Consider the following method: public boolean isprefix(String s1, String s2) { int i = 0; if(s1.length s2.length) return false; while(i

Question

Consider the following method:

public boolean isprefix(String s1, String s2) {

int i = 0;
    if(s1.length > s2.length) 
        return false;

while(i < s1.length) {
        if(s1[i] != s2[i])
            return false;
        i++;
    }
    return true;
}

Exactly how many lines of code (statements) are executed by the method isprefix() in the worst case?    Express your answer in terms of n, the length of the string s1.

Hint:  simplify your final answer as much as possible, and do not put spaces in your answer.  Use juxtaposition for the multiplication operator, for example to write "nine times n" write "9n" not "9xn" or "9*n";  to write "four times (n+2)" write "4(n+2)", not "4x(n+2)" or "4*(n+2)".  Do not write your answer in Big-O notation.  Write the exact number of lines executed.

BlackTom AI · Accepted Answer

We need to count how many statements are executed by isprefix() in the worst-case scenario, expressed in terms of n, the length of s1.

First, the method initializes i to 0. That is one statement executed upfront.

Then there is the if check: if (s1.length > s2.length) return false;. In the worst case we assume this condition is false (so we don’t take the early return). This is one additional statement that is evaluated.

Next, the while loop begins. The loop condition i < s1.length is checked on every iteration, and when i runs from 0 to n-1, this condition is evaluated n+1 times (including the final check that fails when i == n).

Inside the loop, for each iteration, there is the comparison if (s1[i] != s2[i]) return false;. In the worst case, this comparison evaluates to false every time (so we don’t hit the early return). This inner condition is evaluated n times during the loop.

Also inside the loop, after the comparison, there is i++ which is executed once per iteration. That gives n executions of the i++ statement.

After the loop completes, we reach return true;. This is one more executed statement.

Now sum up the contributions: initial i = 0 (1) + if-check (1) + while-condition checks (n+1) + inner equality checks (n) + i++ increments (n) + final return (1) = 1 + 1 + (n+1) + n + n + 1 = 3n + 4.

Therefore, the exact number of statements executed in the worst case is 3n+4, which matches the provided answer.

XLMC0202501 Topic 3 Quiz

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