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Hard
Array
Hash Table

41. First Missing Positive

中文文档

Description

Given an unsorted integer array nums. Return the smallest positive integer that is not present in nums.

You must implement an algorithm that runs in O(n) time and uses O(1) auxiliary space.

 

Example 1:

Input: nums = [1,2,0]
Output: 3
Explanation: The numbers in the range [1,2] are all in the array.

Example 2:

Input: nums = [3,4,-1,1]
Output: 2
Explanation: 1 is in the array but 2 is missing.

Example 3:

Input: nums = [7,8,9,11,12]
Output: 1
Explanation: The smallest positive integer 1 is missing.

 

Constraints:

  • 1 <= nums.length <= 105
  • -231 <= nums[i] <= 231 - 1

Solutions

Solution 1: In-place Swap

We assume the length of the array $nums$ is $n$, then the smallest positive integer must be in the range $[1, .., n + 1]$. We can traverse the array and swap each number $x$ to its correct position, that is, the position $x - 1$. If $x$ is not in the range $[1, n + 1]$, then we can ignore it.

After the traversal, we traverse the array again. If $i+1$ is not equal to $nums[i]$, then $i+1$ is the smallest positive integer we are looking for.

The time complexity is $O(n)$, where $n$ is the length of the array. The space complexity is $O(1)$.

Python3

class Solution:
    def firstMissingPositive(self, nums: List[int]) -> int:
        n = len(nums)
        for i in range(n):
            while 1 <= nums[i] <= n and nums[i] != nums[nums[i] - 1]:
                j = nums[i] - 1
                nums[i], nums[j] = nums[j], nums[i]
        for i in range(n):
            if nums[i] != i + 1:
                return i + 1
        return n + 1

Java

class Solution {
    public int firstMissingPositive(int[] nums) {
        int n = nums.length;
        for (int i = 0; i < n; ++i) {
            while (nums[i] > 0 && nums[i] <= n && nums[i] != nums[nums[i] - 1]) {
                swap(nums, i, nums[i] - 1);
            }
        }
        for (int i = 0; i < n; ++i) {
            if (nums[i] != i + 1) {
                return i + 1;
            }
        }
        return n + 1;
    }

    private void swap(int[] nums, int i, int j) {
        int t = nums[i];
        nums[i] = nums[j];
        nums[j] = t;
    }
}

C++

class Solution {
public:
    int firstMissingPositive(vector<int>& nums) {
        int n = nums.size();
        for (int i = 0; i < n; ++i) {
            while (nums[i] > 0 && nums[i] <= n && nums[i] != nums[nums[i] - 1]) {
                swap(nums[i], nums[nums[i] - 1]);
            }
        }
        for (int i = 0; i < n; ++i) {
            if (nums[i] != i + 1) {
                return i + 1;
            }
        }
        return n + 1;
    }
};

Go

func firstMissingPositive(nums []int) int {
	n := len(nums)
	for i := range nums {
		for 0 < nums[i] && nums[i] <= n && nums[i] != nums[nums[i]-1] {
			nums[i], nums[nums[i]-1] = nums[nums[i]-1], nums[i]
		}
	}
	for i, x := range nums {
		if x != i+1 {
			return i + 1
		}
	}
	return n + 1
}

TypeScript

function firstMissingPositive(nums: number[]): number {
    const n = nums.length;
    for (let i = 0; i < n; i++) {
        while (nums[i] >= 1 && nums[i] <= n && nums[i] !== nums[nums[i] - 1]) {
            const j = nums[i] - 1;
            [nums[i], nums[j]] = [nums[j], nums[i]];
        }
    }
    for (let i = 0; i < n; i++) {
        if (nums[i] !== i + 1) {
            return i + 1;
        }
    }
    return n + 1;
}

Rust

impl Solution {
    pub fn first_missing_positive(mut nums: Vec<i32>) -> i32 {
        let n = nums.len();
        for i in 0..n {
            while nums[i] > 0 && nums[i] <= n as i32 && nums[i] != nums[nums[i] as usize - 1] {
                let j = nums[i] as usize - 1;
                nums.swap(i, j);
            }
        }
        for i in 0..n {
            if nums[i] != (i + 1) as i32 {
                return (i + 1) as i32;
            }
        }
        return (n + 1) as i32;
    }
}

C#

public class Solution {
    public int FirstMissingPositive(int[] nums) {
        int n = nums.Length;
        for (int i = 0; i < n; ++i) {
            while (nums[i] >= 1 && nums[i] <= n && nums[i] != nums[nums[i] - 1]) {
                Swap(nums, i, nums[i] - 1);
            }
        }
        for (int i = 0; i < n; ++i) {
            if (i + 1 != nums[i]) {
                return i + 1;
            }
        }
        return n + 1;
    }

    private void Swap(int[] nums, int i, int j) {
        int t = nums[i];
        nums[i] = nums[j];
        nums[j] = t;
    }
}

C

int firstMissingPositive(int* nums, int numsSize) {
    for (int i = 0; i < numsSize; ++i) {
        while (nums[i] > 0 && nums[i] <= numsSize && nums[i] != nums[nums[i] - 1]) {
            int j = nums[i] - 1;
            int t = nums[i];
            nums[i] = nums[j];
            nums[j] = t;
        }
    }
    for (int i = 0; i < numsSize; ++i) {
        if (nums[i] != i + 1) {
            return i + 1;
        }
    }
    return numsSize + 1;
}

PHP

class Solution {
    /**
     * @param Integer[] $nums
     * @return Integer
     */
    function firstMissingPositive($nums) {
        $n = count($nums);
        for ($i = 0; $i < $n; $i++) {
            while ($nums[$i] >= 1 && $nums[$i] <= $n && $nums[$i] != $nums[$nums[$i] - 1]) {
                $j = $nums[$i] - 1;
                $t = $nums[$i];
                $nums[$i] = $nums[$j];
                $nums[$j] = $t;
            }
        }
        for ($i = 0; $i < $n; $i++) {
            if ($nums[$i] != $i + 1) {
                return $i + 1;
            }
        }
        return $n + 1;
    }
}