POJ 3264 Balanced Lineup

  
    

   
     /*
   
     
RMQ问题——稀疏表算法
状态转移方程
dp[i,j]=min{dp[i,j-1],dp[i+2j-1,j-1]}

   
     */
   
     
#include 
   
     <
   
     stdio.h
   
     >
   
     
#include 
   
     <
   
     math.h
   
     >
   
     
#include 
   
     <
   
     stdlib.h
   
     >
   
     

   
     const
   
      
   
     int
   
      MAXN 
   
     =
   
      
   
     50001
   
     ;

   
     int
   
      max[MAXN][
   
     16
   
     ],min[MAXN][
   
     16
   
     ]; 
   
     //
   
     2^16 = 65536
   
     

   
     int
   
      a[MAXN];

   
     int
   
      n, Q;
inline 
   
     int
   
      getMax(
   
     int
   
      a, 
   
     int
   
      b){
 
   
     return
   
      a 
   
     >
   
      b 
   
     ?
   
      a : b;
}
inline 
   
     int
   
      getMin(
   
     int
   
      a, 
   
     int
   
      b){
 
   
     return
   
      a 
   
     <
   
      b 
   
     ?
   
      a : b;
}

   
     void
   
      RMQ_init(){
 
   
     int
   
      i, j, m;
 
   
     for
   
     (i 
   
     =
   
      
   
     1
   
     ; i 
   
     <=
   
      n; i
   
     ++
   
     )
 max[i][
   
     0
   
     ] 
   
     =
   
      min[i][
   
     0
   
     ] 
   
     =
   
      a[i]; 
   
     //
   
     i ~ i*2^0 即a[i]
   
     

   
      m 
   
     =
   
      (
   
     int
   
     )(log((
   
     double
   
     )n)
   
     /
   
     log(
   
     2.0
   
     ));
 
   
     for
   
     (j 
   
     =
   
      
   
     1
   
     ; j 
   
     <=
   
      m; 
   
     ++
   
     j){ 
   
     //
   
     自底向上递推
   
     

   
      
   
     for
   
     (i 
   
     =
   
      n; i 
   
     >
   
      
   
     0
   
     ; i
   
     --
   
     ){
 max[i][j] 
   
     =
   
      getMax(max[i][j 
   
     -
   
      
   
     1
   
     ], max[i 
   
     +
   
      (
   
     1
   
      
   
     <<
   
      (j 
   
     -
   
      
   
     1
   
     ))][j 
   
     -
   
      
   
     1
   
     ]);
 min[i][j] 
   
     =
   
      getMin(min[i][j 
   
     -
   
      
   
     1
   
     ], min[i 
   
     +
   
      (
   
     1
   
      
   
     <<
   
      (j 
   
     -
   
      
   
     1
   
     ))][j 
   
     -
   
      
   
     1
   
     ]);
 }
 }
}

   
     int
   
      findMax(
   
     const
   
      
   
     int
   
      f,
   
     const
   
      
   
     int
   
      t){
 
   
     if
   
     ( f 
   
     ==
   
      t )
 
   
     return
   
      max[f][
   
     0
   
     ];
 
   
     int
   
      m 
   
     =
   
      (
   
     int
   
     )(log((
   
     double
   
     )(t 
   
     -
   
      f 
   
     +
   
      
   
     1
   
     ))
   
     /
   
     log(
   
     2.0
   
     ));
 
   
     return
   
      getMax(max[f][m], max[t 
   
     +
   
      
   
     1
   
      
   
     -
   
      (
   
     1
   
      
   
     <<
   
      (m))][m]);
}

   
     int
   
      findMin(
   
     const
   
      
   
     int
   
      f,
   
     const
   
      
   
     int
   
      t){
 
   
     if
   
     ( f 
   
     ==
   
      t )
 
   
     return
   
      min[f][
   
     0
   
     ];
 
   
     int
   
      m 
   
     =
   
      (
   
     int
   
     )(log((
   
     double
   
     )(t 
   
     -
   
      f 
   
     +
   
      
   
     1
   
     ))
   
     /
   
     log(
   
     2.0
   
     ));
 
   
     return
   
      getMin(min[f][m], min[t 
   
     +
   
      
   
     1
   
      
   
     -
   
      (
   
     1
   
      
   
     <<
   
      (m))][m]);
}

   
     int
   
      main(){
 
   
     int
   
      f, t;
 scanf(
   
     "
   
     %d%d
   
     "
   
     ,
   
     &
   
     n, 
   
     &
   
     Q);
 
   
     for
   
     (
   
     int
   
      i 
   
     =
   
      
   
     1
   
     ; i 
   
     <=
   
      n; 
   
     ++
   
     i)
 scanf(
   
     "
   
     %d
   
     "
   
     ,
   
     &
   
     a[i]);
 RMQ_init();
 
   
     for
   
     (
   
     int
   
      i 
   
     =
   
      
   
     0
   
     ; i 
   
     <
   
      Q; 
   
     ++
   
     i){
 scanf(
   
     "
   
     %d%d
   
     "
   
     , 
   
     &
   
     f, 
   
     &
   
     t);
 
   
     if
   
     (f 
   
     >
   
      t)
 f 
   
     ^=
   
      t 
   
     ^=
   
      f 
   
     ^=
   
      t;
 printf(
   
     "
   
     %d\n
   
     "
   
     , findMax(f, t) 
   
     -
   
      findMin(f, t)); 
 }
 
   
     return
   
      
   
     0
   
     ;
}