{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

Fl03hw1

# Fl03hw1 - Complete the stopping conditions(describe as...

This preview shows pages 1–2. Sign up to view the full content.

HW1) [10=10+10] pts 1. Program and compare the complexity of those two algorithms. a) for (i=0; i<n; i++) { complexity++; } b) for (i=0; i<n; i++) { for (j=0; j<=i*i; j++) { for (k=0; k<j; k++) { complexity++; } } } You may pick any 4 different values for n. n Complexity of a Complexity of b 1 1 0 2 2 1 3 2 11 4 4 56 2. Show the changes of the values for each variable (i, j) by hand (n=5). for (i=1; i<n; i++) { for (j=1; j<i*i; j++) { if (j%i==0){ System.out.println(“i=” + i + “ j=” + j); } } } i j 2 2 3 3 3 6 4 4 4 8 4 12 3. A gcd algorithm is provided below based on the following observation (arrange so that a > b). gcd(a,b) = 2gcd(a/2, b/2) if a and b are both even. gcd(a,b) = gcd(a/2,b) if a is even and b is odd. gcd(a,b) = gcd(a,b/2) if a is odd and b is even. gcd(a,b) = gcd((a+b)/2, (a-b)/2) if a and b are both odd.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: Complete the stopping conditions (describe as specifically as possible) public static int gcd (int a, int b) { if (a<b) {int temp=a; a=b; b=temp;} // arrange so that a > b. if ( ? ) { return ? ; /* recursion termination */} if (b==0) return a; if (a==b) return a; if (a==b) return b; if (a%b==0) return b; {if (a==1||b==1) return 1; if (a==b) return b;} if (a%2==0 && b%2==0) // if a and b are both even return 2*gcd(a/2, b/2); else if (a%2==0 && b%2!=0) // if a is even and b is odd return gcd(a/2, b); else if (a%2!=0 && b%2==0) // if a is odd and b is even return gcd (a, b/2); else // if a and b are both odd return gcd ((a+b)/2, (a-b)/2); }...
View Full Document

{[ snackBarMessage ]}

### Page1 / 2

Fl03hw1 - Complete the stopping conditions(describe as...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online