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Page 1263 of 2109
Count number of squares in a rectangle in C++
We are given with a rectangle of length L and breadth B, such that L>=B. The goal is to find the number of squares that a rectangle of size LXB can accommodate.Above figure shows a rectangle of size 3 X 2. It has 2, 2X2 squares and 6, 1X1 squares in it.Total squares= 6+2=8.Every rectangle of size LXB has L*B number of 1X1 squares.Biggest squares are of size BXB.For L=B=1, squares = 1.For L=B=2, squares = 1 + 4 = 5. ( 1 of 2X2, 4 of 1X1 )For L=B=3, squares = 1 + 4 + 9 = 14. ( ...
Read MoreHow to change the color and size of the axes labels of a plot created by using plot function in R?
The default size of axes labels created by using plot function does not seem to be large enough and also it does not look appealing. Therefore, we might want to change their size and color because the appearance of a plot matters a lot. This can be done by setting colors with col.lab and size with cex.lab.Example> x y plot(x,y)OutputChanging the color of axes labels and the size of those axes labels −> plot(x,y,col.lab="blue",cex.lab=2)Output> plot(x,y,col.lab="dark blue",cex.lab=3)Output
Read MoreCount number of right triangles possible with a given perimeter in C++
We are given a perimeter P of a triangle. Perimeter is the sum of all sides of the triangle. The goal is to find the number of right triangles that can be made which have the same perimeter.If the sides of the triangle are a, b and c. Then a + b + c = P and a2 + b2 = c2 ( pythagoras theorem for any combination of a, b, and c )We will check this by taking a from 1 to p/2 and b from a+1 to p/3. Then c = p-a-b (a+b+c=p)For all right triangles, apply Pythagoras ...
Read MoreHow to select rows based on range of values of a column in an R data frame?
Extraction or selection of data can be done in many ways such as based on an individual value, range of values, etc. This is mostly required when we want to either compare the subsets of the data set or use the subset for analysis. The selection of rows based on range of value may be done for testing as well. We can do this by subset function.ExampleConsider the below data frame −> x1 x2 x3 df dfOutput x1 x2 x3 1 3 2 6 2 3 4 9 3 4 4 12 4 4 8 12 5 3 5 11 6 ...
Read MoreCount number of step required to reduce N to 1 by following certain rule in C++
We are given a number N. The goal is to count the number of steps required to reduce the number to 1 by following rules −If the number is power of 2, reduce it to its half.Else reduce it to the N-(nearest power of 2 which is less than N).For step 1, we will check if N is power of 2, by checking if ceil(log2(N)), floor(log2(N)) return the same result. If yes then N=N/3, increment count of operation.If the result of step 1 is false then we will perform step 2 and subtract the nearest power of 2 less than ...
Read MoreHow to draw gridlines in a graph with abline function in R?
Gridlines are the horizontal and vertical dotted lines, and they help to organize the chart so that the values on the labels becomes better readable to viewers. This is helpful specially in situations where we plot a large number of data points. A graph drawn by plot function can have gridlines by defining the vertical and horizontal lines using abline.ExampleConsider the below data and scatterplot −> x y plot(x,y)OutputAdding gridlines using abline function −> abline(h=seq(0,5,0.5),lty=5) > abline(v=seq(-2,2,0.5),lty=5)Output
Read MoreCount number of triplets (a, b, c) such that a^2 + b^2 = c^2 and 1<=a<=b<=c<= n in C++
We are given an integer n. The goal is to find triplets ( set of 3 numbers ) that satisfy the conditions −a2+b2=c21
Read MoreWhy the t.test returns a smallest p-value of 2.2e – 16 in R?
When we perform a t test in R and the difference between two groups is very large then the p-value of the test is printed as 2.2e – 16 which is a printing behaviour of R for hypothesis testing procedures. The actual p-value can be extracted by using the t test function as t.test(“Var1”, ”Var2”, var.equal=FALSE)$p.value. This p-value is not likely to be the same as 2.2e – 16.Example1> x1 y1 t.test(x1, y1, var.equal=FALSE)Output Welch Two Sample t-test data: x1 and y1 t = -3617.2, df = 10098, p-value < 2.2e-16 alternative hypothesis: true difference in means is not equal ...
Read MoreCount number of triplets in an array having sum in the range [a,b] in C++
We are given an array of integers, Arr[] and two variables a and b to define a range [a,b]. The goal is to find the number of triplets whose sum lies in between this range [a,b].We will do this by using three for loops. Increment count if arr[i]+arr[j]+arr[k]>=a and arr[i]+arr[j]+arr[k]
Read MoreHow to show all X-axis labels in a bar graph created by using barplot function in R?
In base R, the barplot function easily creates a barplot but if the number of bars is large or we can say that if the categories we have for X-axis are large then some of the X-axis labels are not shown in the plot. Therefore, if we want them in the plot then we need to use las and cex.names.ExampleConsider the below data and bar graph −> x names(x) barplot(x)OutputShowing all the X-axis labels −> barplot(x,las=2,cex.names=0.5)Output
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