数据结构--ArrayList12 求主元素

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最新推荐文章于 2025-03-20 20:26:22 发布

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分类专栏：数据结构算法文章标签：数据结构顺序表

本文链接：https://blog.youkuaiyun.com/u012441545/article/details/89739085

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这篇博客探讨了如何在整数序列中找到主元素，即出现次数超过序列一半的元素。通过举例说明主元素的概念，并提供了一种高效算法的思路，利用自定义实现的ArrayList来解决此问题。如果序列中不存在主元素，则输出-1。相关源码链接已给出。

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1）题目：已知一个整数序列A=(a0，a1...an)，其中0<=ai<n(0<=i<n)，若存在ap1=ap2.....=apm=x,且m>n/2(0<=pk<n,1<=k<m),则称x为A的主元素，例如A=(0,5,5,3,5,7,5,5),则5为主元素；又如A=(0,5,5,3,5,1,5,7),则A中没有主元素，假设A中的n个元素存在一个一维数组中，请设计一个尽可能高效的算法，找出A的主元素，则输出该元素，否则输出-1。

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.HashMap;
import java.util.Map;

public class P2_12 {
	/*
	 * 思路：
	 * 时间复杂度O(n)
	 * 空间复杂度O(1)*/
	public Integer function(int[] s){
		if (s.length == 0) {
			return -1;
		}
		if(s.length == 1){
			return s[0];
		}
		
		Map<Integer, Integer> count = new HashMap<>();
		
		for (Integer i : s) {
			if (count.containsKey(i)) {
				count.put(i, count.get(i) + 1);
			}else {
				count.put(i, 1);
			}
		}
		
		for (Integer integer : count.keySet()) {
			if (count.get(integer) > s.length / 2) {
				return integer;
			}
		}
		
		return -1;
	}
	
	/*
	 * 思路：当数组中存在某个出现次数大于n/2的时候，将数组中所有不等的数两两消去后剩下的就是该数，不过反之不成立，故需要进行验证
	 * 时间复杂度O(n)
	 * 空间复杂度O(n)*/
	public Integer function1(int[] s){
		int index = 0;
		int[] ss = new int[s.length];  //复制s的数据用于最后的验证（在前面会把s中的数据消掉部分，故不能用s进行验证）
		for(int i = 1; i < s.length; ++i){
			ss[i] = s[i];
			if (s[index] != s[i]) {  //两个数不相等，需要消去
				s[index] = -1;
				s[i] = -1;
				if (s.length - 1 == i) {  //i是最后一个数不需要继续消数据
					break;
				}
				for(int j = index; j <= i + 1; ++j){ //index指向下一个不为-1的数的，由于数组为自然数，故最多在i+1的位置能够找到数据
					if (-1 != s[j]) {
						index = j;
						break;
					}
				}
			}
		}
		int target = -1;
		for(int i = 0; i < s.length; ++i){
			if (-1 != s[i]) {
				target = s[i];
				return target
			}
		}
		if (target != -1) {
			int count = 0;
			for (int i : ss) {
				if (i == target) {
					++ count;
				}
			}
			if (count > ss.length / 2) {
				return target;
			}
		}
		return -1;
	}
	
	public static void main(String[] args) {
		P2_12 p = new P2_12();
		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);
	}

}