First Missing Positive

描述

Given an unsorted integer array, find the first missing positive integer.

For example,Given [1,2,0] return 3,and [3,4,-1,1] return 2.

Your algorithm should run in O(n) time and uses constant space.

分析

本质上是桶排序(bucket sort)，每当 A[i]!= i+1 的时候，将A[i]与A[A[i]-1]交换，直到无法交换为止，终止条件是 A[i]== A[A[i]-1]。

代码

  1. // First Missing Positive
  2. // 时间复杂度O(n)，空间复杂度O(1)
  3. class Solution {
  4. public:
  5.     int firstMissingPositive(vector<int>& nums) {
  6.         bucket_sort(nums);
  8.         for (int i = 0; i < nums.size(); ++i)
  9.             if (nums[i] != (i + 1))
  10.                 return i + 1;
  11.         return nums.size() + 1;
  12.     }
  13. private:
  14.     static void bucket_sort(vector<int>& A) {
  15.         const int n = A.size();
  16.         for (int i = 0; i < n; i++) {
  17.             while (A[i] != i + 1) {
  18.                 if (A[i] <= 0 || A[i] > n || A[i] == A[A[i] - 1])
  19.                     break;
  20.                 swap(A[i], A[A[i] - 1]);
  21.             }
  22.         }
  23.     }
  24. };

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原文: https://soulmachine.gitbooks.io/algorithm-essentials/content/cpp/sorting/bucket-sort/first-missing-positive.html