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Problem: Maximum Value at a Given Index in a Bounded Array

Medium
30 min
Explore how to construct an array where the element at a specified index is maximized while adhering to constraints like limited sum and adjacent differences. Understand the application of modified binary search to solve the problem efficiently. Practice developing solutions that meet array length and sum boundaries, strengthening skills for coding interview pattern recognition.

Statement

Given three positive integers, n, index, and maxSum, output the nums[index] by constructing an array of nums with the length of n, which satisfies the following conditions:

  • The length of the array nums is equal to n.

  • Each element nums[i] is a positive integer, where 11\leq i <\lt n.

  • The absolute difference between two consecutive elements, nums[i] and nums[i+1], is at most 11.

  • The sum of all elements in nums does not exceed maxSum.

  • The element at nums[index] contains the maximum value.

Constraints:

  • 11\leqn \leqmaxSum \leq10910^9

  • 00\leqindex <\ltn

Problem
Ask
Submissions

Problem: Maximum Value at a Given Index in a Bounded Array

Medium
30 min
Explore how to construct an array where the element at a specified index is maximized while adhering to constraints like limited sum and adjacent differences. Understand the application of modified binary search to solve the problem efficiently. Practice developing solutions that meet array length and sum boundaries, strengthening skills for coding interview pattern recognition.

Statement

Given three positive integers, n, index, and maxSum, output the nums[index] by constructing an array of nums with the length of n, which satisfies the following conditions:

  • The length of the array nums is equal to n.

  • Each element nums[i] is a positive integer, where 11\leq i <\lt n.

  • The absolute difference between two consecutive elements, nums[i] and nums[i+1], is at most 11.

  • The sum of all elements in nums does not exceed maxSum.

  • The element at nums[index] contains the maximum value.

Constraints:

  • 11\leqn \leqmaxSum \leq10910^9

  • 00\leqindex <\ltn