Leetcode #2557: Maximum Number of Integers to Choose From a Range II
In this guide, we solve Leetcode #2557 Maximum Number of Integers to Choose From a Range II in Python and focus on the core idea that makes the solution efficient.
You will see the intuition, the step-by-step method, and a clean Python implementation you can use in interviews.
Problem Statement
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].
Quick Facts
- Difficulty: Medium
- Premium: Yes
- Tags: Greedy, Array, Binary Search, Sorting
Intuition
The problem structure suggests a monotonic decision, which makes binary search a natural fit.
By halving the search space each step, we reach the answer efficiently.
Approach
Search either directly on a sorted array or on the answer space using a check function.
Each check is fast, and the logarithmic search keeps the overall runtime low.
Steps:
- Define the search bounds.
- Check the mid point condition.
- Narrow the bounds until convergence.
Example
Input: banned = [1,4,6], n = 6, maxSum = 4
Output: 1
Explanation: You can choose the integer 3.
3 is in the range [1, 6], and do not appear in banned. The sum of the chosen integers is 3, which does not exceed maxSum.
Python Solution
class Solution:
def maxCount(self, banned: List[int], n: int, maxSum: int) -> int:
banned.extend([0, n + 1])
ban = sorted(set(banned))
ans = 0
for i, j in pairwise(ban):
left, right = 0, j - i - 1
while left < right:
mid = (left + right + 1) >> 1
if (i + 1 + i + mid) * mid // 2 <= maxSum:
left = mid
else:
right = mid - 1
ans += left
maxSum -= (i + 1 + i + left) * left // 2
if maxSum <= 0:
break
return ans
Complexity
The time complexity is , and the space complexity is . The space complexity is .
Edge Cases and Pitfalls
Watch for boundary values, empty inputs, and duplicate values where applicable. If the problem involves ordering or constraints, confirm the invariant is preserved at every step.
Summary
This Python solution focuses on the essential structure of the problem and keeps the implementation interview-friendly while meeting the constraints.