How to find the missing number without using arrays?

Question

I have to find a missing number in a sequence of numbers. The input consists of a positive integer n, between 0 and 35000, and n unique numbers with range [0..n]. (So this range contains n+1 numbers).

I already tried some things with sum={n*(n+1)}/2 and then misNum=sum-SumOfNum;, but I couldn't find a way to make this work.

I wrote some code, but not with the examples I mentioned before. Obviously, this code is not complete, but I don't know how to make it complete.

#include <stdio.h>
#include <stdlib.h>
int main (int argc, char *v[]) {
 int length;
 int num; 
 scanf("%d", &length);
 /*scanf(???)*/
 int goal=length;
 int i;
 for(i=0; i!=length; i++){
 goal=goal+i-num[i];
 };
 return goal;
}

Input and outcome should be:

Input: 2 "enter" 0 2. Output: 1

Input: 3 "enter" 0 3 1. Output: 2

• Bodo: Do you have to check that the sequence of numbers matches the expectation, i.e. that the numbers are in the correct range, that their count is correct and that you don't have duplicate numbers? (The last one may be impossible without using an array.)
• Bodo: But the possible duplicate is for C# not C.

Answer 1

Sum of all numbers from 0 to n is

n(a1+an)/2 = (in your case a1 = 0 and an = n+1) n*(n+1)/2

so the missing number is n*(n+1)/2 - (sum of input numbers after the length)

#include <stdio.h>
#include <stdlib.h>
int main(int argc, char* v[]) {
 int length;
 int i = 0;
 int sum = 0;
 scanf_s("%d", &length);
 // calculate arithmetic series sum
 auto series_sum = ((length + 1) * (length)) / 2;
 while (i < length)
 {
 int next;
 scanf_s("%d", &next);
 sum += next;
 ++i;
 }
 printf("missing num is %d ", series_sum - sum);
}

Answer 2

You have n number of integers to be scanned. Use mathematical equation to calculate the sum of first n+1 natural numbers. Then run a loop for n times and then run a loop to add all the n numbers scanned. Then subtract this sum with the sum of n+1 natural number. Result will be the missing number.

Answer 3

The calculation from the question is also correct and can be made to work with a few modifications.

#include <stdio.h>
#include <stdlib.h>
int main (int argc, char *v[]) {
 int length;
 int num; 
 // printf("enter maximum number: ");
 scanf("%d", &length);
 int goal=length;
 int i;
 for(i=0; i!=length; i++){
 // printf("number[%d]: ", i);
 if(scanf("%d", &num) != 1) { 
 fprintf(stderr, "invalid input\n");
 return 1;
 }
 if((num < 0) || (num > length)) {
 fprintf(stderr, "invalid number %d\n", num);
 return 2;
 }
 goal=goal+i-num;
 };
 // printf("missing number: ");
 printf("%d\n", goal);
 return 0;
}