数据结构--ArrayList13 求数组中未出现的最小正整数

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博客给出一个算法题目，要求设计时间上尽可能高效的算法，找出含n个整数的数组中未出现的最小正整数，并给出示例。还提到源码中使用自己实现的ArrayList，给出了其源码地址。

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1）题目：给定一个含n(n>=1)个整数的数组，请设计一个在时间上尽可能高效的算法，找出数组中未出现的最小正整数。例如，数组{-5,3,2,3}中未出现的最小正整数是1；数组{1,2,3}中未出现的最小正整数是4

2）思路与代码：

源码中使用到的ArrrayList，是调用的是自己实现的ArrayList,自己实现的ArrayList源码地址：https://blog.youkuaiyun.com/u012441545/article/details/89667486

package com.sam.datastruct.arrayList;

import java.util.HashSet;
import java.util.Set;

public class P2_13 {
   /*
    * 思路：使用Java set自带的contains方法查看数值是否存在
    * 时间复杂度O(nlogn)
    * 空间复杂度O(1)*/
   public Integer function(int[] s){
      Set<Integer> exist = new HashSet<>();
      for (int i : s) {
         if (i > 0) {
            exist.add(i);
         }
      }
      for (int i = 1; i <= Integer.MAX_VALUE; ++i) {
         if (!exist.contains(i)) {
            return i;
         }
      }
      return -1;
      
   }
   
   /*
    * 思路：使用位图记录数据是否存在的信息，因为每个int有32个bit，故可以记录32个数据的存在情况
    * 时间复杂度O(n)
    * 空间复杂度O(1)*/
   public Integer function1(int[] s){
      int[] exist = new int[Integer.MAX_VALUE/32];
      for (int i : s) {
         if (i > 0) {
            exist[i/32] |= 1<<i%32;    //数据i的信息记录在exist数组的第i/32个数据的第i%32位上 |= 表示左边与右边做或运算并将结果赋予左边，1<<n表示1左移n位，即乘以2^n
         }
      }
      for (int i = 1; i <= Integer.MAX_VALUE; ++i) {
         if ((exist[i/32] & (1<<i%32)) == 0) {
            return i;
         }
      }
      return -1;
   }
   /*
    * 思路：使用数组记录1到最大值间数据是否出现，之后遍历找出未出现的第一个数据，如果没有则返回最大值+1
    * 时间复杂度O(n)
    * 空间复杂度O(1)*/
   public int function2(int[] s){
      int maxValue = s[0];
      for (int i : s) {
         if (i > maxValue) {
            maxValue = i;
         }
      }
      int[] exist = new int[maxValue + 1];
      for (int i : s){
         if (i > 0) {
            exist[i] = 1;
         }
      }
      for (int i = 1; i <= maxValue; ++i){
         if (exist[i] == 0) {
            return i;
         }
      }
      return maxValue + 1;
   }
   
