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The linear recursive implementation of the Fibonacci sequence, which returns a pair of values `{fib(n), fib(n-1)}`, has a time complexity of O(log n).

Any problem that can be solved recursively can also be solved iteratively (using loops).

What is the output of the following Java code? public static int mystery(int n) { if (n < 10) { return n; } else { return mystery(n / 10) + (n % 10); } } // Call: System.out.println(mystery(345));

Analyze the following recursive method. What does it compute? public static int compute(int a, int b) { if (b == 0) { return 0; } if (b > 0) { return a + compute(a, b – 1); } return -compute(a, -b); }

What is the time complexity of the naive, binary recursive implementation of the Fibonacci sequence, as discussed in the chapter?

Ms. Johnson is 83 and has mobility problems that caused her children to put her in a nursing home for rehabilitation. She broke her hip and had a surgical repair that has been slow to heal. Prior to breaking her hip, the woman lived in her own home alone with minimal assistance from a cleaning service. She was independent and active in her church and community. She has been at the facility for less than a month. Since entering the nursing home, she has lost her appetite and is losing weight. She has developed difficulty sleeping at night. Ms. Johnson has been a very independent and energetic woman. She has begun to ask for help with tasks she can easily accomplish and is moving in a slower manner. In addition, she has become demanding and irritable when not acknowledged or assisted quickly enough. In the past two weeks, she has become somewhat confused about the layout of the facility and mildly disoriented at times. Ms. Johnson, who is gregarious and friendly, has become socially withdrawn and has vague complaints of pain. This morning, she was telling an attendant a story that was clearly delusional. Her family members were notified, and Ms. Johnson was referred to the local hospital for an evaluation. After numerous tests, the report indicated that Ms. Johnson likely had which of the following conditions?

What is the base case for the recursive `reverseArray` method discussed in the chapter? public static void reverseArray(int[] A, int i, int j) { … }

A sound wave travels along a tube oriented in the direction of the -axis. The displacement is given by

Janie, a 31-year-old woman, has come to the emergency room with chest pains, faintness, and shortness of breath. “I feel as if I am down in a well and I can’t breathe,” she says. She fears that she is having a heart attack, but when questioned, Janie states. “This should be the happiest time of my life; I am pregnant with my first child. My husband and I have moved into our dream house, and he is being promoted to vice president of the company, with a big raise and increased responsibilities. This has been a great year. They say this is not a heart attack. What is happening to me?” Diagnose Janie’s problem?  

Josh, a 32-year-old man diagnosed with moderate/severe schizophrenia, has been having hallucinations for 12 years since his first psychotic episode. His mother, Gertrude, 55, developed schizophrenia in her 20s and has both mood-congruent delusions and hallucinations. Josh indicates that he has the most common type of hallucinations. What type of hallucinations would this be?