10. Longest subarray with sum divisible by K
The problem can be found at the following link: Question Link
My Approach
I approached this problem using a hashmap to store the remainder of the cumulative sum when divided by k
. The key idea is to find two indices with the same remainder to get a subarray whose sum is divisible by k
.
I initialized a hashmap
mp
with an initial entry of {0, -1}, indicating that the sum 0 is seen at index -1.I iterated through the array, updating the cumulative sum and calculating the remainder when divided by
k
.To handle negative remainders, I added
k
to the remainder if it was negative.If the remainder was already in the hashmap, I updated the maximum subarray length
out
by comparing it with the difference between the current index and the index stored in the hashmap for that remainder. Otherwise, I added a new entry in the hashmap.The final result is the length of the longest subarray with a sum divisible by
k
.
Time and Auxiliary Space Complexity
Time Complexity:
O(n)
, where n is the size of the array. The algorithm processes each element of the array once.Auxiliary Space Complexity:
O(min(n, k))
, wheren
is the size of the array. The hashmapmp
stores at mostmin(n, k)
entries.
Code (C++)
class Solution {
public:
int longSubarrWthSumDivByK(int arr[], int n, int k) {
unordered_map<int, int> mp;
mp[0] = -1;
int out = 0, sum = 0;
for (int i = 0; i < n; i++) {
sum += arr[i];
int rem = sum % k;
if (rem < 0)
rem += k;
if (mp.find(rem) != mp.end())
out = max(out, i - mp[rem]);
else
mp[rem] = i;
}
return out;
}
};
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