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Articles by Arnab Chakraborty
Page 377 of 377
Asymptotic Notation - O(), o(), Ω(), ω(), and θ()
Asymptotic NotationsAsymptotic notations are used to represent the complexities of algorithms for asymptotic analysis. These notations are mathematical tools to represent the complexities. There are three notations that are commonly used.Big Oh NotationBig-Oh (O) notation gives an upper bound for a function f(n) to within a constant factor.Little o NotationsThere are some other notations present except the Big-Oh, Big-Omega and Big-Theta notations. The little o notation is one of them.Little o notation is used to describe an upper bound that cannot be tight. In other words, loose upper bound of f(n).Big Omega NotationBig-Omega (Ω) notation gives a lower bound for ...
Read MoreAsymptotic Complexity
Asymptotic AnalysisUsing asymptotic analysis, we can get an idea about the performance of the algorithm based on the input size. We should not calculate the exact running time, but we should find the relation between the running time and the input size. We should follow the running time when the size of input is increased.For the space complexity, our goal is to get the relation or function that how much space in the main memory is occupied to complete the algorithm.Asymptotic BehaviorFor a function f(n) the asymptotic behavior is the growth of f(n) as n gets large. Small input values ...
Read MoreC++ Program for Zeckendorf's Theorem?
Here we will see how to check whether the given sum is found by adding some nonneighbouring Fibonacci numbers or not, if so, what are the numbers? For example if the give sum value is 10, this is sum of 8 and 2. Both 8 and 2 are Fibonacci terms and they are not adjacent. Let us see the algorithm to get the idea.AlgorithmnonNeighbourFibo(sum)Begin while sum > 0, do fibo := greatest Fibonacci term but not greater than sum print fibo sum := sum - fibo done EndExample#include using ...
Read MoreC++ Internals?
Here we will see the Class internals. Before that we will see Default constructors, which are related to internals. The default constructor is one constructor (defined by user or compiler) that does not take any argument. Now the question comes, why the default constructor is used?If the default constructor is not given, the compiler will implicitly declare default constructor. Default constructors are used to initialize some class internals. It will not affect the data member of the class. The compiler inserts default constructor in some different situations. Suppose a class is derived from another class with default constructor, or one ...
Read MoreA Boolean Matrix Question in C++?
Here we will see one interesting Boolean matrix problem. One Boolean matrix is given which contains 0’s and 1’s. Our goal is to find where 1 is marked. If the 1 is marked at position mat[i, j], then we will make all entries to 1 of the row i and column j. Let us see an example. If the matrix is like below −1 0 0 1 0 0 0 0 0 0 0 0 0 1 0 0Then after modification, it will be −1 1 1 1 1 1 0 1 1 1 0 1 1 1 1 1AlgorithmmatrixUpdate(matrix[R, ...
Read MoreC++ Program for Sum of squares of first n natural numbers?
In this problem we will see how we can get the sum of squares of first n natural numbers. Here we are using one for loop, that runs from 1 to n. In each step we are calculating square of the term and then add it to the sum. This program takes O(n) time to complete. But if we want to solve this in O(1) or constant time, we can use this series formula −AlgorithmsquareNNatural(n)begin sum := 0 for i in range 1 to n, do sum := sum + i^2 done return ...
Read MoreC++ tricks for competitive programming (for C++ 11)?
Here we will see some good tricks of C++ programming language that can help us in different area. Like if we want to participate in some competitive programming events, then these tricks will help us to reduce the time for writing codes. Let us see some of these examples one by one.Checking whether a number is odd or even without using % operator. This trick is simple. We can perform bitwise AND operation with the number and 1. If the result is non-zero then this is odd, otherwise this is even. The logic is too simple. All odd numbers have ...
Read MoreC++ Program for Comb Sort?
The basic idea of comb sort and the bubble sort is same. In other words, comb sort is an improvement on the bubble sort. In the bubble sorting technique, the items are compared with the next item in each phase. But for the comb sort, the items are sorted in a specific gap. After completing each phase, the gap is decreased. The decreasing factor or the shrink factor for this sort is 1.3. It means that after completing each phase the gap is divided by 1.3. Time Complexity is O(n log n) for best case. O(n2/2nP) (p is number of ...
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