Problem#4.py

"""
Given an array of integers, find the first missing positive integer in linear time and constant space. 
In other words, find the lowest positive integer that does not exist in the array. The array can contain duplicates and negative numbers as well.
For example, the input [3, 4, -1, 1] should give 2. The input [1, 2, 0] should give 3.
"""
def firstMissingPositive(nums):
    """
    if nums == []:
        return 1
    for i in range(0,len(nums)):
        if nums[i] <= 0 or nums[i] > len(nums):
            continue
        val = nums[i]
        while nums[val-1] != val:
            nextVal = nums[val-1]
            nums[val-1] = val
            val = nextVal
            if val <= 0 or val > len(nums):
                break
    for i in range(0,len(nums)):
        if nums[i] != i+1:
            return i+1
    return len(nums)+1
    """
    nums = list(set(nums)) + [0]
    n = len(nums)
    for i in range(len(nums)):  # delete those useless elements
        if nums[i] < 0 or nums[i] >= n:
            nums[i] = 0
    for i in range(len(nums)):  # use the index as the hash to record the frequency of each number
        nums[nums[i] % n] += n
    for i in range(1, len(nums)):
        if nums[i] // n == 0:
            return i
    return n