POJ 3460 Booksort

题目链接：http://poj.org/problem?id=3460

题意：有一些高度不等的书，可以一次取出一摞相对顺序不变的书插入任意位置，问最少多少次操作才能使书的高度递增有序。

IDA*，刘汝佳黑书P169的例题，经典题目，启发函数的设计十分巧妙。

以“h(s)=后继书本高度正确的书本个数”为估价函数，假设每次把一摞书本S从P1后面移动到P2后面，只有P1，S1的最后一本，P2三本书的后继有变化，h每次最多减少3，令h'=h(s)/3作为估价函数值，则每次h最多减少1。

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

const int MAXN = 20;

int N, limit;
int book[MAXN];
bool find;

int min( int a, int b )
{
    return a < b ? a : b;
}

int h( int *a )
{
    int cnt = 0;
    if ( a[0] != 1 ) ++cnt;
    if ( a[N - 1] != N ) ++cnt;
    for ( int i = 1; i < N - 1; ++i )
            if ( a[i] + 1 != a[i + 1] ) ++cnt;
    return ceil( cnt / 3.0 );
}

void chuli( int st, int mid, int ed )
{
    int temp[MAXN];
    for ( int i = mid + 1; i <= ed; ++i )
        temp[i] = book[i];
    for ( int i = mid, j = ed; i >= st; --i, --j )
        book[j] = book[i];
    for ( int i = st, j = mid + 1; j <= ed; ++i, ++j )
        book[i] = temp[j];
    return;
}

int DFS( int dv )
{
    int temp[MAXN];
    int hv = h( book );
    if ( hv + dv > limit ) return hv + dv;
    if ( hv == 0 )
    {
        find = true;
        return dv;
    }

    int next_limit = 1e5;

    for ( int i = 0; i < N - 1; ++i )
    for ( int j = i + 1; j < N; ++j )
    for ( int k = i; k < j; ++k )
    {
        for ( int x = 0; x < N; ++x )
            temp[x] = book[x];

        chuli( i, k, j );

        int new_limit = DFS( dv + 1 );

        if ( find ) return new_limit;

        next_limit = min( next_limit, new_limit );
        for ( int x = 0; x < N; ++x )
            book[x] = temp[x];
    }

    return next_limit;
}

void IDA_Star()
{
    find = false;
    limit = h( book );
    while ( !find && limit < 5 )
        limit = DFS( 0 );
    return;
}

int main()
{
    int T;
    scanf( "%d", &T );
    while ( T-- )
    {
        scanf( "%d", &N );
        for ( int i = 0; i < N; ++i )
            scanf( "%d", &book[i] );

        IDA_Star();
        if ( find ) printf( "%d\n", limit );
        else puts("5 or more");
    }
    return 0;
}