What is the time complexity T(n) of the following program? a) int n, d, i, j; cin >> n; for (d=1; d<=n; d++) for (i=1; i<=d; i++) for (j=1; j<=n; j += n/10) cout << d << " " << i << " " << j << endl; b) void main() { int n, s, t; cin >> n; for (s = 1; s <= n/4; s++) {t = s; while (t >= 1) { cout << s << " " << t << endl; t--; } } } c) void main() { int n, r, s, t; cin >> n; for (r = 2; r <= n; r = r * 2) for (s = 1; s <= n/4; s++) { t = s; while (t >= 1) { cout << s << " " << t << endl; t--; } } }
3 9005Coin Problem You are given 9 gold coins that look identical. One is counterfeit and weighs a bit greater than the others, but the difference is very small that only a balance scale can tell it from the real one. You have a balance scale that costs 25 USD per weighing. Give an algorithm that finds the counterfeit coin with as little weighting as possible. Of primary importance is that your algorithm is correct; of secondary importance is that your algorithm truly uses the minimum number of weightings possible. HINT: THE BEST ALGORITHM USES ONLY 2 WEIGHINGS!!!
1 14808Performance Algorithm A performs 10n2 basic operations and algorithm B performs 300 lg n basic operations. For what value of n does algorithm B start to show its better performance?
7336Complexity T(n) What is the time complexity T(n) of the following portions of code? For simplicity, you may assume that n is a power of 2. That is, n = 2k for some positive integer k. a) ? for (i = 1; i <= n; i++) { j = n; cout << i << ? ? j << ? ? << endl; } b) ? for (i = 0; i <= n; i += 2) { j = n; cout << i << ? ? j << ? ? << endl; } c) ? for (i = n; i >= 1; i = i/2) { j = n; cout << i << ? ? j << ? ? << endl; } d) for (i = 1; i <= n; i++) { j = n; while (j >= 0) { cout << i << ? ? j << ? ? << endl; j = j - 2; } }
2619Complexity T(n) Write a linear-time algorithm that sorts n distinct integers, each of which is between 1 and 500. Hint: Use a 500-element array. (Linear-time means your algorithm runs in time c*n + b, where c and b are any constants that do not depend on n. For example, your algorithm can run in time n, or time 2n + 1, or time 5n + 10, or time 100n + 6, but not time c*n*n = c*n?.)
1 6443Subsets Write an algorithm that prints out all the subsets of 3 elements of a set of n elements. The elements of the set are stored in a list that is the input to the algorithm. (Since it is a set, you may assume all elements in the list are distinct.)
1 13158Min-Max Write an algorithm that finds both the smallest and largest numbers in a list of n numbers and calculate its complexity T(n).
1 6249Min-Max Write an algorithm that finds both the smallest and largest numbers in a list of n numbers and with complexity T(n) is at most about (1.5)n comparisons.
10 43439Faster Computers Suppose you have a computer that requires 1 minute to solve problem instances of size 1000. What instance sizes can be run in 1 minute if you buy a new computer that runs 1000 times faster than the old one, assuming the following time complexities T(n) for our algorithm? (a) T(n) = O(n). (b) T(n) = O(n3). (c) T(n) = O(10n).
1 10661Algorithm in O(2n) Presently we can solve in our hypothetical machine problem instances of size 100 in 1 minute using algorithm A, which is a O(2n). We would like to solve instances of size 200 in 1 minute using algorithm A on a new machine. What is the speed of the new machine should be?
2 6059Post New Qatar University Interview Questions
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1. A 380 / 220 V r.m.s. 3-phase 4-wire circuit carries loads of 8 + j8.1 ohm; 4 + j4.1 ohm; and 2 +j2.1 ohmin the three phases respectively. The length of the circuit is 100 m, and the resistivity of the phase conductors is 0.0005 Ω/m. The neutral conductor is of the same size as the phase conductors. a) Select a reference angle 0for the first phase. Then write down the three phase voltages in both polar format and complex number format. b) Make appropriate assumptions, and take temperature effects on resistance is insignificant. Calculate the currents in the three phases. (Note: Determine conductor resistance, and apply Kirchhoff’s Voltage Law) Based on the result, suggest a main switch rating for the circuit. c) Show your preferred direction of neutral current in a diagram, and then determine its value. (Note: Apply superposition principle, and Kirchhoff’s Current Law) Use its magnitude to show that in this circuit, the unbalanced load may increase the voltage drop in some of the phases. (Note: Also observe the common volt drip in neutral) State your assumptions, if there are any. d) Suddenly the neutral wire of the circuit is broken. Estimate the new currents in the first phase, i.e. Phase L1. State your assumptions, if there are any.
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