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Applying the method of node voltages at a and using (1), we get vab Vs p 2 vab Is 0 R1 Rearrangement and substitution of given values lead to p vab 10 vab 25 0 Letting x2 vab and applying the quadratic formula, we obtain q 10 10 2 4 25 2:071 or x 2

If the name we are searching for is in the list, on average the algorithm will have to look at half the names on the list before finding a match If the name we are searching for is not on the list, the algorithm will have to look at all the names on the list If the list is twice as long, approximately twice as many comparisons will be necessary If the list is a million times as long, approximately a million times as many comparisons will be necessary In that case, the time devoted to the statements executed only once will become insignificant with respect to the execution time overall The running time of the sequential search algorithm grows in proportion to the size of the list being searched We say that the order of growth of the sequential search algorithm is n The notation for this is T(n).

public double valueAt(double x) { // returns the y-value p(x) of p at the specified x-value // This implements Horner's method. if (this.isZero()) { return 0.0; } ListIterator<Term> it = list.listIterator(); Term term = null; while (it.hasNext()) { // move to last element term = it.next(); } term = it.previous(); double y = term.coef; int n = term.exp; while (it.hasPrevious()) { term = it.previous(); y *= Math.pow(x, n - term.exp); y += term.coef; n = term.exp; } y *= Math.pow(x, n); return y; } public Polynomial times(double factor) { // returns a new polynomial that is equal to this polynomial if (this.isZero() || factor == 0.0) { return ZERO; } Polynomial p = new Polynomial(this); for (Term t : p.list) { t.coef *= factor; } return p; }

12:071

The negative root is extraneous, since the resulting value of vab would not satisfy KVL; thus, vab 2:071 2 4:289 V and i 2 2:071 4:142 A

A hash table (also called a map, a lookup table, an associative array, or a dictionary) is a container that allows direct access by any index type. It works like an array or vector except that the index variable need not be an integer. A good analogy is a dictionary; the index variable is the word being looked up, and the element that it indexes is its dictionary definition. A table is a sequence of pairs. The first component of the pair is called the key. It serves as the index into the table, generalizing the subscript integer used in arrays. The second component is called the value of its key component. It contains the information being looked up. In the dictionary example, the key is the word being looked up, and the value is that word s definition (and everything else listed for that word). A table is also called a map because we think of the keys being mapped into their values, like a mathematical function: f(key) = value. Tables are also called an associative arrays because they can be implemented using two parallel arrays; the keys in one array and the Figure 8.1 The Map classes of the JCF values in the other. THE JAVA Map INTERFACE The Java Collections Framework includes a Map interface, as shown in Figure 8.1. It is defined in the java.util package like this:

We also say that an algorithm whose order of growth is within some constant factor of T(n) has a theta of NL say The sequential search has a theta of n The size of the problem is n, the length of the list being searched Since for large problems the one-time-only or a-few-times-only statements make little difference, we ignore those constant or nearly constant times and simply focus on the fact that the running time will grow in proportion to the length of the list being searched Of course, for any particular search, the time required will depend on where in the list the match occurs If the first name is a match, then it doesn t matter how long the list is If the name does not occur in the list, the search will always require comparing the search name with all the names in the list.

CHAP. 1]

public interface Map { int size(); boolean isEmpty(); boolean containsKey(Object key); boolean containsValue(Object value); Object get(Object key); Object put(Object key, Object value); Object remove(Object key); void putAll(Map map); void clear();