Well, the basic idea is fairly straightforward. We maintain a mapping mp from a value in nums to its position (index) i. Each time we meet an unseen value, we add it to the map (mp[nums[i]] = i). Otherwise, depending on whether the recorded index mp[nums[i]] and the current index isatisfy i - mp[nums[i]] <= k (node that the new index i is larger than the old indexmp[nums[i]]), we return true or update the index (mp[nums[i]] = i). If all the elements have been visited and we have not returned true, we will return false.

1     bool containsNearbyDuplicate(vector
     
      & nums, int k) {2         unordered_map
      
        mp; 3         for (int i = 0; i < nums.size(); i++) {4             if (mp.find(nums[i]) != mp.end() && i - mp[nums[i]] <= k)5                 return true;6             mp[nums[i]] = i; 7         }8         return false; 9     }