HDU 6447 Yjj ' s salesman (tree-like array + DP + discrete)

Test Instructions:

N points on two-dimensional plane, from (0,0) to (1E9,1E9), each time can only go to the right, upper, upper right three direction of movement,
The n points are available only from the lower-left grid point, at which time the proceeds can be obtained. Maximize the benefits of the process.

Analysis: We can easily think of using DP, assuming this position is relative to the direction of the previous position, but the complexity of reaching n^2, this is not possible;

We can use the information of the coordinates, after all the points are discretized, in x priority by small to large sort, press Y to a small order, then maintain a DP (i), the maximum value of column I.

J=0→i? 1 J=0→i?1
DP[I]←m ax (d P[i [, Dp[ j] +va l) Dp[i]←max (dp[i[,dp[j]+val)

because X has been ordered from small to large, Y is also from the big to the small update, so to ensure the accessibility.

for each update, the maximum value can be maintained with a segment tree or a tree array, when the algorithm complexity o(nlogn)

#include <bits/stdc++.h>using namespacestd;intn,hashx[100001],hashy[100001],dp[100001],tree[100001];structno{intX,y,w;} a[100001];BOOLCMP (no A, no b) {if(a.x==b.x)returnA.y>b.y; returna.x<b.x; }//discretization ofvoidinit () { for(intI=1; I<=n; i++) {Hashx[i]=a[i].x; Hashy[i]=a[i].y; } sort (Hashx+1, hashx+1+N); Sort (hashy+1, hashy+1+N); intCntx = Unique (hashx+1, hashx+1+n)-hashx; intCnty = Unique (hashy+1, hashy+1+n)-hashy;  for(intI=1; I<=n; i++) {a[i].x= Lower_bound (hashx+1, hashx+1+cntx,a[i].x)-hashx; A[i].y= Lower_bound (hashy+1, hashy+1+CNTY,A[I].Y)-hashy; }}intLowbit (intx) {    returnx& (-x);}voidUpdateintPOS) {     while(Pos <=N) {Tree[pos]=Dp[pos];  for(intI=1; I<lowbit (POS); i<<=1) Tree[pos]= Max (tree[pos],tree[pos-i]); POS+=Lowbit (POS); }}intQueryintLintR) {    intAns =0;  while(r>=l) {ans=Max (Ans,dp[r]); if(L==R) Break;  for(--r;r-l>=lowbit (R); r-=Lowbit (R)) Ans=Max (Ans,tree[r]); }    returnans;}intMain () {intT; scanf ("%d",&t);  while(t--) {scanf ("%d",&N);  for(intI=1; I<=n; i++) {scanf ("%d%d%d",&a[i].x,&a[i].y,&A[I].W); } sort (A+1, A +1+n,cmp);        Init (); Memset (DP,0,sizeof(DP)); memset (Tree,0,sizeof(tree));  for(intI=1; I<=n; i++) {DP[A[I].Y]=max (Dp[a[i].y],query (1, a[i].y-1)+A[I].W);                   Update (A[I].Y); }        intAns =0;  for(intI=1; i<=n;++i) ans=Max (ans,dp[i]); printf ("%d\n", ans); }    return 0;}

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HDU 6447 Yjj ' s salesman (tree-like array + DP + discrete)