Majority Number
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Given an array of integers, the majority number is the number that occurs more than half of the size of the array. Find it.
Example
Given [1, 1, 1, 1, 2, 2, 2], return 1
Challenge
O(n) time and O(1) extra space
最直观的想法就是,建立HashMap,记录list中的每一个integer元素的个数,如果大于1/2 list长度,即可返回。
进一步分析发现,其实并不需要记录所有的integer元素的个数,可以只记录当前最多的那一个majority。这种方法也称为
The Boyer-Moore Vote Algorithm solves the majority vote problem in linear time O(n) and logarithmic space O(log n)
As we sweep we maintain a pair consisting of a current candidate and a counter. Initially, the current candidate is unknown and the counter is 0.
When we move the pointer forward over an element e:
If the counter is 0, we set the current candidate to e and we set the counter to 1.
If the counter is not 0, we increment or decrement the counter according to whether e is the current candidate.
When we are done, the current candidate is the majority element, if there is a majority.
换一种角度,是否可以直接从list中读取这个majority呢?如果对list进行排序,那么1/2处的元素,也就是majority的那个integer了。当然这种方法有个问题,就是对于没有majority的情况下(没有一个达到了1/2 总长度),是无法判断是否存在majority的,如果题目中明确一定存在这样的majority,那么这种方法也是可行的。
时间 O(n), 空间 O(1)
HashMap Solution