> For the complete documentation index, see [llms.txt](https://windmising.gitbook.io/introduction-to-algorithms/llms.txt). Markdown versions of documentation pages are available by appending `.md` to page URLs; this page is available as [Markdown](https://windmising.gitbook.io/introduction-to-algorithms/acm-jie-ti-bao-gao/2888.md).

# 2888 二维RMQ

HDU2888二维RMQ dp\[row]\[col]\[i]\[j] 表示\[row,row+2^i-1]x\[col,col+2^j-1] 二维区间内的最小值 这是RMQ-ST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轴不变,x轴二分 （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轴不变,y轴二分 (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] ) 查询\[x1,x2]x\[y1,y2] 令 kx = (int)log2(x2-x1+1); ky = (int)log2(y2-y1+1); 查询结果为 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]; 结果 = min(m1,m2,m3,m4)