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  • 计蒜客-自建物流的无人机实验

    题意

    (n)点带权树((v_i)),需要确定一个选点的方案,令(g_i=sumlimits_{x,y}[lca(x,y)=i]),使得(g_ige v_i)

    做法

    (s_1,s_2,...,s_k)(x)的子节点(令(x)也为(x)的子节点,但(x)的子树定义不变),(cnt_i)为以(i)为根的子树中选了多少个点,令(f_i)为当前(lca=i)的对数

    [egin{aligned} f_x&=frac{(cnt_x(cnt_x-1))}{2}-sumlimits_{i}frac{(cnt_{s_i})(cnt_{s_i}-1)}{2}\ &=frac{cnt_x^2-cnt_x-sumlimits_{i}cnt_{s_i}^2+sumlimits_{i}cnt_{s_i}}{2}\ &=frac{cnt_x^2-sumlimits_{i}cnt_{s_i}^2}{2}\ end{aligned}]

    也就是在(cnt_x)不变的情况下,(cnt_{s_i})越平均越优

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  • 原文地址:https://www.cnblogs.com/Grice/p/12828781.html
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