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f you aspire to be a highly effective leader, people must trust your judgment and ethics and have confidence in your leadership abilities, believing that you are worthy of authority. In the absence of trust and confidence, nothing else follows. A first task of every aspiring leader, therefore, is to earn the trust and confidence of those they seek to lead. Barack Obama has done this with great success, gaining the trust and confidence of the broad array of people who make up his diverse coalition everyday citizens, politicians, large donors, policymakers, members of the media establishment. He has drawn on this trust and confidence to capture key opportunities and expand his influence. Key communication practices have aided Obama in his quest. Using

public static void sort(int[] a) { // POSTCONDITION: a[0] <= a[1] <= ... <= a[a.length-1]; for (int i = a.length-1; i > 0; i--) { // step 1 int m = 0; // step 2 for (int j = 1; j <= i; j++) { if (a[j] > a[m]) { m = j; } } // INVARIANT: a[m] >= a[j] for all j <= i; swap(a, i, m); // step 3 // INVARIANTS: a[j] <= a[i] for all j <= i; // a[i] <= a[i+1] <= ... <= a[a.length-1]; } }

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Theorem 14.3 The selection sort is correct. See the solution to Problem 14.19 on page 276 for a proof of this theorem. Theorem 14.4 The selection sort runs in O(n2) time. See the solution to Problem 14.20 on page 276 for a proof of this theorem. Note that even though the bubble sort and the selection sort have the same complexity function, the latter runs quite a bit faster. That fact is suggested by the two traces: The bubble sort made 18 swaps while the selection sort made only 7. The selection sort has the advantage of swapping elements that are far apart, so it makes one swap where the bubble sort could require several. (See Exercise 11.8.) THE INSERTION SORT Like the two previous algorithms, the insertion sort makes n 1 passes through a sequence of n elements. On each pass it inserts the next element into the subarray on its left, thereby leaving that subarray sorted. When the last element is inserted this way, the entire array is sorted. Algorithm 14.3 The Insertion Sort (Precondition: s = {s0 . . . sn 1} is a sequence of n ordinal values.) (Postcondition: The entire sequence s is sorted.) 1. Do steps 2 4 for i = 1 up to n 1. 2. Hold the element si in a temporary space. 3. Locate the least index j for which sj >= si . 4. Shift the subsequence {sj . . . si 1} up one position to {sj+1 . . . si}. 5. Copy the held value of si into sj. 6. (Invariant: the subsequence { s0..si} is sorted.) EXAMPLE 14.6 The Insertion Sort

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public static void sort(int[] a) { // POSTCONDITION: a[0] <= a[1] <= ... <= a[a.length-1];

CHAP. 14]

WHAT IS COMPUTER SCIENCE Computer Science is defined in different ways by different authors. Wikipedia (http://en.wikipedia.org/ wiki/Computer_science) defines computer science as the collection of a variety of disciplines related to computing, both theoretical and practical: theoretical foundations of information and computation, language theory, algorithm analysis and development, implementation of computing systems, computer graphics, databases, data communications, etc. The US National Coordination Office for Networking and Information Technology Research and Development (NITRD) defines computer science in a similarly broad way:

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22

public class TestPolynomial { public static void main(String[] args) { Polynomial p = new Polynomial(3, -8, 0, 0, 2, 1); Polynomial q = new Polynomial(0, 5, 6, 9); System.out.println("p: " + p); System.out.println("p.degree(): " + p.degree()); System.out.println("q: " + q); System.out.println("q.degree(): " + q.degree()); System.out.println("p.plus(q): " + p.plus(q)); System.out.println("q.plus(p): " + q.plus(p)); System.out.println("p.plus(q).degree(): " + p.plus(q).degree()); Polynomial z = new Polynomial(0); System.out.println("z: " + z); System.out.println("z.degree(): " + z.degree()); System.out.println("p.plus(z): " + p.plus(z)); System.out.println("z.plus(p): " + z.plus(p)); System.out.println("p: " + p); Polynomial t = new Polynomial(8.88, 44); System.out.println("t: " + t); System.out.println("t.degree(): " + t.degree()); } }

the systematic study of computing systems and computation. The body of knowledge resulting from this discipline contains theories for understanding computing systems and methods; design methodology, algorithms, and tools; methods for the testing of concepts; methods of analysis and verification; and knowledge representation and implementation. (http://www.nitrd.gov/pubs/bluebooks/1995/section.5.html)

The output is:

p: 3.00 - 8.00x + 2.00x^4 + 1.00x^5 p.degree(): 5 q: 5.00x + 6.00x^2 + 9.00x^3 q.degree(): 3 p.plus(q): 3.00 - 3.00x + 6.00x^2 + q.plus(p): 3.00 - 3.00x + 6.00x^2 + p.plus(q).degree(): 5 z: 0 z.degree(): -1 p.plus(z): 3.00 - 8.00x + 2.00x^4 + z.plus(p): 3.00 - 8.00x + 2.00x^4 + p: 3.00 - 8.00x + 2.00x^4 + t: 8.88x^44 t.degree(): 44

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