How to Fix: Easy interview question got harder: given numbers 1..100, find the missing number(s) given exactly k are missing
Find the missing number(s) in a sequence of numbers from 1 to 100, given exactly k are missing.
📋 Table of Contents
The problem of finding the missing number(s) in a sequence from 1 to 100, given that exactly k numbers are missing, is more complex than initially perceived. The initial naive approach of calculating the sum of the first N natural numbers does not directly apply when there are missing values.
⚠️ Common Causes
- Assuming the sequence is continuous and every number from 1 to 100 appears exactly once.
🛠️ Step-by-Step Verified Fixes
Method 1: Using the Sum of Arithmetic Series Formula
- Step 1: Calculate the total sum of numbers from 1 to 100 using the formula for the sum of an arithmetic series: S = N * (N + 1) / 2, where N is the last number in the sequence. For this problem, S = 100 * (100 + 1) / 2.
Method 2: Finding Missing Numbers Directly
- Step 1: Calculate the sum of numbers from 1 to k, where k is the number of missing values. This represents the total value that should be present in the sequence if all numbers were there.
💡 Conclusion
To find the missing number(s), subtract the sum of numbers from 1 to k from the total sum of numbers from 1 to 100. This will give you the value that is missing in the sequence.
❓ Frequently Asked Questions
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