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09-07feb20recursion

09-07feb20recursion - CS100J February 20 Recursion Read pp...

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1 CS100J February 20 Recursion Recursion : If you get the point, stop; otherwise, see Recursion. Infinite recursion : See Infinite recursion. Read: pp. 403-408 but SKIP sect. 15.1.2 Look in ProgramLive CD, page 15-3, for some interesting recursive methods. Download presented algorithms from the website Recursive definition : A definition that is defined in terms of itself. Recursive method : a method that calls itself (directly or indirectly). Recursion is often a good alternative to iteration (loops), which we cover next. Recursion is an important programming tool. Functional languages have no loops —only recursion. 2 Turn recursive definition into recursive function Factorial : !0 = 1 base case !n = n * !(n-1) for n > 0 recursive case Thus, !3 = 3 * !2 = 3 * 2 * !1 = 3 * 2 * 1 * !0 = 3 * 2 * 1 * 1 (= 6) // = !n (for n 0) public static int fact( int n) { if (n == 0) { return 1; base case } // {n > 0} an assertion return n * fact(n-1); recursive case } (a recursive call) note the precise specification 3 Two issues in coming to grips with recursion 1. How are recursive calls executed? 2. How do we understand a recursive method and how do we create one? We discuss the first issue later. Suffice it to say that if you execute a call on a recursive method, carefully using our model of execution, you will see that it works. Briefly, a new frame is created for each recursive call. DON’T try to understand a recursive method by executing its recursive calls! Use execution only to understand how it works.
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