HDU 4302 Holedox Eating （线段树模拟）

题意：一个老鼠在一条长度为L的直线上跑，吃蛋糕，老鼠只能沿直线移动。开始时没有蛋糕，老鼠的初始位置是0.

有两个操作，0 x 代表在位置x添加一个蛋糕； 1 代表老鼠想吃蛋糕。老鼠每次都会选择离自己最近的点，如果两边距离相同，老鼠优先选择与自己当前移动方向相同的点。

求最终移动的总距离。

题解：线段树单点修改+查询区间端点。

设当前位置为pos，每次查询区间[0, pos]的最右端和区间[pos, L]的最左端，比较选择哪个更近。

详细题解见代码注释。

#include <cstdio>
#include <cstdlib>
#include <cstring>
#include <algorithm>
#include <cmath>

#define lson l, m, rt << 1
#define rson m+1, r, rt << 1 | 1

#define LEFT  0
#define RIGHT 1

using std::min;
using std::max;
using std::abs;

const int MAXN = 100010;
const int INF = 1 << 30;

int tr[MAXN << 2];             //标记哪个点有蛋糕
int left[MAXN << 2];           //标记区间[l, r]内有蛋糕的最左端点
int right[MAXN << 2];          //标记区间[l, r]内有蛋糕的最右端点
int N, S;
int findL, findR;              //标记查找到的任意区间[l, r]中有蛋糕的最左端和最右端

void PushUp( int rt )
{
    int lc = rt << 1;
    int rc = rt << 1 | 1;
    left[rt]  = min( left[lc], left[rc] );
    right[rt] = max( right[lc], right[rc] );
    return;
}

void build( int l, int r, int rt )     //建树
{
    tr[rt] = 0;                        //每个点初始蛋糕数目为0
    left[rt] = INF;
    right[rt] = -INF;
    if ( l == r ) return;
    int m = ( l + r ) >> 1;
    build( lson );
    build( rson );
    return;
}

void Update( int pos, int v, int l, int r, int rt )  //更新
{
    if ( l == pos && r == pos )
    {
        tr[rt] += v;                                 //更新该点的蛋糕数目
        if ( tr[rt] == 0 )                           //如果这一点没有蛋糕了
        {
            left[rt]  = INF;
            right[rt] = -INF;
        }
        else                                         //如果这一点有蛋糕
        {
            left[rt] = l;
            right[rt] = l;
        }
        return;
    }

    int m = ( l + r ) >> 1;
    if ( pos <= m ) Update( pos, v, lson );
    else            Update( pos, v, rson );
    PushUp( rt );
    return;
}

void Query( int L, int R, int l, int r, int rt )     //查询
{
    if ( L <= l && r <= R )
    {
        findL = min( left[rt], findL );
        findR = max( right[rt], findR );
        return;
    }
    int m = ( l + r ) >> 1;
    if ( L <= m ) Query( L, R, lson );
    if ( R > m )  Query( L, R, rson );
    return;
}

int main()
{
    int T, cas = 0;
    scanf( "%d", &T );
    while ( T-- )
    {
        scanf( "%d%d", &N, &S );
        ++N;                             //原题目中pipe长度为L,编号为0-L，实际上是有(L+1)个点，
                                         //之前没注意，RE了一次，在这里我把每个点编号为1-(L+1)

        int curPos = 1;                  //当前位置
        int curDirection = RIGHT;        //当前方向
        int sum = 0;                     //移动总路程

        build( 1, N, 1 );                //建树

        while ( S-- )
        {
            //printf("**************curPos=%d curDir=%d\n", curPos, curDirection );
            int op, pos;
            scanf( "%d", &op );
            if ( op == 0 )
            {
                scanf( "%d", &pos );
                Update( pos+1, 1, 1, N, 1 );
            }
            else
            {
                bool find = false;
                int findpos;

                if ( curDirection == LEFT )                   //如果当前方向向左
                {
                    int LL, RR;
                    findL = INF;
                    findR = -INF;
                    Query( 1, curPos, 1, N, 1 ), LL = findR;  //向左走，找离当前点最近的右端点
                    findL = INF;
                    findR = -INF;
                    Query( curPos, N, 1, N, 1 ), RR = findL;  //向右走，找离当前点最近的左端点

                    if ( LL == -INF && RR == INF )            //两边都没有蛋糕
                    {
                        find = false;
                    }
                    else if ( LL == -INF && RR != INF )       //只有右边有蛋糕
                    {
                        find = true;
                        findpos = RR;
                        curDirection = RIGHT;
                    }
                    else if ( LL != -INF && RR == INF )       //只有左边有蛋糕
                    {
                        find = true;
                        findpos = LL;
                        curDirection = LEFT;
                    }
                    else                                      //两边都有蛋糕
                    {
                        find = true;
                        if ( curPos - LL <= RR - curPos )     //注意等号，两边距离相等时优先选择左边
                        {
                            findpos = LL;
                            curDirection = LEFT;
                        }
                        else
                        {
                            findpos = RR;
                            curDirection = RIGHT;
                        }
                    }

                    //printf("LEFT: ");
                }
                else
                {
                    int LL, RR;
                    findL = INF;
                    findR = -INF;
                    Query( curPos, N, 1, N, 1 ), RR = findL;
                    findL = INF;
                    findR = -INF;
                    Query( 1, curPos, 1, N, 1 ), LL = findR;

                    if ( LL == -INF && RR == INF )
                    {
                        find = false;
                    }
                    else if ( LL == -INF && RR != INF )
                    {
                        find = true;
                        findpos = RR;
                        curDirection = RIGHT;
                    }
                    else if ( LL != -INF && RR == INF )
                    {
                        find = true;
                        findpos = LL;
                        curDirection = LEFT;
                    }
                    else
                    {
                        find = true;
                        if ( curPos - LL < RR - curPos )        //注意没有等号，两边距离相等时优先选择右边
                        {
                            findpos = LL;
                            curDirection = LEFT;
                        }
                        else
                        {
                            findpos = RR;
                            curDirection = RIGHT;
                        }
                    }

                    //printf("RIGHT: ");
                }
                //printf( "findL=%d findR=%d\n", findL, findR );

                //printf( "findpos = %d\n", findpos );
                if ( find )
                {
                    sum += abs( findpos - curPos );
                    curPos = findpos;
                    Update( findpos, -1, 1, N, 1 );
                }
            }
        }

        printf( "Case %d: %d\n", ++cas, sum );
    }
    return 0;
}