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Pankaj Tanwar

Posted on • Updated on • Originally published at pankajtanwar.in

# Challenge #15 - Count Number of Pairs With Absolute Difference K

Bonjour!

Thanks for sticking along, it's day 15 of my coding diary. Well, I started this journey to discipline my self and I feel, now I am literally enjoying it. Let's jump to the problem statement for today.

TLDR;

• Never settle down by just seeing green tick with brute force approach. Think harder to reach the optimized one. (I found 3 approaches for the problem)
• Easy problems might have interesting hidden challenges

Problem of the day - Count Number of Pairs With Absolute Difference K

Tag - Easy

Given an integer array `nums` and an integer `k`, return the number of pairs `(i, j)` where `i < j` such that `|nums[i] - nums[j]| == k`.

The value of `|x|` is defined as:

• `x` if `x >= 0`.
• `-x` if `x < 0`.

Example 1:

Input: nums = [1,2,2,1], k = 1
Output: 4

Just after reading the problem statement carefully, like any other dev, a brute force, O(n2), the slowest approach came to my mind and I just started typing without wasting a second.

``````class Solution {
public:
int countKDifference(vector<int>& nums, int k) {
int res = 0;
for(int i=0;i<nums.size();i++) {
for(int j=i+1;j<nums.size();j++) {
if(abs(nums[i]- nums[j]) == k) res++;
}
}
return res;
}
};
``````

As expected, the worst approach. It took 39ms, faster than 7%, Arghhhh. I knew it.

I again read the problem statement. A quick thought came to my mind, why not store count for each value and check count of `val + k` and `val - k`.

``````class Solution {
public:
int countKDifference(vector<int>& nums, int k) {
map<int,int> list;
int res = 0;
for(auto val: nums) list[val]++;

for(auto val: nums) {
list[val]--;
res += list[val+k] + list[val-k];
}
return res;
}
};
``````

Approach -

• Store count of each value
• Iterate over the `nums` array
• For each element, reduce the count for the current value first, and check the count of `val - k` and `val + k`
• return the final value, that's the answer

I hit submit in the excitement of O(n) approach, BUT leetcode said, Ummm, it's a good try but still slower than 60% submission, think harder. WTH, I thought I cracked it.

I kept on digging more. I again read the problem statement, no luck! Suddenly, I looked at the constraints. It was a light bulb moment.....

Constraints:

• `1 <= nums.length <= 200`
• `1 <= nums[i] <= 100`
• `1 <= k <= 99`

Let's remove the sluggish hashmap and use an array of length 200.

``````class Solution {
public:
int countKDifference(vector<int>& nums, int k) {
int list[201] = {0};
int res = 0;

for(auto val: nums) {
res += (val-k >= 0 ? list[val-k] : 0) + list[val+k];
list[val]++;
}
return res;
}
}
``````

Hit submit, and boom! It's 9ms, faster than 90% of solutions. Oh man, that was fun. I am gradually recognizing the patterns.

You might like previous editions of my coding diary