Given these methods: METHOD math1: public int math1( int n ) { if (n <= 1) { return 1; } // if...
Given these methods:
METHOD math1:
public int math1( int n ) {
if (n <= 1) {
return 1;
} // if
else {
return ( n * 2 ) + math1( n-1 );
} // else
} // math1
METHOD math2:
public int math2( int n ) {
if (n <= 1) {
return 1;
} // if
else {
return n + math1( n ) * math2( n/2 );
} // else
} // math2
(a) Set up a recurrence relation for the running time of the method math1 as a function of n. Solve your recurrence relation to specify theta bound of math1.
(b) Now set up a recurrence relation for the running time of the method math 2 as a function of n. Solve your recurrence relation to specify the Big-Oh bound of math 2.
HINT: When doing this, the call to math 1 can be replaced by the equation that you found when solving the recurrence relation for math 1 in part a).
Homework Answers
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Given these methods: METHOD math1: public int math1( int n ) { if (n <= 1) { return 1; } // if...
Consider the following recursive method for finding the maximum element in an int array: public int...
Consider the following recursive method for finding the maximum element in an int array: public int static max(int[] a, int lo, int hi) { if (lo > hi) return a[lo]; int mid = (lo + hi) / 2; int loMax = max(a, lo, mid); int hiMax = max(a, mid+1, hi); if (loMax > hiMax) return loMax; else return hiMax; } Write down the recurrence relation for counting the number of times the comparison if (loMax > hiMax) is performed. Use...
Compute the recurrence relation, T(n), for the following function, solve it, and give a e bound....
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1. public int function(int x, int n) { if (n == 0) return 1; return x...
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