BSTnode* &myroot){
if (myroot->left!=NULL)
inorder(myroot->left);
if (myroot->right!=NULL){
inorder(myroot->right);
}
if (myroot!=NULL){
visit (myroot);
}
}

void visit(BSTnode* &node){
cout << node->data<<"->";
}

void delete_node (BSTnode** node){
if (node==NULL) return;
BSTnode *old_node = *node;
if ((*node)->left == NULL){
*node = (*node)->right;
delete old_node;
} else if ((*node)->right == NULL){
*node = (*node)->left;
delete old_node;
} else {
/* NODE with 2 children */
// find inorder predecessor
BSTnode **pred = &(*node)->left;
while ((*pred)->right != NULL) {
*pred = (*pred)->right;
}
// swap pred's data
swap ((*pred)->data, (*node)->data);
delete_node (pred);
}
}

BSTnode** find_node (int data){
BSTnode** node = &root;
while (*node != NULL) {
if (data < (*node)->data)
node = &(*node)->left;
else if ((*node)->data < data)
node = &(*node)->right;
else
break;
}
return node;
}
};

int main(){
BST b;
b.insert (4,b.root);
b.insert (10,b.root);
b.insert (6,b.root);
b.insert (3,b.root);
b.insert (12,b.root);
b.insert (2,b.root);

cout << "inorder traversal - ";
b.inorder (b.root);
cout << endl;

cout << "deleting 4\n";
b.delete_node (b.find_node(4));

cout << "preorder traversal - ";
b.preorder (b.root);
cout << endl;

cout << "postorder traversal - ";
b.postorder (b.root);
cout << endl;

if (b.search(13,b.root))
cout << "13 found!\n";
else
cout << "13 not found\n";

if (b.search(2,b.root))
cout << "2 found!\n";
else
cout << "2 not found\n";

system ("pause");

return 0;
}

Labels: , ,

Thursday, October 30, 2008

Infix to Postfix conversion

Here is a classic example of application of stacks - postfix conversion.
Also called the RPN (Reverse Polish Notation). You might as well solve the ONP problem on spoj.pl and get some points once you understand the logic!
#include <iostream>
#include <stack>

using namespace std;

int prec (char ch){
// Gives precedence to different operators
switch (ch) {
case '^':
return 5;
case '/':
return 4;
case '*':
return 4;
case '+':
return 2;
case '-':
return 1;
default :
return 0;
}
}

bool isOperand(char ch){
// Finds out is a character is an operand or not
if ((ch>='0' && ch<='9') || (ch>='a' && ch<='z'))
return true;
else
return false;
}

string postFix (string infix){
string pfix = "";
stack<char> opstack;

for (int i=0; i<infix.length(); i++){
// Scan character by character
if (isOperand(infix[i]))
{
pfix += infix[i];
}
else if (infix[i] == '(')
{
opstack.push(infix[i]);
}
else if (infix[i] == ')')
{
// Retrace to last ( closure
while (opstack.top() != '(')
{
pfix += opstack.top();
opstack.pop();
}
// Remove the '(' found by while loop
opstack.pop();
}
else
{
// pop out stuff till we find '(' or stack is empty or
// precedence of current op is <= the op on top
while ( !opstack.empty() &&
opstack.top()!='(' &&
prec(infix[i]) <= prec(opstack.top()) )
{
pfix += opstack.top();
opstack.pop();
}

opstack.push(infix[i]);
}
}

// pop out remaining characters of stack
while (!opstack.empty())
{
pfix += opstack.top();
opstack.pop();
}
return pfix;
}

int main (){
string infix;
while (cin >> infix)
cout << postFix (infix)<<endl;

//system ("pause");
return 0;
}
Read this article to get the idea how it is done.
You can also test it from sample inputs at - http://www.cs.man.ac.uk/~pjj/cs2121/fix.html

Labels: ,

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

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Thursday, October 02, 2008

How object oriented programming saved me from working for hours!

A week back I was meddling with my 2-D game called nincompoop to be put to Pwned!- the game programming contest at Shaastra 2008, iit madras. Just 2 days left for submission... and I was done with the basic class for hero and level collisions. What to do?? How much still left to do?? Will this ever finish?! These were the questions daunting me hour by hour...
Untill a simple idea struck my mind! I asked to myself... What are enemies in the game? and the lord said "Nothing but a hero who is controlled by the computer" and that was precisely the point where I felt the game was almost done! What basically I mean here is that, remove all the keyboard controls from a hero class, automate its motion, and to do that we just have to modify the hero class a bit.
Here's how it works -
// The hero class
class nincompoops {
public:
// *** Bitmap & allegro assets for hero
BITMAP *sprite_walk[4][12]; // 12 frame animation for walk

// *** Motion variables
bool walking, onGround,jumping,attacking;
int heroFrame, direction,oldDirection;
int jumpVel;
int xvel, yvel;
int recoil;
.
.
.

nincompoops(){
// *** initial motion settings
score=0;
jumping=onGround = walking = dropping = false;
velMax = 3;
.
.
.
.

}
bool loadSprites();
void levelCollision(BITMAP *lev);

void draw (BITMAP *bmp);

void decideKeys();
};
And the enemies class is a very similar class with some modifications in the decideKeys() functions, where desideKeys() actually never checks for keys.
class enemies {
public:
// *** Bitmap & allegro assets for enemy
BITMAP *sprite_walk[2][12]; // 12 frame animation for walk

// *** Motion variables
bool walking, onGround,jumping,attacking;
int heroFrame, direction,oldDirection;
int jumpVel;
int xvel, yvel;
int recoil;
int MaxFrames;
.
.
.

enemies(){
// *** initial motion settings
score=0;
jumping=onGround = walking = dropping = false;
velMax = 3;
.
.
.
.

}

bool loadSprites(int type);

void levelCollision(BITMAP *lev);

void draw (BITMAP *bmp);

void decideKeys() {

// doesn't look for keyboard keys, manages by collisions etc to the level
... rest of the hero class code
}
};
So, what about the items in the game!! The answer is simple again, items are nothing but enemies that don't move! So, I come up with an item class in another 10 or so minutes. :)

Finally we do something like this -
vector<enemies> enemyset;
vector<enemies>::iterator ei;

vector<items> itemset;
vector<items>::iterator ii;
And load all enemies and items from a file, and the game loop goes like this
// pseudocode
while (!key[KEY_ESC]) {
nin.decideKeys();
nin.levelCollision (cmap);

for_each item in itemset {
item.draw(work,x,y);
item.testCollision(hero);
}


for_each enemy in enemyset {
enemy.draw(work,x,y);
enemy.decideKeys();
enemy.testCollision(hero);
}

blit_all_to_screen();
}
The game finally finished around 1 AM on 30th of September which happened to be the last date. Thanks to understanding machhas @ iit, they had no problem for late submissions. And thanks to OOP, I finished major chunk of game within four hours... and that means I couldn't work on giving finishing touches, adding a story, animations, humour etc. more about the fest soon...

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Wednesday, October 01, 2008

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!

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