[Solution] High Frequency CodeChef Solution

Problem

Chef has an array $A$ of length $N$.

Let $F(A)$ denote the maximum frequency of any element present in the array.

For example:

• If $A = [1, 2, 3, 2, 2, 1]$, then $F(A) = 3$ since element $2$ has the highest frequency $= 3$.
• If $A = [1, 2, 3, 3, 2, 1]$, then $F(A) = 2$ since highest frequency of any element is $2$.

Chef can perform the following operation at most once:

• Choose any subsequence $S$ of the array such that every element of $S$ is the same, say $x$. Then, choose an integer $y$ and replace every element in this subsequence with $y$.

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For example, let $A = [1, 2, 2, 1, 2, 2]$. A few examples of the operation that Chef can perform are:

• $[1, \textcolor{red}{2, 2}, 1, 2, 2] \to [1, \textcolor{blue}{5, 5}, 1, 2, 2]$
• $[1, \textcolor{red}{2}, 2, 1, \textcolor{red}{2, 2}] \to [1, \textcolor{blue}{19}, 2, 1, \textcolor{blue}{19, 19}]$
• $[\textcolor{red}{1}, 2, 2, 1, 2, 2] \to [\textcolor{blue}{2}, 2, 2, 1, 2, 2]$

Determine the minimum possible value of $F(A)$ Chef can get by performing the given operation at most once.

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Input Format

• The first line of input will contain a single integer $T$, denoting the number of test cases.
• Each test case consists of two lines of input.
  • The first line of each test case contains a single integer $N$ denoting the length of array $A$.
  • The second line contains $N$ space-separated integers denoting the array $A$.

Output Format

For each test case, output the minimum value of $F(A)$ Chef can get if he performs the operation optimally.

Explanation:

Test case $1$: Chef cannot reduce the value of $F(A)$ by performing any operation.

Test case $2$: Chef can perform the operation $[\textcolor{red}{1}, 1, \textcolor{red}{1}, 1, \textcolor{red}{1}] \to [\textcolor{blue}{2}, 1, \textcolor{blue}{2}, 1, \textcolor{blue}{2}]$. The value of $F(A)$ in this case is $3$, which is the minimum possible.

Test case $3$: Chef can perform the operation $[1, \textcolor{red}{2, 2}, 1, 2, 2] \to [1, \textcolor{blue}{5, 5}, 1, 2, 2]$. The value of $F(A)$ in this case is $2$, which is the minimum possible.