1. Pairs

Consider two arrays of integers, a[n] and b[n]. What is the maximum number of pairs that can be formed where a[i] > b[j]? Each element can be in no more than one pair.

Find the maximum number of such possible pairs.

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Example:

Input:

n = 3
a = [1, 2, 3]
b = [2, 1, 1]

Explanation:

Two ways the maximum number of pairs can be selected:

• {a[1], b[0]} = {2, 1} and {a[2], b[2]} = {3, 1} are valid pairs.
• {a[1], b[0]} = {2, 1} and {a[2], b[1]} = {3, 2} are valid pairs.

No more than 2 pairs can be formed, so return 2.

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Function Description:

Complete the function findNumOfPairs in the editor below.

Function Signature:

def findNumOfPairs(a: List[int], b: List[int]) -> int:

Parameters:

• a[n]: an array of integers
• b[n]: an array of integers

Returns:

• int: the maximum number of pairs

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Constraints:

• 1 ≤ n ≤ 10^5
• 1 ≤ a[i] ≤ 10^9
• 1 ≤ b[i] ≤ 10^9

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Input Format for Custom Testing:

Sample Input:

5
1
2
3
4
5
5
6
6
1
1
1

Sample Output:

3

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Explanation:

Valid pairs are:

• {a[1], b[2]}
• {a[2], b[3]}
• {a[3], b[4]}

Other possible valid pairs include:

• {2, 1}, {3, 1}, {4, 1}.

The maximum number of pairs is 3. Return 3 as the answer.

2. Two Operations

Two integer operations are defined as:

1. ADD_1: Increment the integer by 1
2. MULTIPLY_2: Multiply the integer by 2

Given an integer value k, determine the minimum number of operations it takes to get from 0 to k using the two operations specified above.

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Example:

Input:

kValues[i] = 8

Explanation:

Starting from 0:

• Add 1 → then multiply by 2 three times.

It takes a minimum of 4 operations to get to 8, so store 4 in index 0 of the return array.

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Function Description:

Complete the function getMinOperations in the editor.

Function Signature:

def getMinOperations(kValues: List[int]) -> List[int]:

Parameters:

• kValues[n]: an array of integers representing the target values.

Returns:

• List[int]: answers to a list of queries in the given order.

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Constraints:

• 1 ≤ n ≤ 10000
• 0 ≤ kValues[i] ≤ 10^16

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Input Format for Custom Testing:

Sample Input:

2
5
3

Sample Output:

4
3

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Explanation:

1. To get from 0 to kValues[0] = 5:
   ADD_1 → MULTIPLY_2 → MULTIPLY_2 → ADD_1
   • 0 + 1 → 1 × 2 → 2 × 2 → 4 + 1 = 5
   Because it took 4 operations, store 4 in index 0 of the return array.
2. To get from 0 to kValues[1] = 3:
   ADD_1 → MULTIPLY_2 → ADD_1
   • 0 + 1 → 1 × 2 → 2 + 1 = 3
   Because it took 3 operations, store 3 in index 1 of the return array.

Final Output:

Return the array [4, 3] as the answer.

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