LeetCode #2670 — EASY

Find the Distinct Difference Array

Build confidence with an intuition-first walkthrough focused on array fundamentals.

The Problem

Problem Statement

You are given a 0-indexed array nums of length n.

The distinct difference array of nums is an array diff of length n such that diff[i] is equal to the number of distinct elements in the suffix nums[i + 1, ..., n - 1] subtracted from the number of distinct elements in the prefix nums[0, ..., i].

Return the distinct difference array of nums.

Note that nums[i, ..., j] denotes the subarray of nums starting at index i and ending at index j inclusive. Particularly, if i > j then nums[i, ..., j] denotes an empty subarray.

Example 1:

Input: nums = [1,2,3,4,5]
Output: [-3,-1,1,3,5]
Explanation: For index i = 0, there is 1 element in the prefix and 4 distinct elements in the suffix. Thus, diff[0] = 1 - 4 = -3.
For index i = 1, there are 2 distinct elements in the prefix and 3 distinct elements in the suffix. Thus, diff[1] = 2 - 3 = -1.
For index i = 2, there are 3 distinct elements in the prefix and 2 distinct elements in the suffix. Thus, diff[2] = 3 - 2 = 1.
For index i = 3, there are 4 distinct elements in the prefix and 1 distinct element in the suffix. Thus, diff[3] = 4 - 1 = 3.
For index i = 4, there are 5 distinct elements in the prefix and no elements in the suffix. Thus, diff[4] = 5 - 0 = 5.

Example 2:

Input: nums = [3,2,3,4,2]
Output: [-2,-1,0,2,3]
Explanation: For index i = 0, there is 1 element in the prefix and 3 distinct elements in the suffix. Thus, diff[0] = 1 - 3 = -2.
For index i = 1, there are 2 distinct elements in the prefix and 3 distinct elements in the suffix. Thus, diff[1] = 2 - 3 = -1.
For index i = 2, there are 2 distinct elements in the prefix and 2 distinct elements in the suffix. Thus, diff[2] = 2 - 2 = 0.
For index i = 3, there are 3 distinct elements in the prefix and 1 distinct element in the suffix. Thus, diff[3] = 3 - 1 = 2.
For index i = 4, there are 3 distinct elements in the prefix and no elements in the suffix. Thus, diff[4] = 3 - 0 = 3.

Constraints:

1 <= n == nums.length <= 50
1 <= nums[i] <= 50

Step 01

Brute Force Baseline

Problem summary: You are given a 0-indexed array nums of length n. The distinct difference array of nums is an array diff of length n such that diff[i] is equal to the number of distinct elements in the suffix nums[i + 1, ..., n - 1] subtracted from the number of distinct elements in the prefix nums[0, ..., i]. Return the distinct difference array of nums. Note that nums[i, ..., j] denotes the subarray of nums starting at index i and ending at index j inclusive. Particularly, if i > j then nums[i, ..., j] denotes an empty subarray.

Baseline thinking

Start with the most direct exhaustive search. That gives a correctness anchor before optimizing.

Pattern signal: Array · Hash Map

Example 1

[1,2,3,4,5]

Example 2

[3,2,3,4,2]

Core Insight

What unlocks the optimal approach

Which data structure will help you maintain distinct elements?
Iterate over all possible prefix sizes. Then, use a nested loop to add the elements of the prefix to a set, and another nested loop to add the elements of the suffix to another set.

Interview move: turn each hint into an invariant you can check after every iteration/recursion step.

Step 03

Algorithm Walkthrough

Iteration Checklist

Define state (indices, window, stack, map, DP cell, or recursion frame).
Apply one transition step and update the invariant.
Record answer candidate when condition is met.
Continue until all input is consumed.

Use the first example testcase as your mental trace to verify each transition.

Step 04

Edge Cases

Minimum Input

Single element / shortest valid input

Validate boundary behavior before entering the main loop or recursion.

Duplicates & Repeats

Repeated values / repeated states

Decide whether duplicates should be merged, skipped, or counted explicitly.

Extreme Constraints

Upper-end input sizes

Re-check complexity target against constraints to avoid time-limit issues.

Invalid / Corner Shape

Empty collections, zeros, or disconnected structures

Handle special-case structure before the core algorithm path.

Step 05

Full Annotated Code

Source-backed implementations are provided below for direct study and interview prep.

