【转】POJ 2104 归并排序树+二分查找

1. 二分查找容易死循环,注意 (low+high+1 )/2 , 以及 mid = high-1 或者 mid = low+1

2. 最小或者最大等极限情况要做特殊处理

3.手工调试程序结束后一定要删除检测语句

思路: 用线段树记录归并排序的过程,那么

(1)可以在log(n)时间内查找到 任意数c 在区间(i,j)之间的 名次, 也就是区间内比c小的数的个数+1,

(2)从而我们可以通过二分x来找到在区间(i,j)排名为k的数,注意满足此条件的数可能不止一个,举例 区间数列为

{3, 7,7, 5} k=4

那么满足排名3为的数有5,6,7, 显然我们要找的是7

(1)过程的也需要二分查找,只需要记录比c小的数的个数就可以了

// algorihm:
#include <iostream>
#include <algorithm>
#include <vector>
#include <string>
#include <cctype>
#include <queue>
#include"stdio.h"
/*
#include <list>
#include <stack>
#include <set>
#include <map>
#include <cmath>
*/

using namespace std;

#define ma(a,b) (a)>(b)?(a):(b)
#define mi(a,b) (a)<(b)?(a):(b)
#define FF(i,a,b) for(int i=(a);i<=(b);i++)
#define RR(i,b) for(int i=(0);i<(b);i++)
#define clr(x) memset(x,0,sizeof(x))
#define pb push_back
#define mp make_pair
#define sz size()
#define F first
#define S second

#define vv vector
#define ii iterator
/*
#include <sstream>
#include <iterator>
#define ssm stringstream
*/
#define cn continue
#define br break

typedef int type;
const int ST = 0;
#define out(x) cout << #x << "=" << x << endl
template <class T> void show(T a, int n) { for (int i = ST; i < ST+n; i++) { cout<<a[i]<<' '; } cout<<endl; }
template <class T> void show(T a, int r, int l) { for (int i = ST; i < ST+r; i++) show(a[i], l); cout<<endl; }
const int N=110000;
struct node
{
int l,r;
};
node seg[4*N];
int n, m;
int a[N], b[25][N];

void build(int root, int x, int y, int dep)
{
int len=y-x+1;
int mid=(x+y)/2;
seg[root].l = x;
seg[root].r = y;
if(len>1)
{
build(root*2,x,mid, dep+1);
build(root*2+1,mid+1,y, dep+1);

int i=x, j=mid+1,k=x;
while(i<=mid || j<=y)
{
if(j>y || (i<=mid && b[dep+1][i]<=b[dep+1][j] ) )
{
b[dep][k++] = b[dep+1][i++];
}
else
{
b[dep][k++] = b[dep+1][j++];
}
}

}
else
{
b[dep][x] = a[x];
}

}

int query(int root, int c, int x, int y, int dep)
{
int len=seg[root].r-seg[root].l+1;
int mid=(seg[root].l+seg[root].r)/2;
if(x<=seg[root].l && y>=seg[root].r)
{
int low=seg[root].l, high=seg[root].r, mid;
if(c <= b[dep][low])return 0;
if(c > b[dep][high])return len;
while(low < high)
{
mid = (low+high+1)/2;
if(b[dep][mid] >= c) high=mid-1;
else low=mid;
}
return low-seg[root].l+1;
}
else
{
int ret=0;
if(x<=mid)ret += query(root*2,c,x,y,dep+1);
if(y>mid)ret += query(root*2+1,c,x,y,dep+1);
return ret;
}
}
int main()
{
scanf("%d%d", &n, &m);

for(int i=1;i<=n;i++) scanf("%d", &a[i]);
build(1,1,n,1);
//show(b[1], n+1);
while(m--)
{
int i, j, k, low, hig, mid, num;
scanf("%d%d%d", &i, &j, &k);

low = 1;
hig = n;
while(low < hig)
{
mid = (low+hig+1)/2; // hint +1
num = query(1, b[1][mid], i, j, 1);
if(num >= k) hig = mid-1;
else low=mid;
}
printf("%d\n", b[1][low]);
}
//system("pause");         
return 0;
}

原文地址:https://www.cnblogs.com/lzhitian/p/2624050.html