LeetCode #1331 — EASY

Rank Transform of an Array

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

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The Problem

Problem Statement

Given an array of integers arr, replace each element with its rank.

The rank represents how large the element is. The rank has the following rules:

Rank is an integer starting from 1.
The larger the element, the larger the rank. If two elements are equal, their rank must be the same.
Rank should be as small as possible.

Example 1:

Input: arr = [40,10,20,30]
Output: [4,1,2,3]
Explanation: 40 is the largest element. 10 is the smallest. 20 is the second smallest. 30 is the third smallest.

Example 2:

Input: arr = [100,100,100]
Output: [1,1,1]
Explanation: Same elements share the same rank.

Example 3:

Input: arr = [37,12,28,9,100,56,80,5,12]
Output: [5,3,4,2,8,6,7,1,3]

Constraints:

0 <= arr.length <= 10⁵
-10⁹ <= arr[i] <= 10⁹

Step 01

Brute Force Baseline

Problem summary: Given an array of integers arr, replace each element with its rank. The rank represents how large the element is. The rank has the following rules: Rank is an integer starting from 1. The larger the element, the larger the rank. If two elements are equal, their rank must be the same. Rank should be as small as possible.

Baseline thinking

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

Pattern signal: Array · Hash Map

Example 1

[40,10,20,30]

Example 2

[100,100,100]

Example 3

[37,12,28,9,100,56,80,5,12]

Core Insight

What unlocks the optimal approach

Use a temporary array to copy the array and sort it.
The rank of each element is the number of unique elements smaller than it in the sorted array plus one.

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 #1331: Rank Transform of an Array
class Solution {
    public int[] arrayRankTransform(int[] arr) {
        int n = arr.length;
        int[] t = arr.clone();
        Arrays.sort(t);
        int m = 0;
        for (int i = 0; i < n; ++i) {
            if (i == 0 || t[i] != t[i - 1]) {
                t[m++] = t[i];
            }
        }
        int[] ans = new int[n];
        for (int i = 0; i < n; ++i) {
            ans[i] = Arrays.binarySearch(t, 0, m, arr[i]) + 1;
        }
        return ans;
    }
}

// Accepted solution for LeetCode #1331: Rank Transform of an Array
func arrayRankTransform(arr []int) (ans []int) {
	t := make([]int, len(arr))
	copy(t, arr)
	sort.Ints(t)
	m := 0
	for i, x := range t {
		if i == 0 || x != t[i-1] {
			t[m] = x
			m++
		}
	}
	t = t[:m]
	for _, x := range arr {
		ans = append(ans, sort.SearchInts(t, x)+1)
	}
	return
}

# Accepted solution for LeetCode #1331: Rank Transform of an Array
class Solution:
    def arrayRankTransform(self, arr: List[int]) -> List[int]:
        t = sorted(set(arr))
        return [bisect_right(t, x) for x in arr]

// Accepted solution for LeetCode #1331: Rank Transform of an Array
struct Solution;
use std::collections::BTreeSet;
use std::collections::HashMap;

impl Solution {
    fn array_rank_transform(arr: Vec<i32>) -> Vec<i32> {
        let mut bts: BTreeSet<i32> = BTreeSet::new();
        let mut hm: HashMap<i32, i32> = HashMap::new();
        for &x in &arr {
            bts.insert(x);
        }
        for (i, x) in bts.into_iter().enumerate() {
            hm.insert(x, i as i32 + 1);
        }
        arr.into_iter().map(|x| hm[&x]).collect()
    }
}

#[test]
fn test() {
    let arr = vec![40, 10, 20, 30];
    let res = vec![4, 1, 2, 3];
    assert_eq!(Solution::array_rank_transform(arr), res);
    let arr = vec![100, 100, 100];
    let res = vec![1, 1, 1];
    assert_eq!(Solution::array_rank_transform(arr), res);
    let arr = vec![37, 12, 28, 9, 100, 56, 80, 5, 12];
    let res = vec![5, 3, 4, 2, 8, 6, 7, 1, 3];
    assert_eq!(Solution::array_rank_transform(arr), res);
}

// Accepted solution for LeetCode #1331: Rank Transform of an Array
function arrayRankTransform(arr: number[]): number[] {
    const t = [...arr].sort((a, b) => a - b);
    let m = 0;
    for (let i = 0; i < t.length; ++i) {
        if (i === 0 || t[i] !== t[i - 1]) {
            t[m++] = t[i];
        }
    }
    const search = (t: number[], right: number, x: number) => {
        let left = 0;
        while (left < right) {
            const mid = (left + right) >> 1;
            if (t[mid] > x) {
                right = mid;
            } else {
                left = mid + 1;
            }
        }
        return left;
    };
    const ans: number[] = [];
    for (const x of arr) {
        ans.push(search(t, m, x));
    }
    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 × log 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.