Last Updated on November 27, 2023 by Ankit Kochar

In the realm of problem-solving and data manipulation, uncovering the missing element in a sequence embedded within a string can be a perplexing yet intriguing task. This article delves into strategies and algorithms to detect and retrieve the absent number within a sequence represented as a string. Whether the sequence follows a numerical, alphabetical, or pattern-based structure, exploring methodologies to decipher the missing element plays a pivotal role in algorithmic thinking and programming prowess.

## How to Find a Missing Number in a Sequence?How to Find a Missing Number in a Sequence?

Find the missing number in a given in a series as a string with no separator. The maximum length of the number can go up to 6 only. Print -1 if the sequence is invalid, or sequence skips number more than 1 place.

**See original problem statement here**

#### Test Case:

```
Input:
4
1234578
1314151618
123124125127
1213141718
Output:
6
17
126
-1
Explanation:
Case-1:
Given sequence is "1 2 3 4 5 7 8" where 6 is missing from sequence, so 6 is our answer.
Case-2:
Given sequence is "13 14 15 16 18" where 17 is missing from sequence, so 17 is our answer.
Case-3:
Given sequence is "123 124 125 127" where 126 is missing from sequence, so 126 is our answer.
Case-4:
Given sequence is "12 13 14 17 18" where 6 and 7 are missing from sequence, gap can be only of one number so it is an invalid sequence, so -1 is our answer.
```

### Solving Approach :

1) As we know the maximum length of the number goes up to 6, so we can check the number of all lengths from 1 to 6.

2) For each length, we convert numbers of length from string to integer and check if any number is missing from the sequence, if yes we print the number.

3) If the sequence has more than 1 number missing or number have a difference more than 1, that means sequence is invalid. So, we print -1 in this case.

4) Exceptions occur when the number of digits changes when moving to the next number, for example moving from 99 to 100, we use log₁₀A values in such cases, to notice the change in digits.

### Example:

Test Case – 1:Let string s = "12356",

Finding all values of length 1 first,

converting all digits of length 1 in number, we get these values,1,2,3,5,6

As we can see 4 is missing, we print 4 as our result, and we don’t need to check further.

Test Case – 2:Let string s = "1112131516",

Finding all values of length 1 first, we get these values,

1,1,1,2,1,3,1,5,1,6

As we can see this series does not make a sequence, we check for all numbers of length 2, Thus, we get this >sequence,

11,12,13,15,16

As we can see, this sequence lacks 14, hence 14 is our answer and we do not proceed further.

Test Case – 3:

Let string s = "9899100102"

We start checking for all values of length 1, thus we get this sequence,

98,99,10

While reading 10 we get the value of $log_{10}(10)$ which is 1, meaning length has to be increased by 1, and from here we check for number with length 2+1 i.e. 3, hence the sequence becomes,

98,99,100,102

We can see this sequence lacks 101, so we print 101 as our answer.

### Solutions

#include#include #include int len = 0; int getValue(char str[], int i, int m) { if (i + m > len) return -1; int value = 0; for (int j = 0; j < m; j++) { int c = str[i + j] - '0'; if (c < 0 || c > 9) return -1; value = value * 10 + c; } return value; } int findMissingNumber(char str[]) { for (int m=1; m<=6; ++m) { int n = getValue(str, 0, m); if (n == -1) break; int missingNo = -1; int fail = 0; for (int i=m; i!=len; i += 1 + log10(n)) { if ((missingNo == -1) && (getValue(str, i, 1+log10(n+2)) == n+2)) { missingNo = n + 1; n += 2; } else if (getValue(str, i, 1+log10(n+1)) == n+1) n++; else { fail = 1; break; } } if (fail==0) return missingNo; } return -1; } int main() { int test; scanf("%d",&test); while(test--){ char str[1001]; scanf("%s",str); len = strlen(str); printf("%d\n",findMissingNumber(str)); } }

