最小的k个数

题目描述

输入n个整数，找出其中最小的K个数。例如输入4,5,1,6,2,7,3,8这8个数字，则最小的4个数字是1,2,3,4。

思路一：基于partition函数的算法，时间复杂度可达到O(n)

class Solution{    vector<int> GetLeastNumbers_Solution( vector<int> input, int k )    {        if ( k <= 0 )            return vector<int>();        if ( input.size() < k )            return vector<int>();        int start = 0, end = input.size()-1;        int kIndex = k - 1;        int index;        vector<int> output;        while ( kIndex != ( index = partition( input, start, end ) ) )         {            if ( kIndex > index )                start = index+1;            else                 end = index-1;        }        for ( int i = 0; i < k; i++ )        {            output.push_back( input[i] );        }        return output;    }    //[start, end]    int partition( vector<int> &input, int start, int end )    {        int sentry = start;        start++;        while ( start <= end )        {            if ( input[start] <= input[sentry] )            {                start++;                continue;            }            if ( input[end] > input[sentry] )            {                end--;                continue;            }            swap( &input[start], &input[end] );            start++;            end--;        }        swap( &input[end], &input[sentry] );        return end;    }    void swap( int *a, int *b )    {        int temp = *a;        *a = *b;        *b = temp;    }}

思路二：借助最大堆时间复杂度可达到O(nlogk)的算法：

class Solution {public:    vector<int> GetLeastNumbers_Solution( vector<int> input, int k )    {        intSet leastNumbers;        if ( k < 1 || k > input.size() )            return vector<int>();        vector<int>::const_iterator iter = input.begin();        for ( ; iter != input.end(); ++iter )        {            if ( leastNumbers.size() < k )                leastNumbers.insert( *iter );            else             {                setIterator iterGreatest = leastNumbers.begin();                if ( *iter < *(leastNumbers.begin()) )                {                    leastNumbers.erase( iterGreatest );                    leastNumbers.insert( *iter );                }            }        }        return vector<int>( leastNumbers.begin(), leastNumbers.end() );    }private:    typedef multiset<int, greater<int> >    intSet;    typedef multiset<int, greater<int> >::iterator setIterator;};