// Accepted solution for LeetCode #2670: Find the Distinct Difference Array
class Solution {
    public int[] distinctDifferenceArray(int[] nums) {
        int n = nums.length;
        int[] suf = new int[n + 1];
        Set<Integer> s = new HashSet<>();
        for (int i = n - 1; i >= 0; --i) {
            s.add(nums[i]);
            suf[i] = s.size();
        }
        s.clear();
        int[] ans = new int[n];
        for (int i = 0; i < n; ++i) {
            s.add(nums[i]);
            ans[i] = s.size() - suf[i + 1];
        }
        return ans;
    }
}

// Accepted solution for LeetCode #2670: Find the Distinct Difference Array
func distinctDifferenceArray(nums []int) []int {
	n := len(nums)
	suf := make([]int, n+1)
	s := map[int]bool{}
	for i := n - 1; i >= 0; i-- {
		s[nums[i]] = true
		suf[i] = len(s)
	}
	ans := make([]int, n)
	s = map[int]bool{}
	for i, x := range nums {
		s[x] = true
		ans[i] = len(s) - suf[i+1]
	}
	return ans
}

# Accepted solution for LeetCode #2670: Find the Distinct Difference Array
class Solution:
    def distinctDifferenceArray(self, nums: List[int]) -> List[int]:
        n = len(nums)
        suf = [0] * (n + 1)
        s = set()
        for i in range(n - 1, -1, -1):
            s.add(nums[i])
            suf[i] = len(s)
        s.clear()
        ans = [0] * n
        for i, x in enumerate(nums):
            s.add(x)
            ans[i] = len(s) - suf[i + 1]
        return ans

// Accepted solution for LeetCode #2670: Find the Distinct Difference Array
use std::collections::HashSet;

impl Solution {
    pub fn distinct_difference_array(nums: Vec<i32>) -> Vec<i32> {
        let n = nums.len();
        let mut suf = vec![0; n + 1];
        let mut s = HashSet::new();

        for i in (0..n).rev() {
            s.insert(nums[i]);
            suf[i] = s.len();
        }

        let mut ans = Vec::new();
        s.clear();
        for i in 0..n {
            s.insert(nums[i]);
            ans.push((s.len() - suf[i + 1]) as i32);
        }

        ans
    }
}

// Accepted solution for LeetCode #2670: Find the Distinct Difference Array
function distinctDifferenceArray(nums: number[]): number[] {
    const n = nums.length;
    const suf: number[] = Array(n + 1).fill(0);
    const s: Set<number> = new Set();
    for (let i = n - 1; i >= 0; --i) {
        s.add(nums[i]);
        suf[i] = s.size;
    }
    s.clear();
    const ans: number[] = Array(n).fill(0);
    for (let i = 0; i < n; ++i) {
        s.add(nums[i]);
        ans[i] = s.size - suf[i + 1];
    }
    return ans;
}

Step 06

Interactive Study Demo

Use this to step through a reusable interview workflow for this problem.

Custom checkpoints (one per line)

Press Step or Run All to begin.

Step 07

Complexity Analysis

Time

O(n)

Space

O(n)

Approach Breakdown

BRUTE FORCE

O(n²) time

O(1) space

Two nested loops check every pair or subarray. The outer loop fixes a starting point, the inner loop extends or searches. For n elements this gives up to n²/2 operations. No extra space, but the quadratic time is prohibitive for large inputs.

OPTIMIZED

O(n) time

O(1) space

Most array problems have an O(n²) brute force (nested loops) and an O(n) optimal (single pass with clever state tracking). The key is identifying what information to maintain as you scan: a running max, a prefix sum, a hash map of seen values, or two pointers.

Shortcut: If you are using nested loops on an array, there is almost always an O(n) solution. Look for the right auxiliary state.

Coach Notes

Common Mistakes

Review these before coding to avoid predictable interview regressions.

Off-by-one on range boundaries

Wrong move: Loop endpoints miss first/last candidate.

Usually fails on: Fails on minimal arrays and exact-boundary answers.

Fix: Re-derive loops from inclusive/exclusive ranges before coding.

Mutating counts without cleanup

Wrong move: Zero-count keys stay in map and break distinct/count constraints.

Usually fails on: Window/map size checks are consistently off by one.

Fix: Delete keys when count reaches zero.