bzoj.4753. [JSOI2016] Best Group (01 score Plan Tree Backpack DP)

Topic links

\ (description\)

Each point has a cost Si and value pi, which requires selecting some connected blocks with a root, the total size is k, making \ (\frac{∑pi}{∑si}\) the largest

\ (solution\)

01 Fractional plan, then DP, set F[I][J] indicates the maximum weight of the I subtree selected J and, direct violent backpack transfer can be
When enumerating the number of child nodes selected, assume X has 1.2.3.4 four child nodes with a complexity of \ (1*sz[1]+sz[1]*sz[2]+ (sz[1]+sz[2)) *sz[3]+ (sz[1]+sz[2]+sz[3]) *sz[4]\)
Equivalent to each pair of points in the LCA contribution, there will be a total of n^2 LCA, so this part of the complexity of O (n^2)
Total O (n^2*log ans)
Note: The initial value should not be 0 because there will be a large negative number. For example, must stipulate f[0][1] for-inf
Why EPS needs 1e-5. Is <1e-4 over? (perhaps because this is not an exact answer?) card when Dafa is good )

//50024 KB 3512 ms so slow. #include <cstdio>#include <cctype>#include <cstring>#include <algorithm>#define GC () GetChar ()Const intn=2505;Const Doubleeps=1e-5, inf=1e10;intN,m,enum,h[n],nxt[n],to[n],sz[n];DoubleCost[n],p[n],val[n],f[n][n];inline intRead () {intnow=0;Register CharC=GC (); for(;! IsDigit (c); C=GC ()); for(; IsDigit (c); now=now*Ten+c-' 0 ', C=GC ());returnNow;}inline voidAddedge (intUintV) {to[++enum]=v, nxt[enum]=h[u], h[u]=enum;}voidDFS (intx) {intMn= (x>0); SZ[X]=MN; for(intI=2; i<=m;    ++i) F[x][i]=-inf; f[x][1]=VAL[X]; for(intV,I=H[X]; I I=nxt[i]) {DFS (v=to[i]); for(intJ=SZ[X]; j>=mn; --J)//reverse//update upper limit is the sum of SZ and sub-node sz             for(intk=1; k<=sz[v];        ++k) F[x][j+k]=std::max (F[x][j+k],f[x][j]+f[v][k]);    SZ[X]+=SZ[V]; }}DoubleSolve (Doublex) { for(intI=1; i<=n; ++i) Val[i]=p[i]-x*cost[i];//memset (f,0xc2,sizeof f), F[0][0]=0;//too slowDFS (0);returnf[0][m]>=0;}intMain () {M=read (), N=read (); for(intI=1; i<=n; ++i) Cost[i]=read (), P[i]=read (), Addedge (read (), i);DoubleL=0.0, r=1e4, Mid; val[0]=-inf;//f[0][1]     while(r-l>eps) {if(Solve (mid= (l+r)/2.0)) L=mid;ElseR=mid; } printf ("%.3LF", mid);return 0;}

bzoj.4753. [JSOI2016] Best Group (01 score Plan Tree Backpack DP)