PAT1057

题目链接：http://pat.zju.edu.cn/contests/pat-a-practise/1057

普通算法会超时，用树状数组+二分逼近查找第K小即可

#include<cstdio>
#include<cstring>
#include<stack>
using namespace std;

int a[100005];

int lowbit(int t)
{
    return t&(t^(t-1));
}

void add(int pos, int i)
{
    while(pos <= 100004)
    {
        a[pos]+=i;
        pos += lowbit(pos);
    }
}

int sum(int pos)
{
    int sum(0);
    while(pos > 0)
    {
        sum+=a[pos];
        pos -= lowbit(pos);
    }
    return sum;
}

int findk(int k)
{
    int low(1), high(100004), median;
    while(low < high)
    {
        median=(low+high)/2;
        if(sum(median) < k)
            low=median+1;
        else
            high=median;
    }
    return low;
}

int str2num(char *choice)
{
    int len=strlen(choice);
    int radix(1), sum(0);
    while(choice[len-1] != ' ')
    {
        sum += (choice[len-1]-'0')*radix;
        radix *= 10;
        --len;
    }
    return sum;
}

int main()
{
    int N;
    char choice[50];
    scanf("%d",&N);
    gets(choice);
    stack<int> s;
    memset(a, 0, sizeof(a));
    for(int i=0; i<N; ++i)
    {
        gets(choice);
        if(strcmp(choice,"Pop") == 0)
        {
            if(s.empty())
                printf("Invalid
");
            else
            {
                printf("%d
", s.top());
                add(s.top(), -1);
                s.pop();
            }
        }
        else if(strcmp(choice, "PeekMedian") == 0)
        {
            if(s.empty())
                printf("Invalid
");
            else
            {
                int mid;
                if(s.size()%2 == 0)
                    mid = s.size()/2;
                else
                    mid = s.size()/2 +1;
                printf("%d
", findk(mid));
            }
        }
        else
        {
            int num = str2num(choice);
            add(num, 1);
            s.push(num);
        }
    }
    return 0;
}