Tejav
#3891

Minimum Increase to Maximize Special Indices

Medium
ArrayDynamic ProgrammingGreedyPrefix SumDynamic ProgrammingGreedy Algorithms
LeetCode ↗

Approaches

Brute ForceOptimal
Complexity Comparison
Brute ForceOptimal Solution★
Time
O(n²)
O(n)
Space
O(1)
O(n)
💡

Intuition

Time O(n)Space O(n)

Use dynamic programming to track the maximum special indices and the minimum operations needed as we iterate through the array.

⚙️

Algorithm

3 steps
  1. 1Step 1: Initialize dp array to store (max_special, min_ops) for each index.
  2. 2Step 2: Iterate through nums, updating dp based on previous values and current index conditions.
  3. 3Step 3: Return the minimum operations needed to achieve the maximum special indices.
solution.py9 lines
1def minOperations(nums):
2    n = len(nums)
3    dp = [(0, 0)] * n
4    for i in range(1, n-1):
5        ops = 0
6        if nums[i] <= nums[i-1] or nums[i] <= nums[i+1]:
7            ops = max(0, nums[i-1] - nums[i] + 1) + max(0, nums[i+1] - nums[i] + 1)
8        dp[i] = (dp[i-1][0] + 1, dp[i-1][1] + ops)
9    return dp[n-2][1]
ℹ

Complexity note: Linear complexity due to single pass through the array with constant space for each index.

  • 1Identifying special indices requires comparing neighbors.
  • 2Dynamic programming can efficiently track operations needed.

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