LeetCode #1338 — MEDIUM

Reduce Array Size to The Half

Move from brute-force thinking to an efficient approach using array strategy.

The Problem

Problem Statement

You are given an integer array arr. You can choose a set of integers and remove all the occurrences of these integers in the array.

Return the minimum size of the set so that at least half of the integers of the array are removed.

Example 1:

Input: arr = [3,3,3,3,5,5,5,2,2,7]
Output: 2
Explanation: Choosing {3,7} will make the new array [5,5,5,2,2] which has size 5 (i.e equal to half of the size of the old array).
Possible sets of size 2 are {3,5},{3,2},{5,2}.
Choosing set {2,7} is not possible as it will make the new array [3,3,3,3,5,5,5] which has a size greater than half of the size of the old array.

Example 2:

Input: arr = [7,7,7,7,7,7]
Output: 1
Explanation: The only possible set you can choose is {7}. This will make the new array empty.

Constraints:

2 <= arr.length <= 10⁵
arr.length is even.
1 <= arr[i] <= 10⁵

Step 01

Brute Force Baseline

Problem summary: You are given an integer array arr. You can choose a set of integers and remove all the occurrences of these integers in the array. Return the minimum size of the set so that at least half of the integers of the array are removed.

Baseline thinking

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

Pattern signal: Array · Hash Map · Greedy

Example 1

[3,3,3,3,5,5,5,2,2,7]

Example 2

[7,7,7,7,7,7]

Step 02

Core Insight

What unlocks the optimal approach

Count the frequency of each integer in the array.
Start with an empty set, add to the set the integer with the maximum frequency.
Keep Adding the integer with the max frequency until you remove at least half of the integers.

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 #1338: Reduce Array Size to The Half
class Solution {
    public int minSetSize(int[] arr) {
        int mx = 0;
        for (int x : arr) {
            mx = Math.max(mx, x);
        }
        int[] cnt = new int[mx + 1];
        for (int x : arr) {
            ++cnt[x];
        }
        Arrays.sort(cnt);
        int ans = 0;
        int m = 0;
        for (int i = mx;; --i) {
            if (cnt[i] > 0) {
                m += cnt[i];
                ++ans;
                if (m * 2 >= arr.length) {
                    return ans;
                }
            }
        }
    }
}

// Accepted solution for LeetCode #1338: Reduce Array Size to The Half
func minSetSize(arr []int) (ans int) {
	mx := slices.Max(arr)
	cnt := make([]int, mx+1)
	for _, x := range arr {
		cnt[x]++
	}
	sort.Ints(cnt)
	for i, m := mx, 0; ; i-- {
		if cnt[i] > 0 {
			m += cnt[i]
			ans++
			if m >= len(arr)/2 {
				return
			}
		}
	}
}

# Accepted solution for LeetCode #1338: Reduce Array Size to The Half
class Solution:
    def minSetSize(self, arr: List[int]) -> int:
        cnt = Counter(arr)
        ans = m = 0
        for _, v in cnt.most_common():
            m += v
            ans += 1
            if m * 2 >= len(arr):
                break
        return ans

// Accepted solution for LeetCode #1338: Reduce Array Size to The Half
struct Solution;
use std::collections::BinaryHeap;
use std::collections::HashMap;

impl Solution {
    fn min_set_size(arr: Vec<i32>) -> i32 {
        let n = arr.len();
        let mut hm: HashMap<i32, usize> = HashMap::new();
        for x in arr {
            *hm.entry(x).or_default() += 1;
        }
        let mut pq: BinaryHeap<usize> = BinaryHeap::new();
        for (_, v) in hm {
            pq.push(v);
        }
        let mut sum = 0;
        let mut res = 0;
        while sum * 2 < n {
            sum += pq.pop().unwrap();
            res += 1;
        }
        res
    }
}

#[test]
fn test() {
    let arr = vec![3, 3, 3, 3, 5, 5, 5, 2, 2, 7];
    let res = 2;
    assert_eq!(Solution::min_set_size(arr), res);
    let arr = vec![7, 7, 7, 7, 7, 7];
    let res = 1;
    assert_eq!(Solution::min_set_size(arr), res);
    let arr = vec![1, 9];
    let res = 1;
    assert_eq!(Solution::min_set_size(arr), res);
    let arr = vec![1000, 1000, 3, 7];
    let res = 1;
    assert_eq!(Solution::min_set_size(arr), res);
    let arr = vec![1, 2, 3, 4, 5, 6, 7, 8, 9, 10];
    let res = 5;
    assert_eq!(Solution::min_set_size(arr), res);
}

// Accepted solution for LeetCode #1338: Reduce Array Size to The Half
function minSetSize(arr: number[]): number {
    const cnt = new Map<number, number>();
    for (const v of arr) {
        cnt.set(v, (cnt.get(v) ?? 0) + 1);
    }
    let [ans, m] = [0, 0];
    for (const v of Array.from(cnt.values()).sort((a, b) => b - a)) {
        m += v;
        ++ans;
        if (m * 2 >= arr.length) {
            break;
        }
    }
    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

EXHAUSTIVE

O(2ⁿ) time

O(n) space

Try every possible combination of choices. With n items each having two states (include/exclude), the search space is 2ⁿ. Evaluating each combination takes O(n), giving O(n × 2ⁿ). The recursion stack or subset storage uses O(n) space.

GREEDY

O(n log n) time

O(1) space

Greedy algorithms typically sort the input (O(n log n)) then make a single pass (O(n)). The sort dominates. If the input is already sorted or the greedy choice can be computed without sorting, time drops to O(n). Proving greedy correctness (exchange argument) is harder than the implementation.

Shortcut: Sort + single pass → O(n log n). If no sort needed → O(n). The hard part is proving it works.

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.

Using greedy without proof

Wrong move: Locally optimal choices may fail globally.

Usually fails on: Counterexamples appear on crafted input orderings.

Fix: Verify with exchange argument or monotonic objective before committing.