# Python: Find the first missing positive integer that does not exist in a given list

## Python Basic - 1: Exercise-80 with Solution

Write a Python program to find the first missing positive integer that does not exist in a given list.

**Sample Solution**:

**Python Code:**

```
# Define a function to find the first missing positive integer in a list
def first_missing_number(nums):
# Check if the list is empty, return 1 if it is
if len(nums) == 0:
return 1
# Sort the list in ascending order
nums.sort()
# Initialize the smallest positive integer as 0
smallest_int_num = 0
# Iterate through the sorted list
for i in range(len(nums) - 1):
# Skip non-positive or duplicate numbers
if nums[i] <= 0 or nums[i] == nums[i + 1]:
continue
else:
# Check for a gap between consecutive numbers
if nums[i + 1] - nums[i] != 1:
smallest_int_num = nums[i] + 1
return smallest_int_num
# If no gap is found, the smallest missing positive integer is after the last element
if smallest_int_num == 0:
smallest_int_num = nums[-1] + 1
# Return the smallest missing positive integer
return smallest_int_num
# Test the function with different lists of numbers
print(first_missing_number([2, 3, 7, 6, 8, -1, -10, 15, 16]))
print(first_missing_number([1, 2, 4, -7, 6, 8, 1, -10, 15]))
print(first_missing_number([1, 2, 3, 4, 5, 6, 7]))
print(first_missing_number([-2, -3, -1, 1, 2, 3]))
```

Sample Output:

4 3 8 4

**Explanation: **

Here is a breakdown of the above Python code:

- The function "first_missing_number()" takes a list of numbers ('nums') as input.
- It checks if the list is empty and returns 1 if it is.
- The function sorts the list in ascending order.
- It initializes the smallest positive integer as 0.
- It iterates through the sorted list, skipping non-positive or duplicate numbers.
- It checks for a gap between consecutive numbers, indicating a missing positive integer.
- If a gap is found, the smallest missing positive integer is determined and returned.
- If no gap is found, the smallest missing positive integer is after the last element.
- The function is tested with different lists of numbers.

**Flowchart:**

**Python Code Editor:**

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