#includeusing namespace std; int len = 0; int getValue(char str[], int i, int m) { if (i + m > len) return -1; int value = 0; for (int j = 0; j < m; j++) { int c = str[i + j] - '0'; if (c < 0 || c > 9) return -1; value = value * 10 + c; } return value; } int findMissingNumber(char str[]) { for (int m=1; m<=6; ++m) { int n = getValue(str, 0, m); if (n == -1) break; int missingNo = -1; bool fail = false; for (int i=m; i!=len; i += 1 + log10l(n)) { if ((missingNo == -1) && (getValue(str, i, 1+log10l(n+2)) == n+2)) { missingNo = n + 1; n += 2; } else if (getValue(str, i, 1+log10l(n+1)) == n+1) n++; else { fail = true; break; } } if (!fail) return missingNo; } return -1; } int main() { int test; cin>test; while(test--){ char str[1001]; cin>str; len = strlen(str); cout<

import java.util.*; import java.io.*; public class Main { static int len = 0; static int getValue(String str, int i, int m){ if (i + m > len) return -1; int value = 0; for (int j = 0; j < m; j++){ int c = str.charAt(i + j) - '0'; if (c < 0 || c > 9) return -1; value = value * 10 + c; } return value; } static int findMissingNumber(String str) { for (int m=1; m<=6; ++m) { int n = getValue(str, 0, m); if (n == -1) break; int missingNo = -1; int fail = 0; for (int i=m; i!=len; i += 1 + (int)Math.log10(n)) { if ((missingNo == -1) && (getValue(str, i, 1+(int)Math.log10(n+2)) == n+2)) { missingNo = n + 1; n += 2; } else if (getValue(str, i, 1+(int)Math.log10(n+1)) == n+1) n++; else { fail = 1; break; } } if (fail==0) return missingNo; } return -1; } public static void main(String args[]) throws IOException { Scanner sc = new Scanner(System.in); int test = sc.nextInt(); while(test-->0){ String str = sc.next(); len = str.length(); System.out.println(findMissingNumber(str)); } } }

[forminator_quiz id="867"]

**Conclusion:**

Discovering the absent number within a sequence concealed within a string demands analytical thinking, pattern recognition, and algorithmic dexterity. Whether the sequence string follows a numeric, alphabetic, or structured pattern, employing systematic approaches to identify and retrieve the missing element elucidates the significance of problem-solving methodologies in programming and computational thinking. By harnessing these strategies, developers and problem-solvers can tackle diverse sequence-related challenges, enhancing their proficiency in algorithm design and data interpretation.

## FAQ: Finding the Missing Number in a Sequence String

Here are some FAQs for Finding the Missing Number in a Sequence String.

**1. What defines a sequence represented as a string?**

A sequence within a string refers to a collection of elements (numbers, letters, or symbols) arranged in a particular order. The sequence may follow a numerical progression, an alphabetical series, or adhere to a distinct pattern.

**2. How does one identify the missing number in a sequence string?**

To identify the missing number in a sequence string, one needs to parse the string, extract the sequence elements, and discern the pattern or logic governing their order. Subsequently, analyzing this pattern facilitates the determination of the absent element in the sequence.

**3. What are some common strategies to find the missing number in a sequence string?**

Various strategies include parsing the string to extract the sequence, converting elements to numerical values (if applicable), detecting the pattern or progression, and then deducing the missing number by filling in the gap based on the established sequence logic.

**4. Are there specific challenges or complexities in identifying missing elements in different types of sequences?**

Yes, challenges can arise when dealing with irregular or complex sequences. For instance, sequences might have hidden patterns, discontinuities, or ambiguous elements, making it harder to discern the missing number without a clear logic or pattern to follow.

**5. What programming languages or tools are commonly used to solve such problems?**

Programming languages like Python, JavaScript, and Java are often employed due to their versatility in string manipulation and algorithmic problem-solving. Additionally, specialized libraries or regex functions aid in extracting and processing sequence strings efficiently.