HDU2888二維RMQ

 

HDU2888二維RMQ
dp[row][col][i][j] 表示[row,row+2^i-1]x[col,col+2^j-1] 二維區間內的最小值
這是RMQ-ST演算法的核心: 倍增思想
== min( [row,row+ 2^(i-1)-1]x[col,col+2^j-1], [row+2^(i-1),row+2^i-1]x[col,col+2^j-1] )
= min(dp[row][col][i-1][j], dp[row+(1<<(i-1))][col][i-1][j] )
//y軸不變,x軸二分　（i!=0)
或
== min( [row,row+2^i-1]x[col,col+2^(j-1)-1],  [row,row+2^i-1]x[col+2^(i-1),col+2^j-1] )
= min(dp[row][col][i][j-1], dp[row][col+(1<<(j-1))][i][j-1] ) 
//x軸不變,y軸二分　(j!=0)
即:
dp[row][col][i][j] = min(dp[row][col][i-1][j], dp[row + (1<<(i-1))][col][i-1][j] )   
             或    = min(dp[row][col][i][j-1], dp[row][col+(1<<(j-1))][i][j-1] )
查詢[x1,x2]x[y1,y2]
令 kx = (int)log2(x2-x1+1);
   ky = (int)log2(y2-y1+1);
查詢結果為
   m1 = dp[x1][y1][kx][ky]                    = dp[x1][y1][kx][ky];
   m2 = dp[x2-2^kx+1][y1][kx]ky]              = dp[x2-(1<<kx)+1][y1][kx][ky];
   m3 = dp[x1][y2-2^ky+1][kx][ky]             = dp[x1][y2-(1<<ky)+1][kx][ky];
   m4 = dp[x2-2^kx+1][y2-2^ky+1][kx][ky]      = dp[x2-(1<<kx)+1][y2-(1<<ky)+1][kx][ky];

結果 = min(m1,m2,m3,m4)

#include<iostream>#include<cmath>using namespace std;const int maxn = 301;int val[maxn][maxn];int M,N;//RMQ 2Dint dp[maxn][maxn][9][9];void RMQ_2D_PRE(){for(int row = 1; row <= N; row++)for(int col = 1; col <=M; col++)dp[row][col][0][0] = val[row][col];    int mx = log(double(N)) / log(2.0);    int my = log(double(M)) / log(2.0);    for(int i=0; i<= mx; i++){        for(int j = 0; j<=my; j++)        {if(i == 0 && j ==0) continue;            for(int row = 1; row+(1<<i)-1 <= N; row++){for(int col = 1; col+(1<<j)-1 <= M; col++){if(i == 0)//y軸二分dp[row][col][i][j]=max(dp[row][col][i][j-1],dp[row][col+(1<<(j-1))][i][j-1]);  else//x軸二分dp[row][col][i][j]=max(dp[row][col][i-1][j],dp[row+(1<<(i-1))][col][i-1][j]);  }            }}}}int RMQ_2D(int x1,int x2,int y1,int y2){int kx = log(double(x2-x1+1)) / log(2.0);    int ky = log(double(y2-y1+1)) / log(2.0);int m1 = dp[x1][y1][kx][ky];int m2 = dp[x2-(1<<kx)+1][y1][kx][ky];int m3 = dp[x1][y2-(1<<ky)+1][kx][ky];int m4 = dp[x2-(1<<kx)+1][y2-(1<<ky)+1][kx][ky];    return max( max(m1,m2) , max(m3,m4));}//ENDint  main(){int Q,x1,y1,x2,y2,i,j;while(scanf("%d%d",&N,&M)!=EOF){for(i = 1; i <= N; i++)for(j = 1; j <= M; j++)scanf("%d",&val[i][j]);        RMQ_2D_PRE();scanf("%d",&Q);while(Q--){scanf("%d%d%d%d",&x1,&y1,&x2,&y2);int ans = RMQ_2D(x1,x2,y1,y2);printf("%d",ans);if(ans == val[x1][y1] || ans == val[x2][y1] || ans == val[x1][y2] || ans == val[x2][y2])printf(" yes\n");else printf(" no\n");}}    return 0;}