Find the Missing Number

You are given a list of n-1 integers and these integers are in the range of 1 to n. There are no duplicates in list. One of the integers is missing in the list. Write an efficient code to find the missing integer.

Example:
I/P    [1, 2, 4, ,6, 3, 7, 8]
O/P    5



METHOD 1(Use sum formula)

Algorithm:

1. Get the sum of numbers 
       total = n*(n+1)/2
2  Subtract all the numbers from sum and
   you will get the missing number.
#include<stdio.h>

/* getMissingNo takes array and size of array as arguments*/
int getMissingNo (int a[], int n)
{
    int i, total;
    total  = (n+1)*(n+2)/2;   
    for ( i = 0; i< n; i++)
       total -= a[i];
    return total;
}

/*program to test above function */
int main()
{
    int a[] = {1,2,4,5,6};
    int miss = getMissingNo(a,5);
    printf("%d", miss);
    getchar();
}

Time Complexity: O(n)

There can be overflow if n is large. In order to avoid Integer Overflow, we can pick one number from known numbers and subtract one number from given numbers. This way we wont have Integer Overflow ever. Thanks to Sahil Rally for suggesting this improvement.



METHOD 2(Use XOR)

  1) XOR all the array elements, let the result of XOR be X1.
  2) XOR all numbers from 1 to n, let XOR be X2.
  3) XOR of X1 and X2 gives the missing number.
#include<stdio.h>

/* getMissingNo takes array and size of array as arguments*/
int getMissingNo(int a[], int n)
{
    int i;
    int x1 = a[0]; /* For xor of all the elements in array */
    int x2 = 1; /* For xor of all the elements from 1 to n+1 */
    
    for (i = 1; i< n; i++)
        x1 = x1^a[i];
           
    for ( i = 2; i <= n+1; i++)
        x2 = x2^i;         
   
    return (x1^x2);
}

/*program to test above function */
int main()
{
    int a[] = {1, 2, 4, 5, 6};
    int miss = getMissingNo(a, 5);
    printf("%d", miss);
    getchar();
}

Time Complexity: O(n)

Please write comments if you find anything incorrect, or you want to share more information about the topic discussed above.



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