关于右端点的证明(违规紫衫)
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关于右端点的证明(违规紫衫)
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a16_楼主2024/11/20 17:04

感觉题解证的有些冗长

对于 i\forall i 满足 ni=nL\lfloor \frac{n} {i}\rfloor=\lfloor\frac{n}{L}\rfloor R=nnL=nninni=iR=\lfloor\frac{n}{\lfloor \frac{n} {L}\rfloor}\rfloor=\lfloor\frac{n}{\lfloor \frac{n} {i}\rfloor} \rfloor\geq \lfloor\frac{n}{ \frac{n} {i}}\rfloor=i

对于 i\forall i' 满足 ni=nL1\lfloor \frac{n} {i'}\rfloor=\lfloor\frac{n}{L}\rfloor-1 R=nnL=nni+1<nni=iR=\lfloor\frac{n}{\lfloor \frac{n} {L}\rfloor}\rfloor=\lfloor\frac{n}{\lfloor \frac{n} {i'}\rfloor+1} \rfloor < \lfloor\frac{n}{ \frac{n} {i'}}\rfloor=i'

即证 R=nnLR=\lfloor\frac{n}{\lfloor \frac{n} {L}\rfloor}\rfloor 是这个块的右端点

2024/11/20 17:04
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