Minimum Number of Increments on Subarrays to Form a Target Array Python/Java solution

In Python, Java, C++, or JavaScript, the implementation is nearly identical. Initialize the result with target[0], iterate through the array, and add the positive difference between consecutive elements. The algorithm runs in O(n) time and uses O(1) extra memory across all languages.

What is the best approach for Minimum Number of Increments on Subarrays to Form a Target Array?

The optimal solution uses a greedy difference observation. Scan the array and count only the positive increases between adjacent elements. Whenever target[i] > target[i-1], you must start target[i] - target[i-1] new increment operations. This produces an O(n) time and O(1) space solution.

Is Minimum Number of Increments on Subarrays to Form a Target Array asked at Google/Amazon/Meta?

This style of greedy array transformation problem appears in interviews at companies like Google, Amazon, and Meta. It tests whether candidates can recognize patterns in range updates and reduce them to differences between adjacent elements instead of simulating operations.

What data structure is used in Minimum Number of Increments on Subarrays to Form a Target Array?

The optimal solution mainly relies on arrays and a greedy difference calculation. Conceptually it relates to difference arrays and ideas used in monotonic stack problems, but the final implementation only needs a single pass through the array with constant extra space.

What is the time complexity of Minimum Number of Increments on Subarrays to Form a Target Array?

The optimal greedy or difference-array approach runs in O(n) time because the array is scanned once. Only simple arithmetic comparisons are performed per element. Space complexity is O(1) since the algorithm stores only the previous value and the running total.

Description Hints 1 Solution Video 45:23

1526. Minimum Number of Increments on Subarrays to Form a Target Array

Q: Is Minimum Number of Increments on Subarrays to Form a Target Array easy or hard?

The problem is labeled Hard on LeetCode because the correct insight is not immediately obvious. Once you recognize that only upward differences require new operations, the implementation becomes a simple O(n) greedy scan.

Q: How to solve Minimum Number of Increments on Subarrays to Form a Target Array in O(n)?

Start with result = target[0] because that many operations must begin at index 0. Then iterate from index 1 to n-1 and add max(0, target[i] - target[i-1]) to the result. Each positive increase represents new subarray increments that must start at that position. This single pass computes the minimum number of operations.

Hard78.2% acceptance7 companies

You are given an integer array target. You have an integer array initial of the same size as target with all elements initially zeros.

In one operation you can choose any subarray from initial and increment each value by one.

Return the minimum number of operations to form a target array from initial.

The test cases are generated so that the answer fits in a 32-bit integer.

Example 1:

Input: target = [1,2,3,2,1]
Output: 3
Explanation: We need at least 3 operations to form the target array from the initial array.
[0,0,0,0,0] increment 1 from index 0 to 4 (inclusive).
[1,1,1,1,1] increment 1 from index 1 to 3 (inclusive).
[1,2,2,2,1] increment 1 at index 2.
[1,2,3,2,1] target array is formed.

Example 2:

Input: target = [3,1,1,2]
Output: 4
Explanation: [0,0,0,0] -> [1,1,1,1] -> [1,1,1,2] -> [2,1,1,2] -> [3,1,1,2]

Example 3:

Input: target = [3,1,5,4,2]
Output: 7
Explanation: [0,0,0,0,0] -> [1,1,1,1,1] -> [2,1,1,1,1] -> [3,1,1,1,1] -> [3,1,2,2,2] -> [3,1,3,3,2] -> [3,1,4,4,2] -> [3,1,5,4,2].

Constraints:

1 <= target.length <= 10⁵
1 <= target[i] <= 10⁵

Asked at 7 companies

IBM Dream11

Google Microsoft Oracle Amazon Meta

Topics

Hints open one at a time

Hint 1

For a given range of values in target, an optimal strategy is to increment the entire range by the minimum value. The minimum in a range could be obtained with Range minimum query or Segment trees algorithm.

45:23

Still stuck?Read 3 approaches, or watch a walkthrough.

Open solution

LanguageLoading editor…

1class Solution:
2    def minNumberOperations(self, target: List[int]) -> int:
3        

Starter codePython 3Spaces: 4

Examples

Case 1Case 2Case 3

Input

[1,2,3,2,1]

Input

[3,1,1,2]

Input

[3,1,5,4,2]

Your code is saved on this device.Solution