Task 1 - 19B9029 Task 2 - 19B9046 Task 3 - 19B9052 Task 4 - 19B9046 Task 5 - 19B9027 Task 6 - 19B9029 README. - 19B9027 & 19B9052
Analysis of the Collatz Conjecture
- Assignment questions
- Please also read
INSTRUCTIONS.mdfor specific submission instructions and marking rubric.
#Task 1
Firstly we generate the Collatz function and create an empty tibble. Next we apply the gen_collatz function on integers from 1 to 10,000. Thus we have produce a tibble consist of the sequence of the integer, length, parity (odd and even) and the max_val.
#Task 2
In part 1 we find the top 10 strongest in descending order. We use arrange(desc()) to arrange in the descending order and then use the data.frame function to show in vector form. In Part 2 we find the starting integer that produces a sequence that reaches the highest maximum value. Next we apply the filter() function to subset the data frame, therefore we get 9663 for the max_val. For part 3 we find the average length and the standard deviation for both odd and even. firstly, we need to find the even and odd integer. Then to compare we use the mean() and sd() function. We got the even average length and odd average length which is 79.5936 and 92.3396 respectively. For the standard deviation we got 45.10308 for even and 47.1837 for odd.
#Task 3
In part 1 we use the has_backtracking function, this is used for comparing elements in the sequence. The function we are using also checks if the condition are met the functions TRUE however FALSE for otherwise. Next we use the mutate() and map_lgl, the reason for this function is to apply the method for each element of a vector. Thus, a new tibble will show for the result. Part 2 we find the most frequently occurring number of times sequences backtrack. The result we got was 53. In part 3 we made a tibble to find the each max value backtrack. Finally for part 4 we find the total for even and odd backtrack value which is 567643 for even and 292020 for odd.
#Task 4
First we create the scatter plot for the sequence length using the geom_point function. For the next scatter plot we used to find highest value reached in the sequence on the vertical axis, we also highlight the top 10 with the colour green. The final plotting is the box plot using the geom_boxplot. The different for even and odd is not noticeable however odd is higher than even.
#Task 5
In this question we are trying to find the trend or relation between prime numbers with its parity in collatz sequence. To analyse the data and to look for the trend sort out the prime numbers from collatz_df, by creating a function to sort out the prime numbers. After running the code we found out after the number 2 all of the prime number's parity is odd. Only prime number 2 has even parity. After analysing the table again, we found out the there is alot of repeating maximum value, such as the number 52 and 9232. But in the table number 9232 keeps popping up. In visualisation the collatz conjecture the connecting lines will mostly go to number 9232. When arranging the collatz conjecture diagram just like in the assignment page ( The circle diagram for collatz conjecture ) there will be many numbers connected to the number 9232 where as the maximum value always pops up the number 9232.
#Task 6
For part 1 we use geom_line for the sequence length change over a range of starting integer with sequence length in the x-axis and starting in the y-axis. In part 2 we use the histogram graph to find the fastest sequence to reach 1 when they first reached a value less than their starting integer. Part 3 we use a bar chart graph to find the common specific number appearing in the sequence with frequency in the x-axis and specific number in the y-axis.