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  • Tricky Big-O complexity

    - by timeNomad
    public void foo (int n, int m) { int i = m; while (i > 100) i = i/3; for (int k=i ; k>=0; k--) { for (int j=1; j<n; j*=2) System.out.print(k + "\t" + j); System.out.println(); } } I figured the complexity would be O(logn). That is as a product of the inner loop, the outer loop -- will never be executed more than 100 times, so it can be omitted. What I'm not sure about is the while clause, should it be incorporated into the Big-O complexity? For very large i values it could make an impact, or arithmetic operations, doesn't matter on what scale, count as basic operations and can be omitted?

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  • Recursion problem; completely lost

    - by timeNomad
    So I've been trying to solve this assignment whole day, just can't get it. The following function accepts 2 strings, the 2nd (not 1st) possibly containing *'s (asterisks). An * is a replacement for a string (empty, 1 char or more), it can appear appear (only in s2) once, twice, more or not at all, it cannot be adjacent to another * (ab**c), no need to check that. public static boolean samePattern(String s1, String s2) It returns true if strings are of the same pattern. It must be recursive, not use any loops, static & global variables. Can use local variables & method overloading. Can use only these methods: charAt(i), substring(i), substring(i, j), length(). Examples: 1: TheExamIsEasy; 2: "The*xamIs*y" --- true 1: TheExamIsEasy; 2: "Th*mIsEasy*" --- true 1: TheExamIsEasy; 2: "*" --- true 1: TheExamIsEasy; 2: "TheExamIsEasy" --- true 1: TheExamIsEasy; 2: "The*IsHard" --- FALSE I tried comparing the the chars one by one using charAt until an asterisk is encountered, then check if the asterisk is an empty one by comparing is successive char (i+1) with the char of s1 at position i, if true -- continue recursion with i+1 as counter for s2 & i as counter for s1; if false -- continue recursion with i+1 as counters for both. Continue this until another asterisk is found or end of string. I dunno, my brain loses track of things, can't concentrate, any pointers / hints? Am I in the right direction? Also, it's been told that a backtracking technique is to be used to solve this. My code so far (doesn't do the job, even theoretically): public static boolean samePattern(String s1, String s2) { if (s1.equals(s2) || s2 == "*") { return true; } return samePattern(s1, s2, 1); } public static boolean samePattern(String s1, String s2, int i) { if (s1.equals(s2)) return true; if (i == s2.length() - 1) // No *'s found -- not same pattern. return false; if (s1.substring(0, i).equals(s2.substring(0, i))) samePattern(s1, s2, i+1); else if (s2.charAt(i-1) == '*') samePattern(s1.substring(0, i-1), s2.substring(0, i), 1); // new smaller strings. else samePattern(s1.substring(1), s2, i); }

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  • Big O Complexity of a method

    - by timeNomad
    I have this method: public static int what(String str, char start, char end) { int count=0; for(int i=0;i<str.length(); i++) { if(str.charAt(i) == start) { for(int j=i+1;j<str.length(); j++) { if(str.charAt(j) == end) count++; } } } return count; } What I need to find is: 1) What is it doing? Answer: counting the total number of end occurrences after EACH (or is it? Not specified in the assignment, point 3 depends on this) start. 2) What is its complexity? Answer: the first loops iterates over the string completely, so it's at least O(n), the second loop executes only if start char is found and even then partially (index at which start was found + 1). Although, big O is all about worst case no? So in the worst case, start is the 1st char & the inner iteration iterates over the string n-1 times, the -1 is a constant so it's n. But, the inner loop won't be executed every outer iteration pass, statistically, but since big O is about worst case, is it correct to say the complexity of it is O(n^2)? Ignoring any constants and the fact that in 99.99% of times the inner loop won't execute every outer loop pass. 3) Rewrite it so that complexity is lower. What I'm not sure of is whether start occurs at most once or more, if once at most, then method can be rewritten using one loop (having a flag indicating whether start has been encountered and from there on incrementing count at each end occurrence), yielding a complexity of O(n). In case though, that start can appear multiple times, which most likely it is, because assignment is of a Java course and I don't think they would make such ambiguity. Solving, in this case, is not possible using one loop... WAIT! Yes it is..! Just have a variable, say, inc to be incremented each time start is encountered & used to increment count each time end is encountered after the 1st start was found: inc = 0, count = 0 if (current char == start) inc++ if (inc > 0 && current char == end) count += inc This would also yield a complexity of O(n)? Because there is only 1 loop. Yes I realize I wrote a lot hehe, but what I also realized is that I understand a lot better by forming my thoughts into words...

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