ACM PKU 1177 Picture

最新推荐文章于 2017-08-23 11:13:13 发布

转载最新推荐文章于 2017-08-23 11:13:13 发布 · 984 阅读

文章标签：

#insert #up #build #struct #vector #null

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本文介绍了一种使用线段树解决区间覆盖问题的方法，并提供了详细的代码实现。通过线段树可以有效地处理区间增加与删除操作，进而计算区间的总覆盖长度与覆盖段数。

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http://acm.pku.edu.cn/JudgeOnline/problem?id=1177

//这个题呢，据说是用线段树来求解，下面有一个示例解法，但我觉得好像有点问题，仅供参考，譬如在输入

-1 –1 0 0

0 –1 1 2

-1 1 0 2

时结果应该为12

但该程序的结果是16

#include
#include

using namespace std;

const int MAXINT = 99999999;

struct TSegment //线段树
{
int l, r;
int nLen, nSeg;
int lCover, rCover;
int counter;
TSegment *left, *right;
TSegment()
{
counter = 0;
lCover = rCover = 0;
nLen = nSeg = 0;
left = right = NULL;
}
};

struct TNode
{
int pos;
int up, down;
bool isLeft;
TNode() {}
TNode( int tp, int td, int tu, bool ti ) : pos( tp ), up( tu ), down( td ), isLeft( ti ) {}
};

bool operator<( const TNode &a, const TNode &b )
{
return a.pos < b.pos;
}

vector vec;
int n, miny, maxy;
TSegment* root = NULL;

void read()
{
scanf( "%d", &n );
int i;
int x1, y1, x2, y2;
miny = MAXINT;
maxy = -MAXINT;
for ( i = 0; i < n; i ++ )
{
scanf( "%d %d %d %d", &x1, &y1, &x2, &y2 );
vec.push_back( TNode( x1, y1, y2, true ) );
vec.push_back( TNode( x2, y1, y2, false ) );
miny = min( miny, y1 );
maxy = max( maxy, y2 );
}
sort( vec.begin(), vec.end() );
}

void build( TSegment* crt, int fi, int la )
{
crt->l = fi;
crt->r = la;
if ( la - fi <= 1 ) return;
int mid = ( ( fi + la ) >> 1 );
crt->left = new TSegment();
build( crt->left, fi , mid );
crt->right = new TSegment();
build( crt->right, mid, la );
}

void insert( TSegment* crt, int fi, int la, int down, int up )
{
if ( fi == down ) crt->lCover ++;
if ( la == up ) crt->rCover ++;
if ( fi == down && la == up && crt->counter >= 0 )
{
crt->counter ++;
crt->nLen = up - down;
crt->nSeg = 1;
}
else
{
int mid = ( ( fi + la ) >> 1 );
TSegment* p;
if ( crt->counter > 0 )
{
p = crt->left;
p->counter = p->lCover = p->rCover = crt->counter;
p->nLen = mid - fi;
p->nSeg = 1;
p= crt->right;
p->counter = p->lCover = p->rCover = crt->counter;
p->nLen = la - mid;
p->nSeg = 1;
}
crt->counter = -1;
if ( up <= mid ) insert( crt->left, fi, mid, down, up );
else if ( down >= mid ) insert( crt->right, mid, la, down, up );
else
{
insert( crt->left, fi, mid, down, mid );
insert( crt->right, mid, la, mid, up );
}
crt->nLen = crt->left->nLen + crt->right->nLen;
crt->nSeg = crt->left->nSeg + crt->right->nSeg;
if ( crt->left->rCover && crt->right->lCover && crt->nSeg ) crt->nSeg --;
}
}

void erase( TSegment* crt, int fi, int la, int down, int up )
{
if ( fi == down ) crt->lCover --;
if ( la == up ) crt->rCover --;
if ( fi == down && la == up && crt->counter > 0 )
{
crt->counter --;
if ( crt->counter == 0 )
{
crt->nLen = 0;
crt->nSeg = 0;
}
}
else
{
int mid = ( ( fi + la ) >> 1 );
if ( up <= mid ) erase( crt->left, fi, mid, down, up );
else if ( down >= mid ) erase( crt->right, mid, la, down, up );
else
{
erase( crt->left, fi, mid, down, mid );
erase( crt->right, mid, la, mid, up );
}
crt->nLen = crt->left->nLen + crt->right->nLen;
crt->nSeg = crt->left->nSeg + crt->right->nSeg;
if ( crt->left->rCover && crt->right->lCover && crt->nSeg ) crt->nSeg --;
}
}

void work()
{
root = new TSegment();
build( root, miny, maxy ); //建立Y方向上的线段树
int i, size = vec.size();
int ans = 0;
int lastLength = 0, lastSeg = 0;
for ( i = 0; i < size; i ++ )
{
if ( vec[ i ].isLeft ) insert( root, miny, maxy, vec[ i ].down, vec[ i ].up );
else erase( root, miny, maxy, vec[ i ].down, vec[ i ].up );
ans += abs( root->nLen - lastLength );
lastLength = root->nLen;
if ( i ) ans += 2 * ( vec[ i ].pos - vec[ i - 1 ].pos ) * lastSeg;
lastSeg = root->nSeg;
}
printf( "%dn", ans );
}

int main()
{
read();
work();
return 0;
}