NPTEL Design and analysis of algorithms Assignment 1 Answer 2023

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1. What does f(2000,3) return??
   pythonCopy code

   f(m,n) {
ans = 1;
count = 0;
while (ans <= m) {
count = count + 1;
ans = ans * n;
}
return(count)
}


   Answer: 7

2. Suppose someone designs a new airline routing algorithm called MagicPath and claims that its worst-case complexity is O(n^2 log n). Which of the following statements is inconsistent with this claim.
   • Answer: For every sufficiently large n, there is an input of size n for which MagicPath requires time proportional to n3.
3. You are executing an algorithm with worst-case time complexity O(n^4) on a CPU that can perform 10^8 operations per second. Which of the following is the most accurate guarantee for the time required to solve a worst-case input of size 800?
   • Answer: Under 5 minutes
4. Suppose f(n) is n^2 log n. Consider the following statements. (A) f(n) is O(n √ n) (B) f(n) is O(n^2 √n) (C) f(n) is O(n^3)
   • Answer: (B) is true but (A) and (C) are not true.
5. In the code fragment below, first and last are integer values and composite(x) is a function that returns true if x is not a prime number and false otherwise.
   pythonCopy code

   i = 0; j = 0; k = 0;
   for (m = last; m >= first; m = m - 1){
   k = k + m;
   if (composite(m)){
   i = i + m;
   }else{
   j = j - m;
   }
   }

   if (…) {
print("True");
}else{
print("False");
}


   Which of the following expressions can we put in place of the missing if condition (…) to ensure that the program prints “True”?

   • Answer: k == i + j
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