Write a code fragment that prints yes if xc is in the interval and no if it is not.

Transcription

1 CS2 Lecture 4 28/9/9 Previous Lecture: Branching Logical operators oday s Lecture: Logical operators and values More branching nesting he idea of repetition Announcements: Section this week in the computer lab (Upson B7) Project (P) due hursday at 6pm Register your clicker with CI by Sept 9th Consider the quadratic function q() = 2 + b + c on the interval [L, R]:. Is the function strictly increasing in [L, R]? 2. Which is smaller, q(l) or q(r)? 3. What is the minimum value of q() in [L, R]? q() September 9, 28 Lecture 4 2 Modified Problem 3 Write a code fragment that prints yes if c is in the interval and no if it is not. q ( ) = 2 + b + c c = b / 2 No! L R September 9, 28 Lecture 4 3 September 9, 28 Lecture 4 4 So what is the requirement? % Determine whether c is in % [L,R] c = -b/2; if he value of a boolean epression is either true or false. (L<=c) && (c<=r) his (compound) boolean epression is made up of two (simple) boolean epressions. Each has a value that is either true or false. Connect boolean epressions by boolean operators: and or not && ~ September 9, 28 Lecture 4 7 September 9, 28 Lecture 4 9 Lecture slides

2 CS2 Lecture 4 28/9/9 Logical operators ruth table && logical and: Are both conditions true? E.g., we ask is L c and c R? In our code: L<=c && c<=r logical or: Is at least one condition true? E.g., we can ask if c is outside of [L,R], X Y X && Y and X, Y represent boolean epressions. E.g., d>3.4 X Y or ~Y not i.e., is c L or R c? In code: c<=l R<=c ~ logical not: Negation E.g., we can ask if c is not outside [L,R]. In code: ~(c<=l R<=c) September 9, 28 Lecture 4 3 September 9, 28 Lecture 4 2 ruth table X Y X && Y and Matlab uses to represent false, to represent true X Y or ~Y not Logical operators short-circuit a > b && c > d true Go on a > b && c > d false Stop Entire epression is false since the first part is false A && condition shortcircuits to false if the left operand evaluates to false. A condition shortcircuits to if September 9, 28 Lecture 4 22 September 9, 28 Lecture 4 23 Always use logical operators to connect simple boolean epressions Why is it wrong to use the epression L <= c <= R for checking if c is in [L,R]? Eample: Suppose L is 5, R is 8, and c is. We know that is not in [5,8], but the epression L <= c <= R gives Variables a, b, and c have whole number values. rue or false: his fragment prints Yes if there is a right triangle with side lengths a, b, and c and prints No otherwise. if a^2 + b^2 == c^2 A: true B: false September 9, 28 Lecture 4 25 September 9, 28 Lecture 4 26 Lecture slides 2

3 CS2 Lecture 4 28/9/9 a = 5; b = 3; c = 4; if (a^2+b^2==c^2) his fragment prints No even though we have a right triangle! a = 5; b = 3; c = 4; if ((a^2+b^2==c^2) (a^2+c^2==b^2)... (b^2+c^2==a^2)) September 9, 28 Lecture 4 27 September 9, 28 Lecture 4 28 q() Start with pseudocode Consider the quadratic function on the interval [L, R]: q() = 2 + b + c Is the function strictly increasing in [L, R]? Which is smaller, q(l) or q(r)? What is the minimum value of q() in [L, R]? If c is between L and R Min is at c Otherwise Min is at one of the points September 9, 28 Lecture 4 29 We have decomposed the problem into three pieces! Can choose to work with any piece net: the if- construct/condition, min at c, or min at an point September 9, 28 Lecture 4 34 Set up structure first: if-, condition Refinement: filled in detail for task min at c hen min is at c Min is at one of the points Min is at one of the points Now refine our solution-in-progress. I ll choose to work on the Continue with refining the solution -branch net if-branch September net 9, 28 September 9, 28 Lecture 4 36 Lecture 4 35 Lecture slides 3

4 CS2 Lecture 4 28/9/9 Refinement: detail for task min at an point Refinement: detail for task min at an point % min is at one of the points if %c left of bracket %min is at L %c right of bracket %min is at R % min is at one of the points if c < L Continue with the refinement, i.e., replace comments with code September 9, 28 Lecture 4 37 September 9, 28 Lecture 4 38 inal solution (given b,c,l,r,c) Notice that there are 3 alternatives can use if! % min is at one of the points if c < L An if-statement can appear within a branch just like any other kind of statement! September 9, 28 Lecture 4 39 if c < L September 9, 28 Lecture 4 4 op-down Design if c < L State problem Define inputs & outputs Design algorithm Convert algorithm to program Decomposition Stepwise refinement rue or false: We don t need the if keyword at all (in the Matlab language). A: true B: false September 9, 28 Lecture 4 42 est and debug An algorithm is an idea. o use an algorithm you must choose a programming language and implement the algorithm. Lecture slides 4

5 CS2 Lecture 4 28/9/9 If c is between L and R hen min value is at c Otherwise Min value is at one of the points % min is at one of the points September 9, 28 Lecture 4 45 September 9, 28 Lecture 4 46 % min is at one of the points % min is at one of the points if c < L September 9, 28 Lecture 4 48 September 9, 28 Lecture 4 5 Question % min is at one of the points if c < L September 9, 28 Lecture 4 5 A stick of unit length is split into two pieces. he breakpoint is randomly selected. On average, how long is the shorter piece? Physical eperiment? hought eperiment? analysis Computational eperiment! simulation Need to repeat many trials! September 9, 28 Lecture 4 52 Lecture slides 5