Find the Maximum Number of Marked Indices

arraytwo pointersbinary search

Problem Statement

You are given a 0-indexed integer array nums .

Initially, all of the indices are unmarked. You are allowed to make this operation any number of times:

Pick two different unmarked indices i and j such that 2 * nums[i] <= nums[j] , then mark i and j .

Return the maximum possible number of marked indices in nums using the above operation any number of times .

Examples

Example 1

Input: nums = [3,5,2,4]
Output: 2
In the first operation: pick i = 2 and j = 1, the operation is allowed because 2 * nums[2] <= nums[1]. Then mark index 2 and 1.
It can be shown that there's no other valid operation so the answer is 2.

Example 2

Input: nums = [9,2,5,4]
Output: 4
In the first operation: pick i = 3 and j = 0, the operation is allowed because 2 * nums[3] <= nums[0]. Then mark index 3 and 0.
In the second operation: pick i = 1 and j = 2, the operation is allowed because 2 * nums[1] <= nums[2]. Then mark index 1 and 2.
Since there is no other operation, the answer is 4.

Example 3

Input: nums = [7,6,8]
Output: 0
There is no valid operation to do, so the answer is 0.

Constraints

1 <= nums.length <= 10 ^5

1 <= nums[i] <= 10 ^9

🤔

Medium

Difficulty

Topic Info

ModuleDSA

CategoryArray

Sub-topicTwo Pointers