# Window Limits - Google Top Interview Questions

### Problem Statement :

```You are given a list of integers nums and integers window and limit.

Return whether abs(nums[i] - nums[j]) ≤ limit for every i, j such that abs(i - j) < window.

Constraints

1 ≤ n ≤ 100,000 where n is the length of nums

1 ≤ window ≤ n

0 ≤ limit < 2 ** 31

Example 1

Input

nums = [1, 3, 7, 5]

window = 2

limit = 4

Output

True

Explanation

Every number within a window of size 2 has pair differences of at most 4 (from 3 and 7).

Example 2

Input

nums = [1, 3, 7, 5]

window = 3

limit = 4

Output

False

Explanation

Within a window size of 3 we have abs(1 - 7) > 4, so this is above the limit.```

### Solution :

```                        ```Solution in C++ :

bool solve(vector<int>& nums, int window, int limit) {
multiset<long long> dp;
for (int i = 0; i < nums.size(); i++) {
dp.insert(nums[i]);
if (i >= window) dp.erase(dp.find(nums[i - window]));
if (*dp.rbegin() - *dp.begin() > limit) return false;
}
return true;
}```
```

```                        ```Solution in Java :

import java.util.*;

class Solution {
public boolean solve(int[] nums, int window, int limit) {
Deque<Integer> q = new ArrayDeque();
Deque<Integer> q2 = new ArrayDeque();
int r = 0;
while (r < nums.length) {
while (!q.isEmpty() && q.peekFirst() <= r - window) {
q.removeFirst();
}
while (!q2.isEmpty() && q2.peekFirst() <= r - window) {
q2.removeFirst();
}
while (!q.isEmpty() && nums[q.peekLast()] < nums[r]) {
q.removeLast();
}
while (!q2.isEmpty() && nums[q2.peekLast()] > nums[r]) {
q2.removeLast();
}
q.offerLast(r);
q2.offerLast(r++);
int max = nums[q.peekFirst()];
int min = nums[q2.peekFirst()];
if (max - min > limit) {
return false;
}
}
return true;
}
}```
```

```                        ```Solution in Python :

class Solution:
def solve(self, nums, window, limit):
minq = deque()  # <idx, val>
maxq = deque()  # <idx, val>
for i, x in enumerate(nums):
while minq and minq[-1][1] >= x:
minq.pop()
while maxq and maxq[-1][1] <= x:
maxq.pop()
minq.append((i, x))
maxq.append((i, x))
if minq[0][0] <= i - window:
minq.popleft()
if maxq[0][0] <= i - window:
maxq.popleft()
if maxq[0][1] - minq[0][1] > limit:
return False
return True```
```

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