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Formatted question description: https://leetcode.ca/all/992.html

# 992. Subarrays with K Different Integers (Hard)

Given an array A of positive integers, call a (contiguous, not necessarily distinct) subarray of A good if the number of different integers in that subarray is exactly K.

(For example, [1,2,3,1,2] has 3 different integers: 1, 2, and 3.)

Return the number of good subarrays of A.

Example 1:

Input: A = [1,2,1,2,3], K = 2
Output: 7
Explanation: Subarrays formed with exactly 2 different integers: [1,2], [2,1], [1,2], [2,3], [1,2,1], [2,1,2], [1,2,1,2].


Example 2:

Input: A = [1,2,1,3,4], K = 3
Output: 3
Explanation: Subarrays formed with exactly 3 different integers: [1,2,1,3], [2,1,3], [1,3,4].


Note:

1. 1 <= A.length <= 20000
2. 1 <= A[i] <= A.length
3. 1 <= K <= A.length

Related Topics:
Hash Table, Two Pointers, Sliding Window

Similar Questions:

## Solution 1. Sliding Window

Use [i, j) as a sliding window to find the maximum window which contains no more than K unique elements.

To achieve this, we use a map m to store the last position of each number in the current window.

When m.size() > K, we should move forward i to shrink the window until it become valid again.

When m.size() == K, [i, j) is the maximum window we are looking for.

Within this maximum window [i, j), there is a minimum window [k, j) containing no more than K unique elements. k is the minimal index in m.

Now, the number of valid subarrays in this window is k - i + 1.

Since k is monotonically increasing and must be no less than i, we can use k as a global pointer just like i and j so that the overall time complexity of moving k is O(N).

Whenever m.size() == K, we can move k forward until m[A[k] - '0'] == k, and add k - i + 1 to the answer.

// OJ: https://leetcode.com/problems/subarrays-with-k-different-integers/
// Time: O(N)
// Space: O(N)
class Solution {
public:
int subarraysWithKDistinct(vector<int>& A, int K) {
int ans = 0, i = 0, j = 0, k = 0, N = A.size();
unordered_map<int, int> m;
while (j < N) {
m[A[j] - '0'] = j;
++j;
while (m.size() > K) {
int d = A[i++] - '0';
if (m[d] < i) m.erase(d);
}
if (m.size() == K) {
k = max(i, k);
while (m[A[k] - '0'] != k) ++k;
ans += k - i + 1;
}
}
return ans;
}
};

• class Solution {
public int subarraysWithKDistinct(int[] A, int K) {
if (A == null || A.length == 0 || K == 0)
return 0;
int subarrays = 0;
Map<Integer, Integer> map = new HashMap<Integer, Integer>();
int left = 0, right = 0;
int length = A.length;
while (right < length) {
int rightNum = A[right];
int rightCount = map.getOrDefault(rightNum, 0) + 1;
map.put(rightNum, rightCount);
right++;
while (map.size() > K) {
int leftNum = A[left];
int leftCount = map.getOrDefault(leftNum, 0) - 1;
if (leftCount > 0)
map.put(leftNum, leftCount);
else
map.remove(leftNum);
left++;
}
int pointer = left;
while (map.size() == K) {
subarrays++;
int curNum = A[pointer];
int curCount = map.getOrDefault(curNum, 0) - 1;
if (curCount > 0)
map.put(curNum, curCount);
else
map.remove(curNum);
pointer++;
}
pointer--;
while (pointer >= left) {
int curNum = A[pointer];
int curCount = map.getOrDefault(curNum, 0) + 1;
map.put(curNum, curCount);
pointer--;
}
}
return subarrays;
}
}

############

class Solution {
public int subarraysWithKDistinct(int[] nums, int k) {
int[] left = f(nums, k);
int[] right = f(nums, k - 1);
int ans = 0;
for (int i = 0; i < nums.length; ++i) {
ans += right[i] - left[i];
}
return ans;
}

private int[] f(int[] nums, int k) {
int n = nums.length;
int[] cnt = new int[n + 1];
int[] pos = new int[n];
int s = 0;
for (int i = 0, j = 0; i < n; ++i) {
if (++cnt[nums[i]] == 1) {
++s;
}
for (; s > k; ++j) {
if (--cnt[nums[j]] == 0) {
--s;
}
}
pos[i] = j;
}
return pos;
}
}

• // OJ: https://leetcode.com/problems/subarrays-with-k-different-integers/
// Time: O(N)
// Space: O(N)
class Solution {
public:
int subarraysWithKDistinct(vector<int>& A, int K) {
int ans = 0, i = 0, j = 0, k = 0, N = A.size();
unordered_map<int, int> m;
while (j < N) {
m[A[j] - '0'] = j;
++j;
while (m.size() > K) {
int d = A[i++] - '0';
if (m[d] < i) m.erase(d);
}
if (m.size() == K) {
k = max(i, k);
while (m[A[k] - '0'] != k) ++k;
ans += k - i + 1;
}
}
return ans;
}
};

• # 992. Subarrays with K Different Integers
# https://leetcode.com/problems/subarrays-with-k-different-integers/

class Solution:
def subarraysWithKDistinct(self, nums: List[int], k: int) -> int:
n = len(nums)
left = prefix = res = distinct = 0
count = Counter()

for right, x in enumerate(nums):
if count[x] == 0:
distinct += 1

count[x] += 1

if distinct > k:
count[nums[left]] -= 1
left += 1
prefix = 0
distinct -= 1

while count[nums[left]] > 1:
count[nums[left]] -= 1
prefix += 1
left += 1

if distinct == k:
res += prefix + 1

return res


• func subarraysWithKDistinct(nums []int, k int) (ans int) {
f := func(k int) []int {
n := len(nums)
pos := make([]int, n)
cnt := make([]int, n+1)
s, j := 0, 0
for i, x := range nums {
cnt[x]++
if cnt[x] == 1 {
s++
}
for ; s > k; j++ {
cnt[nums[j]]--
if cnt[nums[j]] == 0 {
s--
}
}
pos[i] = j
}
return pos
}
left, right := f(k), f(k-1)
for i := range left {
ans += right[i] - left[i]
}
return
}