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In this tutorial, we will be discussing a program to find maximum sum of nodes in Binary tree such that no two are adjacent using Dynamic Programming.For this we will be provided with a binary tree. Our task is to find the subset having maximum sum such that no two nodes in the subset are directly connected using Dynamic Programming.Example#include using namespace std; //finding diameter using dynamic programming void dfs(int node, int parent, int dp1[], int dp2[], list* adj, int tree[]){ int sum1 = 0, sum2 = 0; for (auto i = adj[node].begin(); i != adj[node].end(); ... Read More
The standardized coefficients in regression are also called beta coefficients and they are obtained by standardizing the dependent and independent variables. Standardization of the dependent and independent variables means that converting the values of these variables in a way that the mean and the standard deviation becomes 0 and 1 respectively. We can find the standardized coefficients of a linear regression model by using scale function while creating the model.ExampleConsider the below data frame −> set.seed(99) > x y df1 df1Output x y 1 1.7139625 1.2542310 2 1.9796581 2.9215504 3 1.5878287 2.7500544 4 1.9438585 ... Read More
In this tutorial, we will be discussing a program to find maximum sum of nodes in Binary tree such that no two are adjacent.For this we will be provided with a binary tree. Our task is to find the subset having maximum sum such that no two nodes in subset are directly connected.Example#include using namespace std; //binary tree node structure struct node { int data; struct node *left, *right; }; struct node* newNode(int data) { struct node *temp = new struct node; temp->data = data; temp->left = temp->right = NULL; return temp; } ... Read More
We are given an input N which denotes the size of the chessboard. The task here is to find for any value of N, how many bishops can be placed on the NXN chessboard such that no two bishops can attack each other. Let’s understand with examples.Input − N=2Output− Maximum bishops that can be placed on N*N chessboard − 2 ( as shown above )Explanation − As depicted above the only non-contradictory positions are where the bishops are placed. Bishops at-most for 2X2 chessboard.Input − N=5Output− Maximum bishops that can be placed on N*N chessboard: 8 ( as shown above ... Read More
The values of the categorical variable can be represented by numbers, by characters, by a combination of numbers and characters, by special characters, by numerical signs or any other method. But when we create the bar plot, if the size of a label name is large then we might want to reduce it by representing it with a different word or character or sign that gives the same meaning and it can be done by using expression argument inside scale_x_discrete.ExampleConsider the below data frame −> x y df dfOutput x y 1 0 25 2 100 28 3 150 ... Read More
We are given with a circular array. Circular array is the array for which we consider the case that the first element comes next to the last element. It is used to implement queues. So we have to count the maximum no. of consecutive 1’s or 0’s in that array.Let’s understand with examples.Input − Arr[] = { 1, 1, 0, 1, 0, 1, 0, 1, 1, 1 }Output − Maximum consecutive 1’s are 5. Or Maximum consecutive 0’s is 1.Explanation − From Arr[] index 7 to 9 and then indexes 0 and 1. 1’s are 5. No consecutive 0’s but ... Read More
When we create a bar plot or any other plot with legend, the background of the legend is white but it can be changed to any color with the help of scales package. We can make changes in the legend of a plot using alpha in legend.background argument of theme function. This will help us to change the background color of the legend.Example> x y df dfOutput x y 1 0 25 2 100 28 3 150 32 4 200 25Creating a bar plot with legend −> library(ggplot2) > ggplot(df, aes(x, y, fill=x))+geom_bar(stat="identity")OutputChanging the background color of the legend ... Read More
In this tutorial, we will be discussing a program to find maximum sum of pairs with specific difference.For this we will be provided with an array containing integers and a value K. Our task is to pair elements having difference less than K and finally find the maximum sum of the elements in disjoint sets.Example#include using namespace std; //returning maximum sum of disjoint pairs int maxSumPairWithDifferenceLessThanK(int arr[], int N, int K){ sort(arr, arr+N); int dp[N]; dp[0] = 0; for (int i = 1; i < N; i++) { dp[i] = dp[i-1]; ... Read More
We are given a string of alphabets. The task is to find the character which has the longest consecutive repetitions occurring in string. Let’s understand with examples.Input− String[] = “abbbabbbbcdd”Output − bExplanation − In the above string, the longest consecutive sequence is of character ‘b’. Count of consecutive b’s is 4.Input− String[] = “aabbcdeeeeed”Output − bExplanation − In the above string, the longest consecutive sequence is of character ‘e’. Count of consecutive e’s is 5.Approach used in the below program is as followsThe character array string1[] is used to store the string of alphabets.Function maxRepeating(char str[], int n) takes two ... Read More
We are given with an array of prime numbers, arranged in random order. The size of the array is N. The goal is to find the longest sequence of contiguous prime numbers in the array.Prime number is the one which has only two factors, 1 and the number itself. 1, 2, 3, 5, 7, 11, 13….are prime numbers whereas 4, 6, 8, 9, 10….20 are non-prime. Every non-prime number has more than 2 factors. Let’s understand with examples.Input − Arr[] = { 1, 3, 5, 2, 6, 7, 13, 4, 9, 10Output − 3Explanation − The prime numbers in the ... Read More