Design algorithms for the following two tasks and code them in Java:

$1.$ Write a Java method called fillArray that accepts a positive integer n as its only parameter. The method returns an array of length $\backslash ($ n$-1\backslash ).$ This array is filled with unique integers in the range $\backslash (0..\backslash$mathrm$\{$n$\}-1\backslash ).$ In other words, the array contains all but one of the numbers in that range. The numbers are not sorted; they are in random order.

$2.$ Write a second Java method called findMissingNumber that accepts as its only parameter an array of the type produced by fillArray. Find and return the number in the range $\backslash (0..\backslash$mathrm$\{$n$\}-1\backslash )$ that is missing from the array.

For both methods:

$-$ The algorithm must be $\backslash (\backslash$mathrm$\{$O$\}(\backslash$mathrm$\{$n$\})\backslash )$ for time complexity; and

$-$ You are only allowed to use O$(1)$ additional space besides the array itself. In other words, you cannot use a second array.

Include in your class a main method that tests both methods.

Include the following clearly labeled information in your submission document for Question $3$:

a$)$ The code for your complete Java class, including your main method, fillArray, and findMissingNumber.

b$)$ Output for multiple test cases for both $\backslash (\backslash$mathrm$\{$n$\}=10\backslash )$ and $\backslash (\backslash$mathrm$\{$n$\}=20\backslash ).$ For each test case, display $($and clearly label$)$:

$-$ the contents of the array produced by fillArray $($display all numbers on the same line$)$; and

$-$ the missing number as returned by findMissingNumber.

c$)$ An explanation of why your fillArray method is $\backslash (\backslash$mathrm$\{$O$\}(\backslash$mathrm$\{$n$\})\backslash )$ for time complexity

d$)$ An explanation of why your fillArray method is $\backslash (\backslash$mathrm$\{$O$\}(1)\backslash )$ for space usage, other than the array itself

e$)$ An explanation of why your findMissingNumber method is $\backslash (\backslash$mathrm$\{$O$\}(\backslash$mathrm$\{$n$\})\backslash )$ for time complexity

f$)$ An explanation of why your findMissingNumber method is $\backslash (\backslash$mathrm$\{$O$\}(1)\backslash )$ for space usage, other than the array itself