Missing ranges of numbers

You have an inclusive interval [lower, upper] and a sorted array of unique integers arr[], all of which lie within this interval. A number x is considered missing if x is in the range [lower, upper] but not present in arr. Your task is to return the smallest set of sorted ranges that includes all missing numbers, ensuring no element from arr is within any range, and every missing number is covered exactly once.

Examples

Input: arr[] = [14, 15, 20, 30, 31, 45], lower = 10, upper = 50
Output: [[10, 13], [16, 19], [21, 29], [32, 44], [46, 50]]
Explanation: These ranges represent all missing numbers between 10 and 50 not present in the array

Input: arr[] = [-48, -10, -6, -4, 0, 4, 17], lower = -54, upper = 17
Output: [[-54, -49], [-47, -11], [-9, -7], [-5, -5], [-3, -1], [1, 3], [5,16]]
Explanation: These ranges represent all missing numbers between -54 and 17 not present in the array.

Using Linear Scan - O(n) Time and O(1) Space

Since arr[] is sorted, we can efficiently identify gaps between consecutive elements. By iterating through arr[], we check the difference between adjacent numbers:

• If the difference is greater than one, the numbers in between form a missing range.
• Additionally, we handle edge cases where the missing range starts before the first element or ends after the last element of arr[].

// C++ program to calculate missing ranges in an array
#include <iostream>
#include <vector>
using namespace std;

vector<vector<int>> missingRanges(vector<int> &arr, int lower, int upper) {
    int n = arr.size();
    vector<vector<int>> res;

    // Check for missing range before the first element
    if (lower < arr[0])
        res.push_back({lower, arr[0] - 1});

    // Check for missing ranges between consecutive elements
    for (int i = 0; i < n - 1; ++i)
        if (arr[i + 1] - arr[i] > 1)
            res.push_back({arr[i] + 1, arr[i + 1] - 1});

    // Check for missing range after the last element
    if (n > 0 && upper > arr[n - 1])
        res.push_back({arr[n - 1] + 1, upper});

    return res;
}

int main() {
    int lower = 10, upper = 50;
    vector<int> arr{14, 15, 20, 30, 31, 45};
    vector<vector<int>> res = missingRanges(arr, lower, upper);
    for (const vector<int> &v : res)
        cout << v[0] << " " << v[1] << endl;
    return 0;
}

// Java program to calculate missing ranges in an array
import java.util.*;

class GfG {

    public static List<List<Integer>> missingRanges(int[] arr, int lower, int upper) {
        int n = arr.length;
        List<List<Integer>> res = new ArrayList<>();

        // Check for missing range before the first element
        if (lower < arr[0]) {
            res.add(Arrays.asList(lower, arr[0] - 1));
        }

        // Check for missing ranges between consecutive elements
        for (int i = 0; i < n - 1; ++i) {
            if (arr[i + 1] - arr[i] > 1) {
                res.add(Arrays.asList(arr[i] + 1, arr[i + 1] - 1));
            }
        }

        // Check for missing range after the last element
        if (upper > arr[n - 1]) {
            res.add(Arrays.asList(arr[n - 1] + 1, upper));
        }

        return res;
    }

    public static void main(String[] args) {
        int lower = 10;
        int upper = 50;
        int[] arr = {14, 15, 20, 30, 31, 45};
        List<List<Integer>> res = missingRanges(arr, lower, upper);
        for (List<Integer> range : res) {
            System.out.println(range.get(0) + " " + range.get(1));
        }
    }
}

# Python program to calculate missing ranges in an array
def missingRanges(arr, lower, upper):
    n = len(arr)
    res = []

    # Check for missing range before the first element
    if lower < arr[0]:
        res.append([lower, arr[0] - 1])

    # Check for missing ranges between consecutive elements
    for i in range(n - 1):
        if arr[i + 1] - arr[i] > 1:
            res.append([arr[i] + 1, arr[i + 1] - 1])

    # Check for missing range after the last element
    if upper > arr[-1]:
        res.append([arr[-1] + 1, upper])

    return res

if __name__ == "__main__":
    lower = 10
    upper = 50
    arr = [14, 15, 20, 30, 31, 45]
    res = missingRanges(arr, lower, upper)
    for v in res:
        print(v[0], v[1])

// C# program to calculate missing ranges in an array
using System;
using System.Collections.Generic;

public class GfG
{
    public static List<List<int>> MissingRanges(int[] arr, int lower, int upper) {
        int n = arr.Length;
        List<List<int>> res = new List<List<int>>();

        // Check for missing range before the first element
        if (lower < arr[0]) {
            res.Add(new List<int> { lower, arr[0] - 1 });
        }

        // Check for missing ranges between consecutive elements
        for (int i = 0; i < n - 1; i++) {
            if (arr[i + 1] - arr[i] > 1) {
                res.Add(new List<int> { arr[i] + 1, arr[i + 1] - 1 });
            }
        }

        // Check for missing range after the last element
        if (upper > arr[n - 1]) {
            res.Add(new List<int> { arr[n - 1] + 1, upper });
        }

        return res;
    }

    public static void Main(string[] args) {
        int lower = 10;
        int upper = 50;
        int[] arr = { 14, 15, 20, 30, 31, 45 };
        List<List<int>> res = MissingRanges(arr, lower, upper);

        foreach (var range in res) {
            Console.WriteLine($"{range[0]} {range[1]}");
        }
    }
}

// JavaScript program to calculate missing ranges in an array
function missingRanges(arr, lower, upper) {
    const n = arr.length;
    const res = [];

    // Check for missing range before the first element
    if (lower < arr[0]) {
        res.push([lower, arr[0] - 1]);
    }

    // Check for missing ranges between consecutive elements
    for (let i = 0; i < n - 1; i++) {
        if (arr[i + 1] - arr[i] > 1) {
            res.push([arr[i] + 1, arr[i + 1] - 1]);
        }
    }

    // Check for missing range after the last element
    if (upper > arr[n - 1]) {
        res.push([arr[n - 1] + 1, upper]);
    }

    return res;
}

// Driver code
const lower = 10;
const upper = 50;
const arr = [14, 15, 20, 30, 31, 45];
const res = missingRanges(arr, lower, upper);

for (const range of res) {
    console.log(`${range[0]} ${range[1]}`);
}

10 13
16 19
21 29
32 44
46 50