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Articles by Arnab Chakraborty
Page 300 of 377
Bernoulli Distribution in Data Structures
The Bernoulli Distribution is a discrete distribution having two possible outcomes labeled by x = 0 and x = 1. The x = 1 is success, and x = 0 is failure. Success occurs with probability p, and failure occurs with probability q as q = 1 – p. So$$P\lgroup x\rgroup=\begin{cases}1-p\:for & x = 0\p\:for & x = 0\end{cases}$$This can also be written as −$$P\lgroup x\rgroup=p^{n}\lgroup1-p\rgroup^{1-n}$$Example#include #include using namespace std; int main(){ const int nrolls=10000; default_random_engine generator; bernoulli_distribution distribution(0.7); int count=0; // count number of trues for (int i=0; i
Read MoreBinomial Distribution in Data Structures
The Binomial Distribution is a discrete probability distribution Pp(n | N) of obtaining n successes out of N Bernoulli trails (having two possible outcomes labeled by x = 0 and x = 1. The x = 1 is success, and x = 0 is failure. Success occurs with probability p, and failure occurs with probability q as q = 1 – p.) So the binomial distribution can be written as$$P_{p}\lgroup n\:\arrowvert\ N\rgroup=\left(\begin{array}{c}N\ n\end{array}\right) p^{n}\lgroup1-p\rgroup^{N-n}$$Example#include #include using namespace std; int main(){ const int nrolls = 10000; // number of rolls const int nstars = 100; // maximum ...
Read MoreC++ Program for Cocktail Sort?
The Cocktail sort is another variation of bubble sort. In the bubble sort technique, it always searches from left to right, and finds the largest element at the end, in the second phase it finds the second largest element at the second last position. This sorting technique traverses in both directions alternatively. Let us see the algorithm to understand the idea.Algorithmcocktail(array, n)Begin flag := true start := 0, end := n-1 while flag is set, do flag := false for i in range start to end-1, do ...
Read MoreConvex Hull Example in Data Structures
Here we will see one example on convex hull. Suppose we have a set of points. We have to make a polygon by taking less amount of points, that will cover all given points. In this section we will see the Jarvis March algorithm to get the convex hull.Jarvis March algorithm is used to detect the corner points of a convex hull from a given set of data points.Starting from left most point of the data set, we keep the points in the convex hull by anti-clockwise rotation. From a current point, we can choose the next point by checking ...
Read MoreC++ Program for Gnome Sort?
Here we will see how the gnome sort works. This is another sorting algorithm. In this approach if the list is already sorted it will take O(n) time. So best case time complexity is O(n). But average case and worst case complexity is O(n^2). Now let us see the algorithm to get the idea about this sorting technique.AlgorithmgnomeSort(arr, n)begin index := 0 while index < n, do if index is 0, then index := index + 1 end if if arr[index] >= arr[index -1], then ...
Read MoreC++ Program for Largest K digit number divisible by X?
In this problem we will try to find largest K-digit number, that will be divisible by X. To do this task we will take the largest K digit number by this formula ((10^k) – 1). Then check whether the number is divisible by X or not, if not, we will get the exact number by using this formula.𝑚𝑎𝑥−(𝑚𝑎𝑥 𝑚𝑜𝑑 𝑋)One example is like a 5-digit number, that is divisible by 29. So the largest 5-digit number is 99999. This is not divisible by 29. Now by applying the formula we will get −99999−(99999 𝑚𝑜𝑑 29)=99999−7=99992The number 99992 is divisible by ...
Read MoreSort elements of the array that occurs in between multiples of K in C++
Suppose we have an array A, and another integer K. We have to sort the elements that are in between any two multiples of K. Suppose A is like [2, 13, 3, 1, 21, 7, 8, 13, 12], and K = 2. The output will be [2, 1, 3, 7, 13, 21, 8, 13, 12]. Here multiple of 2 are 2, 8 and 12, the elements in between 2 and 8 are 13, 3, 1, 21, 7, they will be sorted as 1, 3, 7, 13, 21, the elements between 8 and 12 is only 13, so that is already ...
Read MoreC++ Program to Split the array and add the first part to the end?
Here we will see how to split an array, and add the first part after splitting at the end position. Suppose the array contents are {0, 1, 2, 3, 4, 5, 6, 7, 8, 9}. We want to cut this intro two parts. The first part is from index 0 to 3 (split size 4), and second part is rest. After adding the first part at the end, the array elements will be like this {4, 5, 6, 7, 8, 9, 0, 1, 2, 3}. To solve this problem, we will follow this algorithm.AlgorithmsplitArray(arr, n, k)begin for i := ...
Read MoreSplit the array into equal sum parts according to given conditions in C++
Here we will see one problem. Suppose one array arr is given. We have to check whether the array can be split into two parts, such that −Sub of both sub-arrays will be the sameAll elements, which are multiple of 5, will be in the same groupAll elements which are multiple of 3, but not multiple of 5, will be in the same groupAll other elements will be in other groups.Suppose the array elements are {1, 4, 3}, then this can be split, because the sum of {1, 3} is the same as the sum of {4}, and the groups ...
Read MoreMedian and Mode using Counting Sort in C++
Consider we have an array of size n, we have to find the Median and Mode using the counting sort technique. This technique is useful, when the array elements are in limited range. Suppose the elements are {1, 1, 1, 2, 7, 1}, then the Mode is 1, and Median is 1.5. Let us see what is Median and what is Mode −Median is the middle number in a sorted list of numbersMode is the element whose occurrences are maximum in the listTo get the Median and Mode, we have to follow these steps −Assume that the size of the ...
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