Given an unsorted array with both positive and negative elements including 0. The task is to find the smallest positive number missing from the array in O(N) time.
Examples:
Input: arr[] = {-5, 2, 0, -1, -10, 15}
Output: 1
Input: arr[] = {0, 1, 2, 3, 4, 5}
Output: 6
Input: arr[] = {1, 1, 1, 0, -1, -2}
Output: 2
We can use hashing to solve this problem. The idea is to build a hash table of all positive elements in the given array. Once the hash table is built. We can look in the hash table for all positive integers, starting from 1. As soon as we find a number which is not there in the hash table, we return it.
We can use the unordered_map in C++ to implement the hash which allows performing look-up operation in almost O(1) time complexity.
Below is the implementation of the above approach:
C++
// C++ program to find the smallest// positive missing number#include <bits/stdc++.h>using namespace std;// Function to find the smallest positive// missing numberint missingNumber(int a[], int n){ // Declaring an unordered_map unordered_map<int, int> mp; // if array value is positive // store it in map for (int i = 0; i < n; i++) { if (a[i] > 0) mp[a[i]]++; } // index value set to 1 int index = 1; // Return the first value starting // from 1 which does not exists in map while (1) { if (mp.find(index) == mp.end()) { return index; } index++; }}// Driver codeint main(){ int a[] = { 1, 1, 1, 0, -1, -2 }; int size = sizeof(a) / sizeof(a[0]); cout << "Smallest positive missing number is : " << missingNumber(a, size) << endl; return 0;} |
Java
// Java program to find the smallest // positive missing number import java.util.*;class GFG { // Function to find the smallest positive // missing number static int missingNumber(int a[], int n) { // Declaring an unordered_map Map<Integer, Integer> mp = new LinkedHashMap<>(); // if array value is positive // store it in map for (int i = 0; i < n; i++) { if (a[i] > 0) { mp.put(a[i], mp.get(a[i]) == null ? 1 : mp.get(a[i]) + 1); } } // index value set to 1 int index = 1; // Return the first value starting // from 1 which does not exists in map while (true) { if (!mp.containsKey(index)) { return index; } index++; } } // Driver code public static void main(String[] args) { int a[] = {1, 1, 1, 0, -1, -2}; int size = a.length; System.out.println("Smallest positive missing number is : " + missingNumber(a, size)); }}// This code has been contributed by 29AjayKumar |
Python3
# Python3 program to find the smallest # positive missing number # Function to find the smallest positive # missing number def missingNumber(a, n) : # Declaring an unordered_map mp = dict(); # if array value is positive # store it in map for i in range(n) : if (a[i] > 0) : if a[i] not in mp.keys() : mp[a[i]] = 0 mp[a[i]] += 1 # index value set to 1 index = 1; # Return the first value starting # from 1 which does not exists in map while (1) : if (index not in mp.keys()) : return index; index += 1; # Driver code if __name__ == "__main__" : a = [ 1, 1, 1, 0, -1, -2 ]; size = len(a); print("Smallest positive missing number is : ",missingNumber(a, size)); # This code is contributed by AnkitRai01 |
C#
// C# program to find the smallest // positive missing number using System;using System.Collections.Generic;class GFG { // Function to find the smallest positive // missing number static int missingNumber(int []a, int n) { // Declaring an unordered_map Dictionary<int,int> m = new Dictionary<int,int>(); // if array value is positive // store it in map for (int i = 0; i < n; i++) { if (a[i] > 0) { if(m.ContainsKey(a[i])) { var val = m[a[i]]; m.Remove(a[i]); m.Add(a[i], val + 1); } else { m.Add(a[i], 1); } } } // index value set to 1 int index = 1; // Return the first value starting // from 1 which does not exists in map while (true) { if (!m.ContainsKey(index)) { return index; } index++; } } // Driver code public static void Main(String[] args) { int []a = {1, 1, 1, 0, -1, -2}; int size = a.Length; Console.WriteLine("Smallest positive missing number is : " + missingNumber(a, size)); }}// This code is contributed by Princi Singh |
Javascript
<script>// JavaScript program to find the smallest// positive missing number// Function to find the smallest positive// missing numberfunction missingNumber(a, n) { // Declaring an unordered_map let mp = new Map(); // if array value is positive // store it in map for (let i = 0; i < n; i++) { if (a[i] > 0) { mp[a[i]]++; if (mp.has(a[i])) { mp.set(a[i], mp.get(a[i]) + 1) } else { mp.set(a[i], 1) } } } // index value set to 1 let index = 1; // Return the first value starting // from 1 which does not exists in map while (1) { if (!mp.has(index)) { return index; } index++; }}// Driver codelet a = [1, 1, 1, 0, -1, -2];let size = a.length;document.write("Smallest positive missing number is : " +missingNumber(a, size) + "<br>");// This code is contributed by gfgking</script> |
Output:
Smallest positive missing number is : 2
Time Complexity: O(N)
Auxiliary Space: O(N)
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