Maximum Number of Integers to Choose From a Range I

Problem Description

You are given an integer array banned and two integers n and maxSum. You are choosing some number of integers following the below rules:

• The chosen integers have to be in the range [1, n].
• Each integer can be chosen at most once.
• The chosen integers should not be in the array banned.
• The sum of the chosen integers should not exceed maxSum.

Return the maximum number of integers you can choose following the mentioned rules.

Key Insights

• The integers must be chosen from the range [1, n].
• The banned array contains integers that cannot be chosen.
• The total sum of the chosen integers must not exceed maxSum.
• A greedy approach can maximize the count of integers chosen by selecting the smallest available integers first.

Space and Time Complexity

Time Complexity: O(n + b), where n is the range of integers to consider and b is the length of the banned list. Space Complexity: O(b), where b is the length of the banned list (for storing banned integers in a set).

Solution

To solve this problem, we can use the following steps:

1. Convert the banned array into a set for O(1) lookups.
2. Iterate through the integers from 1 to n.
3. For each integer, check if it is not in the banned set.
4. If it is not banned and adding it to the current sum does not exceed maxSum, include it in the chosen integers and update the current sum.
5. Continue this process until either all integers in the range are checked or adding the next integer would exceed maxSum.

This greedy approach ensures that we maximize the number of integers chosen while adhering to the constraints.

Code Solutions