AlgoViz

Subarrays with K Different Integers

Medium

atMost(k) minus atMost(k-1), again

Problem

Count subarrays with exactly k distinct integers.

In simple words

Count windows with at most k distinct minus at most k-1 — the difference has exactly k.

The idea

A window cannot directly enforce 'exactly k distinct', but it handles 'at most k' comfortably with a frequency map. Subtracting the at-most-(k-1) count leaves precisely the subarrays with k distinct values.

The trick

  • Two runs of the same helper; do not try to write an exact-k window.
  • In atMost, each right edge contributes (right - left + 1) subarrays.
  • O(n) per run, so O(n) overall.

This one walks through the worked example rather than tracing the algorithm frame by frame — a full walkthrough is still to be drawn. The code and the idea below are the real solution.

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Step 1 of 2. Here's the example — nums=[1,2,1,2,3], k=2 Values: 1, 2, 1, 2, 3.

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Optimal
timeO(n)spaceO(k)
1atMost(k): window with <=k distinct, counting subarrays2answer = atMost(k) - atMost(k-1)

Input

array
[1, 2, 1, 2, 3]

Output

answer

Check yourself

3 quick questions about this walkthrough. A wrong answer costs nothing.

Examples

Example 1

Input:
nums = [1, 2, 1, 2, 3], k = 2
Output:
7
Explanation:
7 subarrays have exactly 2 distinct values.

Example 2

Input:
nums = [1, 2, 1, 3, 4], k = 3
Output:
3
Explanation:
3 subarrays have exactly 3 distinct.

Example 3

Input:
nums = [1, 1, 1], k = 1
Output:
6
Explanation:
All 6 windows have 1 distinct.

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