fair result from an unfair coin

you are given an unfair coin in which head has higher probability of occurring than tails.

solution :

assume

TH as head
HT as tail
TT, HH than toss again

now new head and tail have equal probabilities

Using bit vectors

a nice discussion on why one should use bit vectors and not integer arrays in some particular situations

bit vector

print a unsigned long int using putchar

problem : print an unsigned long integer using only putchar

solution : we'll have to break the number and print the individual digit, we can use % operation to get the digits

code :

void putlong(unsigned long n) {
  if (n < 10) {
    putchar(n + '0');
    return;
  }
  putlong(n / 10);
  putchar(n % 10 + '0');
}

reverse a string using recursion

problem : reverse a string using recursion

: solution

void print_reverse(char* str)
{
	if(*str=='\0')return;
	else
	print_reverse(str+1)
	putchar(*str);
}

permutation of parantheses

problem : generate all the permutations of valid parantheses

e.g.

input 1
output {}

input 2
output {}{}, {{}}

input 3
output: {}{}{}, {{{}}}, {{}{}}, {{}}{}, {}{{}}

solution :

note : number of permutation can be easily found by noticing that it is forming a catalan series, 1,2,5,... so nth term will be (2^n -n).

solution: