Category: Mathematics

• Project Euler Problem 2, solution internals related using ruby debugger

\$ruby -rdebug euler-two.rb Debug.rb Emacs support available. /usr/lib/ruby/2.1.0/rubygems/core_ext/kernel_require.rb:57: RUBYGEMS_ACTIVATION_MONITOR.enter (rdb:1) r /usr/lib/ruby/2.1.0/rubygems/core_ext/kernel_require.rb:57: RUBYGEMS_ACTIVATION_MONITOR.enter (rdb:1) r /usr/lib/ruby/2.1.0/rubygems/core_ext/kernel_require.rb:57: RUBYGEMS_ACTIVATION_MONITOR.enter (rdb:1) next /usr/lib/ruby/2.1.0/rubygems/core_ext/kernel_require.rb:143: RUBYGEMS_ACTIVATION_MONITOR.exit (rdb:1) next euler-two.rb:3:n1, n2 = 1, 2 (rdb:1) next euler-two.rb:4:sum = 0 (rdb:1) print n1 1nil (rdb:1) print n2 2nil (rdb:1) next euler-two.rb:6:while n2 < 4000000 (rdb:1) print n2 2nil (rdb:1) next euler-two.rb:7:sum +=…

• Project Euler Problem 3, solution internals using python debugger

\$python -m pdb euler-three.py > /home/jeffrin/beautifulwork/lib/euler-three.py(7)() -> ”’ (Pdb) r 6857 –Return– > /home/jeffrin/beautifulwork/lib/euler-three.py(17)()->None -> print n (Pdb) next –Return– > (1)()->None (Pdb) next The program finished and will be restarted > /home/jeffrin/beautifulwork/lib/euler-three.py(7)() -> ”’ (Pdb) next > /home/jeffrin/beautifulwork/lib/euler-three.py(9)() -> n = 600851475143 (Pdb) next > /home/jeffrin/beautifulwork/lib/euler-three.py(11)() -> i = 2 (Pdb) next > /home/jeffrin/beautifulwork/lib/euler-three.py(12)()…

• How to write an algorithm to find among natural numbers the sum of multiples of 3 and 5 below 1000 ?

/* This program has been worked on from http://www.s-anand.net/euler.html */ #include <stdio.h> sofmul() { int n, i; n = 0; for (i = 0 ; i < 1000 ; i++) { if ( !(i % 5) || !(i % 3) ) n = n + i; } printf(“Sum of the multiples of 3 and 5…

• How to write a program to multiply a number by 4 using a bitwise operator ?

/* Part of this program copied from http://www.sanfoundry.com/c-program-multiply-number-4-using-bitwise-operators/ */ #include <stdio.h> multbitwise() { long number; printf(“Enter an integer: “); scanf(“%ld”,&number); number = number << 2; printf(“Result is %ld \n”,number); } /* http://stackoverflow.com/questions/4456442/interview-multiplication-of-2-integers-using-bitwise-operators */ /* http://www.geeksforgeeks.org/multiply-two-numbers-without-using-multiply-division-bitwise-operators-and-no-loops/ */ /* http://en.wikipedia.org/wiki/Bitwise_operation */

• How to write an algorithm to do a binary to decimal conversion ?

/* part of work copied from http://www.sanfoundry.com/c-program-binary-number-into-decimal/ */ #include <stdio.h> btd() { int num, binary_val, decimal_val = 0, base = 1, rem; printf(“Enter a binary number : “); scanf(“%d”,&num); binary_val = num; while ( num > 0 ) { rem = num % 10; decimal_val = decimal_val + rem * base; num = num /…

• Hacking with integer divisibility

/* work copied from http://www.sanfoundry.com/c-program-number-divisible-by-5/ */ #include <stdio.h> numberdivi() { int i, num1, num2, count = 0, sum = 0; printf(“Enter the value of num1 and num2 : “); scanf(“%d %d”,&num1,&num2); for (i = num1; i < num2 ; i++) { if ((i % 5) == 0) { printf(“%3d,”,i); count++; sum = sum + i;…

• How to write an algorithm to find factorial of a given number ?

#include <stdio.h> factorial() { int p = 1; int i = 1; int n; printf(“Enter a Number greater than 0 \n”); scanf(“%d”,&n); while ( i <= n) { p = p * i; i = i + 1; } printf(“Factorial of the input is %d \n”,p); }

• Hacking with an algorithm to find prime factor of a number

\$./app Sign detection [1] Power of two [2] Counting No. of bits set [3] Set or clear bits without branching[4] Find maximum value[5] Finding least common multiple[6] Finding the greatest commom divisor[7] Finding if a number is an Armstrong number or not[8] Finding if a given number is prime number[9] Finding the number of twin…

• Tinkering with an Armstrong number finding program function

\$./app Sign detection [1] Power of two [2] Counting No. of bits set [3] Set or clear bits without branching[4] Find maximum value[5] Finding least common multiple[6] Finding the greatest commom divisor[7] Finding if a number is an Armstrong number or not[8] 8 Enter a positive integer: 153 153 is an Armstrong number \$./app Sign…