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// STEP 1:
// Complete the following function as a recursive function
// sumInts:
// sum of the positive integers <= argument n
// Parameter:
// n (integer input) largest integer to include inah s the sum
int sumInts( int n )
{
return -5;
}
// STEP 2:
// Complete the following function as a recursive function
// sumSquares:
// sum of the squares of the positive integers <= argument n
// Parameter:
// n (integer input) largest integer whose square is included in sum
int sumSquares( int n )
{
return 3;
}
// STEP 3:
// Complete the following function as a recursive function
// sumArray:
// sum of the first elements in an array
// Parameters:
// arr (integer array input) array containing values to add up
// n (integer input) number of elements to include in the sum
int sumArray( const int arr[], int n)
{
return 10;
}
// step 4:
// Complete the following function as a recursive function
// intPower
// raises a value to a power that is an integer
// Parameters:
// base (double input) base to multiply as needed
// exponent (integer input) exponent to use
// NOTE: The exponent may be Negative -- but that is an easy
// adjustment to the value you get from a Positive exponent
// (and can use a recursive call to get that)
double intPower( double base, int exponent)
{
return 3.14;
}
// STEP 5:
// Compile and run your program to see how well it does.
// STEP 6:
// Complete the following function as a recursive function
// fibonacci
// returns a number from the fibonacci series:
// f(0) = 1; f(1) = 1; f(2) = 2; f(3) = 3; f(4) = 5
// each successive element is the sum of the preceding two
// Parameter:
// pos (integer input) desired position in Fibonacci sequence
int fibonacci( int pos )
{
return 6;
}
// STEP 7:
// Complete the following function WITHOUT recursion
// fibArray
// fills an array with the fibonacci sequence, as described above
// Paramters:
// arr (integer array output) array to fill
// n (integer input) number of array elements to fill
void fibArray( int arr[], int n )
{
}
// STEP 8:
// Compile and run your code to see how it performs
// STEP 9:
// Compute the following problem using an array like STEP 7 did.
// changeWays:
// counts the number of sequences of dimes and quarters
// that add up to a particular total
// e.g. 60 cents can be supplied four different ways:
// 25+25+10, 25+10+25, 10+25+25, 10+10+10+10+10+10
// Hint: How many ways can I get my result if I first insert a dime?
// How many ways can I get my result if I first insert a quarter?
int changeWays( int cost )
{
int arr[100] = {0}; // enough array spaces for up to 500 cents
// To make best use of this array, divide values by 5
// so 75 cents would be represented at subscript 75/5
return 3;
}
// STEP 10:
// See if your last answer worked, and in a reasonable amount of time
int main()
{
int sample[10] = { 2, 3, 5, 7, 1, 9, 4, 8, 6, 10 };
int fibList[50];
int tick, tock; // for timing fibonacci
int fib; // fibonacci answer
cout << "The sum of the first 5 integers is 15 = " << sumInts(5) << endl;
cout << "The sum of the first 9 integers is 45 = " << sumInts(9) << endl << endl;
cout << "The sum of the first 3 squares is 14 = " << sumSquares(3) << endl;
cout << "The sum of the first 7 squares is 140 = " << sumSquares(7) << endl << endl;
cout << "The first four prime numbers add up to 17 = " << sumArray( sample, 4 ) << endl;
cout << "The sum of the first 10 integers is 55 = " << sumArray( sample, 10 ) << endl << endl;
cout << "2 to the 3rd power is 8 = " << intPower( 2.0, 3 ) << endl;
cout << "4 to the 0th power is 1 = " << intPower( 4.0, 0 ) << endl;
cout << "5 to the 5th power is 3125 = " << intPower( 5.0, 5 ) << endl;
cout << "10 to the -3 power is 0.001 = " << intPower( 10.0, -3 ) << endl;
cout << "0.1 to the -3 power is 1000 = " << intPower( 0.1, -3 ) << endl << endl;
tick = clock();
fib = fibonacci( 10 );
tock = clock();
cout << "Computed fibonacci(10) = 89 = " << fib << " in " <<
((tock-tick)*1.0/CLOCKS_PER_SEC) << " seconds" << endl;
tick = clock();
fib = fibonacci( 40 );
tock = clock();
cout << "Computed fibonacci(40) = " << fib << " in " <<
((tock-tick)*1.0/CLOCKS_PER_SEC) << " seconds" << endl;
tick = clock();
fibArray( fibList, 50 );
tock = clock();
cout << "Filled 50 element fibonacci array in " <<
((tock-tick)*1.0/CLOCKS_PER_SEC) << " seconds" << endl;
cout << "Fib[10] = " << fibList[10] << " and fib[40] = " << fibList[40] << endl << endl;
cout << "There are " << changeWays( 60 ) << " ways to come up with 60 cents." << endl;
cout << "There are " << changeWays( 15 ) << " ways to come up with 15 cents." << endl;
cout << "There are " << changeWays(300 ) << " ways to come up with 3 dollars." << endl;
return 0;
}
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