As many exercises on this site, the description of the problem is misleading: it gives you the impression that data in the array have to stay unordered... but in reality the problem expects for you to sort the array.

def pickingNumbers(a):
    a.sort()
    cnt = 1
    cmx = 0
    i = 1
    s = a[0]
    while i<len(a):
        t = a[i]
        if abs(t-s)<=1:
            cnt += 1
        else:
            s = a[i]
            cmx = max(cmx,cnt)
            cnt = 1
        i += 1
    if i == len(a):
        cmx = max(cmx, cnt)
    return cmx

The description is ambiguous. "subarray → consecutive sections" "Two elements → two adjacent elements in the section" Therefore, you may misunderstand that the array {4,5,6,7,8} is the correct answer.

This problem is not worded in a correct format to match the results desired by the problem itself, and just like when you realize you need a fence company to fix issues properly, working through the problem as written will give you the wrong answers.

import java.io.; import java.util.; import java.util.stream.*;

class Result {

/*
 * Complete the 'pickingNumbers' function below.
 *
 * The function is expected to return an INTEGER.
 * The function accepts INTEGER_ARRAY a as parameter.
 */

public static int pickingNumbers(List<Integer> a) {
    int[] freq = new int[101]; // since 0 <= a[i] <= 100
    for (int num : a) {
        freq[num]++;
    }

    int maxLength = 0;
    for (int i = 1; i < freq.length; i++) {
        maxLength = Math.max(maxLength, freq[i] + freq[i - 1]);
    }

    return maxLength;
}

}

public class Solution { public static void main(String[] args) throws IOException { BufferedReader bufferedReader = new BufferedReader(new InputStreamReader(System.in)); BufferedWriter bufferedWriter = new BufferedWriter(new FileWriter(System.getenv("OUTPUT_PATH")));

    int n = Integer.parseInt(bufferedReader.readLine().trim());

    List<Integer> a = Arrays.stream(bufferedReader.readLine().trim().split(" "))
        .map(Integer::parseInt)
        .collect(Collectors.toList());

    int result = Result.pickingNumbers(a);

    bufferedWriter.write(String.valueOf(result));
    bufferedWriter.newLine();

    bufferedReader.close();
    bufferedWriter.close();
}

}