PLEASE HELP ME

2) 20 points. Big-O Analysis.

a) Use the definition of Big-O, prove that 6n³ + 12n² + 2n + 1 has an upper bound of O(n³)?

b) Give meaningful and Big-O bounds for the following two functions and justify your answers. The algorithms dont compute anything worthwhile so just focus on the runtime.

int algo1(int n)

{

sum = 0;

for( int i = 0; i < n; ++i )

for( int j = 0; j < i * i; ++j )

for( int k = 0; k < j; ++k )

++sum;

return sum;

}

int algo2(int n)

{

sum = 0;

for( int i = 1; i < n; ++i )

for( int j = 1; j < i * i; ++j )

if( j % i == 0 )

for( int k = 0; k < j; ++k )

++sum;

return sum;

}