# 2615. Sum of Distances

## Description

You are given a 0-indexed integer array nums. There exists an array arr of length nums.length, where arr[i] is the sum of |i - j| over all j such that nums[j] == nums[i] and j != i. If there is no such j, set arr[i] to be 0.

Return the array arr.

Example 1:

Input: nums = [1,3,1,1,2]
Output: [5,0,3,4,0]
Explanation:
When i = 0, nums[0] == nums[2] and nums[0] == nums[3]. Therefore, arr[0] = |0 - 2| + |0 - 3| = 5.
When i = 1, arr[1] = 0 because there is no other index with value 3.
When i = 2, nums[2] == nums[0] and nums[2] == nums[3]. Therefore, arr[2] = |2 - 0| + |2 - 3| = 3.
When i = 3, nums[3] == nums[0] and nums[3] == nums[2]. Therefore, arr[3] = |3 - 0| + |3 - 2| = 4.
When i = 4, arr[4] = 0 because there is no other index with value 2.



Example 2:

Input: nums = [0,5,3]
Output: [0,0,0]
Explanation: Since each element in nums is distinct, arr[i] = 0 for all i.


Constraints:

• 1 <= nums.length <= 105
• 0 <= nums[i] <= 109

## Solutions

• class Solution {
public long[] distance(int[] nums) {
int n = nums.length;
long[] ans = new long[n];
Map<Integer, List<Integer>> d = new HashMap<>();
for (int i = 0; i < n; ++i) {
}
for (var idx : d.values()) {
int m = idx.size();
long left = 0;
long right = -1L * m * idx.get(0);
for (int i : idx) {
right += i;
}
for (int i = 0; i < m; ++i) {
ans[idx.get(i)] = left + right;
if (i + 1 < m) {
left += (idx.get(i + 1) - idx.get(i)) * (i + 1L);
right -= (idx.get(i + 1) - idx.get(i)) * (m - i - 1L);
}
}
}
return ans;
}
}

• class Solution {
public:
vector<long long> distance(vector<int>& nums) {
int n = nums.size();
vector<long long> ans(n);
unordered_map<int, vector<int>> d;
for (int i = 0; i < n; ++i) {
d[nums[i]].push_back(i);
}
for (auto& [_, idx] : d) {
int m = idx.size();
long long left = 0;
long long right = -1LL * m * idx[0];
for (int i : idx) {
right += i;
}
for (int i = 0; i < m; ++i) {
ans[idx[i]] = left + right;
if (i + 1 < m) {
left += (idx[i + 1] - idx[i]) * (i + 1);
right -= (idx[i + 1] - idx[i]) * (m - i - 1);
}
}
}
return ans;
}
};

• class Solution:
def distance(self, nums: List[int]) -> List[int]:
d = defaultdict(list)
for i, x in enumerate(nums):
d[x].append(i)
ans = [0] * len(nums)
for idx in d.values():
left, right = 0, sum(idx) - len(idx) * idx[0]
for i in range(len(idx)):
ans[idx[i]] = left + right
if i + 1 < len(idx):
left += (idx[i + 1] - idx[i]) * (i + 1)
right -= (idx[i + 1] - idx[i]) * (len(idx) - i - 1)
return ans


• func distance(nums []int) []int64 {
n := len(nums)
ans := make([]int64, n)
d := map[int][]int{}
for i, x := range nums {
d[x] = append(d[x], i)
}
for _, idx := range d {
m := len(idx)
left, right := 0, -m*idx[0]
for _, i := range idx {
right += i
}
for i := range idx {
ans[idx[i]] = int64(left + right)
if i+1 < m {
left += (idx[i+1] - idx[i]) * (i + 1)
right -= (idx[i+1] - idx[i]) * (m - i - 1)
}
}
}
return ans
}