   public static void main(String[] args) {
      P2_13 p = new P2_13();
      int size = 100;
      int[] s = new int[]{0,5,5,3,5,7,5,5,0,0,0,5,5,6,4,5,5,5,4,5,4,2,5,4,5,5,2,1,6,5,5,7,5,0,5,5,3,5,7,5,5,0,0,0,5,5,6,4,5,5,5,4,5,4,2,5,4,5,5,2,1,6,5,5,7,5,0,5,5,3,5,7,5,5,0,0,0,5,5,6,4,5,5,5,4,5,4,2,5,4,5,5,2,1,6,5,5,7,5,0,5,5,3,5,7,5,5,0,0,0,5,5,6,4,5,5,5,4,5,4,2,5,4,5,5,2,1,6,5,5,7,5,0,5,5,3,5,7,5,5,0,0,0,5,5,6,4,5,5,5,4,5,4,2,5,4,5,5,2,1,6,5,5,7,50,5,5,3,5,7,5,5,0,0,0,5,5,6,4,5,5,5,4,5,4,2,5,4,5,5,2,1,6,5,5,7,5,0,5,5,3,5,7,5,5,0,0,0,5,5,6,4,5,5,5,4,5,4,2,5,4,5,5,2,1,6,5,5,7,5,0,5,5,3,5,7,5,5,0,0,0,5,5,6,4,5,5,5,4,5,4,2,5,4,5,5,2,1,6,5,5,7,5,0,5,5,3,5,7,5,5,0,0,0,5,5,6,4,5,5,5,4,5,4,2,5,4,5,5,2,1,6,5,5,7,5,0,5,5,3,5,7,5,5,0,0,0,5,5,6,4,5,5,5,4,5,4,2,5,4,5,5,2,1,6,5,5,7,5,0,5,5,3,5,7,5,5,0,0,0,5,5,6,4,5,5,5,4,5,4,2,5,4,5,5,2,1,6,5,5,7,5,0,5,5,3,5,7,5,5,0,0,0,5,5,6,4,5,5,5,4,5,4,2,5,4,5,5,2,1,6,5,5,7,5,0,5,5,3,5,7,5,5,0,0,0,5,5,6,4,5,5,5,4,5,4,2,5,4,5,5,2,1,6,5,5,7,5,0,5,5,3,5,7,5,5,0,0,0,5,5,6,4,5,5,5,4,5,4,2,5,4,5,5,2,1,6,5,5,7,5,0,5,5,3,5,7,5,5,0,0,0,5,5,6,4,5,5,5,4,5,4,2,5,4,5,5,2,1,6,5,5,7,50,5,5,3,5,7,5,5,0,0,0,5,5,6,4,5,5,5,4,5,4,2,5,4,5,5,2,1,6,5,5,7,5,0,5,5,3,5,7,5,5,0,0,0,5,5,6,4,5,5,5,4,5,4,2,5,4,5,5,2,1,6,5,5,7,5,0,5,5,3,5,7,5,5,0,0,0,5,5,6,4,5,5,5,4,5,4,2,5,4,5,5,2,1,6,5,5,7,5,0,5,5,3,5,7,5,5,0,0,0,5,5,6,4,5,5,5,4,5,4,2,5,4,5,5,2,1,6,5,5,7,5,0,5,5,3,5,7,5,5,0,0,0,5,5,6,4,5,5,5,4,5,4,2,5,4,5,5,2,1,6,5,5,7,5,0,5,5,3,5,7,5,5,0,0,0,5,5,6,4,5,5,5,4,5,4,2,5,4,5,5,2,1,6,5,5,7,5,0,5,5,3,5,7,5,5,0,0,0,5,5,6,4,5,5,5,4,5,4,2,5,4,5,5,2,1,6,5,5,7,5,0,5,5,3,5,7,5,5,0,0,0,5,5,6,4,5,5,5,4,5,4,2,5,4,5,5,2,1,6,5,5,7,5,0,5,5,3,5,7,5,5,0,0,0,5,5,6,4,5,5,5,4,5,4,2,5,4,5,5,2,1,6,5,5,7,5,0,5,5,3,5,7,5,5,0,0,0,5,5,6,4,5,5,5,4,5,4,2,5,4,5,5,2,1,6,5,5,7,50,5,5,3,5,7,5,5,0,0,0,5,5,6,4,5,5,5,4,5,4,2,5,4,5,5,2,1,6,5,5,7,5,0,5,5,3,5,7,5,5,0,0,0,5,5,6,4,5,5,5,4,5,4,2,5,4,5,5,2,1,6,5,5,7,5,0,5,5,3,5,7,5,5,0,0,0,5,5,6,4,5,5,5,4,5,4,2,5,4,5,5,2,1,6,5,5,7,5,0,5,5,3,5,7,5,5,0,0,0,5,5,6,4,5,5,5,4,5,4,2,5,4,5,5,2,1,6,5,5,7,5,0,5,5,3,5,7,5,5,0,0,0,5,5,6,4,5,5,5,4,5,4,2,5,4,5,5,2,1,6,5,5,7,5};
      /*Random random = new Random();
      for(int i = 0; i < size; ++ i){
         s[i] = 1 + random.nextInt(2);
      }*/
      for(int integer : s){
         System.out.print(integer + ", ");
      }
      System.out.println();
      long t1 = System.nanoTime();
      System.out.println(p.function(s));
      System.out.println(System.nanoTime() - t1);
      t1 = System.nanoTime();
      System.out.println(p.function1(s));
      System.out.println(System.nanoTime() - t1);
      t1 = System.nanoTime();
      System.out.println(p.function2(s));
      System.out.println(System.nanoTime() - t1);
   }

}