# Delete Sublist to Make Sum Divisible By K - Amazon Top Interview Questions

### Problem Statement :

```You are given a list of positive integers nums and a positive integer k. Return the length of the shortest sublist (can be empty sublist ) you can delete such that the resulting list's sum is divisible by k. You cannot delete the entire list. If it's not possible, return -1.

Constraints

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

Example 1

Input

nums = [1, 8, 6, 4, 5]

k = 7

Output

2

Explanation

We can remove the sublist [6, 4] to get [1, 8, 5] which sums to 14 and is divisible by 7.```

### Solution :

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

int solve(vector<int>& nums, int k) {
if (nums.empty()) return -1;

int target = 0;
for (int num : nums) target = (target + num) % k;
if (target == 0) return 0;

unordered_map<int, int> memo;
memo[0] = 0;
int pos = 0, now = 0, ans = nums.size();
for (int num : nums) {
pos++;
now = (now + num) % k;
if (memo.count((now + k - target) % k)) ans = min(ans, pos - memo[(now + k - target) % k]);
memo[now] = pos;
}
return ans == nums.size() ? -1 : ans;
}```
```

```                        ```Solution in Java :

import java.util.*;

class Solution {
public int solve(int[] nums, int k) {
//(totalSUm - delete) % k == 0;
// totalSUm % k = delet%k
// let totalSum % k = totalMod
// totalMod % k = totalMod;
// delet%k = prefix[j] % k - prefix[i] %k = totalMod %k;
// pre[i] % k = (pre[j] - totalMod) % k;
int total = 0;
for (int n : nums) {
total += n;
}
int totalMod = Math.floorMod(total, k);

Map<Integer, Integer> map = new HashMap();
map.put(0, -1);
int prefix = 0;
int res = nums.length;
for (int i = 0; i < nums.length; i++) {
prefix += nums[i];
int curMod = Math.floorMod(prefix, k);
map.put(curMod, i);
int afterMod = Math.floorMod(prefix - totalMod, k);
// System.out.println(afterMod + "total" + totalMod +"pre" + prefix);
if (map.containsKey(afterMod)) {
int len = i - map.get(afterMod);
System.out.println(i);
res = len < res ? len : res;
}
}
return res == nums.length ? -1 : res;
}
}```
```

```                        ```Solution in Python :

class Solution:
def solve(self, nums, k):
tar_remainder = (sum(nums) + k) % k
if tar_remainder == 0:
return 0
n, presum = len(nums), 0
hashmap = {0: -1}
res = n
for i in range(n):
presum += nums[i]
modulus = (presum + k) % k
hashmap[modulus] = i
if (modulus - tar_remainder + k) % k in hashmap:
res = min(res, i - hashmap[(modulus - tar_remainder + k) % k])
return res if res != n else -1```
```

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