結果

問題 No.703 ゴミ拾い Easy
ユーザー vwxyz
提出日時 2023-01-03 17:45:25
言語 PyPy3
(7.3.15)
結果
AC  
実行時間 1,455 ms / 1,500 ms
コード長 12,201 bytes
コンパイル時間 366 ms
コンパイル使用メモリ 82,432 KB
実行使用メモリ 164,540 KB
最終ジャッジ日時 2024-11-27 02:19:57
合計ジャッジ時間 22,607 ms
ジャッジサーバーID
（参考情報） 		judge2 / judge3
このコードへのチャレンジ
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ファイルパターン 結果
sample AC * 4
other AC * 46
権限があれば一括ダウンロードができます

ソースコード

diff #
プレゼンテーションモードにする

import sys
readline=sys.stdin.readline
class AVL_Node_dict:
    """ノード
 
    Attributes:
        key (any): ノードのキー。比較可能なものであれば良い。(1, 4)などタプルも可。
        val (any): ノードの値。
        left (Node): 左の子ノード。
        right (Node): 右の子ノード。
        bias (int): 平衡度。(左部分木の高さ)-(右部分木の高さ)。
        size (int): 自分を根とする部分木の大きさ
 
    """
 
    def __init__(self,parent,key,value):
        self.parent=parent
        self.key=key
        self.value=value
        self.left=None
        self.right=None
        self.bias=0
        self.size=1
 
class AVLTree_dict:
    def __init__(self):
        self.root=None
    def Rotate_Left(self,node):
        node_right=node.right
        node_right.size=node.size
        node.size-=1
        if node_right.right!=None:
            node.size-=node_right.right.size
        if node_right.bias==-1:
            node_right.bias=0
            node.bias=0
        else:
            #assert node_right.bias==0
            node_right.bias=1
            node.bias=-1
        node.right=node_right.left
        node_right.left=node
        return node_right
    def Rotate_Right(self,node):
        node_left=node.left
        node_left.size=node.size
        node.size-=1
        if node_left.left!=None:
            node.size-=node_left.left.size
        if node_left.bias==1:
            node_left.bias=0
            node.bias=0
        else:
            #assert node_left.bias==0
            node_left.bias=-1
            node.bias=1
        node.left=node_left.right
        node_left.right=node
        return node_left
    def Rotate_Left_Right(self,node):
        node_left=node.left
        node_left_right=node_left.right
        #assert node.bias==2
        #assert node_left.bias==-1
        #assert node_left_right.bias in (-1,0,1)
        node_left_right.size=node.size
        node.size-=node_left.size
        if node_left_right.right!=None:
            node.size+=node_left_right.right.size
        node_left.size-=1
        if node_left_right.right!=None:
            node_left.size-=node_left_right.right.size
        node_left.right=node_left_right.left
        node_left_right.left=node_left
        node.left=node_left_right.right
        node_left_right.right=node
        self.Update_Bias_Double(node_left_right)
        return node_left_right
    def Rotate_Right_Left(self,node):
        node_right=node.right
        node_right_left=node_right.left
        #assert node.bias==-2
        #assert node_right.bias==1
        #assert node_right_left.bias in (-1,0,1)
        node_right_left.size=node.size
        node.size-=node_right.size
        if node_right_left.left!=None:
            node.size+=node_right_left.left.size
        node_right.size-=1
        if node_right_left.left!=None:
            node_right.size-=node_right_left.left.size
        node_right.left=node_right_left.right
        node_right_left.right=node_right
        node.right=node_right_left.left
        node_right_left.left=node
        self.Update_Bias_Double(node_right_left)
        return node_right_left
    def Update_Bias_Double(self,node):
        #assert node.right.bias*node.left.bias==-2
        #assert node.right.bias>0
        if node.bias==1:
            node.right.bias=-1
            node.left.bias=0
        elif node.bias==-1:
            node.right.bias=0
            node.left.bias=1
        else:
            node.right.bias=0
            node.left.bias=0
        node.bias=0
    def __getitem__(self,key):
        v=self.root
        while v!=None:
            if key<v.key:
                v=v.left
            elif v.key<key:
                v=v.right
            else:
                return v.value
        return None
    def __setitem__(self,key,value):
        if self.root==None:
            self.root=AVL_Node_dict(None,key,value)
            return
        v=self.root
        stack=[]
        while v!=None:
            if key<v.key:
                stack.append((v,1))
                v=v.left
            elif v.key<key:
                stack.append((v,-1))
                v=v.right
            elif v.key==key:
                v.value=value
                return
        p,direction=stack[-1]
        if direction==1:
            p.left=AVL_Node_dict(p,key,value)
        else:
            p.right=AVL_Node_dict(p,key,value)
        while stack:
            v,direction=stack.pop()
            v.bias+=direction
            v.size+=1
            vv=None
            if v.bias==2:
                if v.left.bias==-1:
                    vv=self.Rotate_Left_Right(v)
                else:
                    vv=self.Rotate_Right(v)
                #assert vv!=None
                break
            if v.bias==-2:
                if v.right.bias==1:
                    vv=self.Rotate_Right_Left(v)
                else:
                    vv=self.Rotate_Left(v)
                #assert vv!=None
                break
            if v.bias==0:
                break
        if vv!=None:
            if len(stack)==0:
                self.root=vv
                return
            p,direction=stack.pop()
            p.size+=1
            if direction==1:
                p.left=vv
            else:
                p.right=vv
        while stack:
            p,direction=stack.pop()
            p.size+=1
    def __delitem__(self,key):
        v=self.root
        stack=[]
        while v!=None:
            if key<v.key:
                stack.append((v,1))
                v=v.left
            elif v.key<key:
                stack.append((v,-1))
                v=v.right
            else:
                break
        else:
            return False
        if v.left!=None:
            stack.append((v,1))
            lmax=v.left
            while lmax.right!=None:
                stack.append((lmax,-1))
                lmax=lmax.right
            v.key=lmax.key
            v.value=lmax.value
            v=lmax
        c=v.right if v.left==None else v.left
        if stack:
            p,direction=stack[-1]
            if direction==1:
                p.left=c
            else:
                p.right=c
        else:
            self.root=c
            return True
        while stack:
            pp=None
            p,direction=stack.pop()
            p.bias-=direction
            p.size-=1
            if p.bias==2:
                if p.left.bias==-1:
                    pp=self.Rotate_Left_Right(p)
                else:
                    pp=self.Rotate_Right(p)
            elif p.bias==-2:
                if p.right.bias==1:
                    pp=self.Rotate_Right_Left(p)
                else:
                    pp=self.Rotate_Left(p)
            elif p.bias!=0:
                break
            if pp!=None:
                if len(stack)==0:
                    self.root=pp
                    return True
                p,direction=stack[-1]
                if direction==1:
                    p.left=pp
                else:
                    p.right=pp
                if pp.bias!=0:
                    break
        while stack:
            p,direction=stack.pop()
            p.size-=1
        return True
    def __contain__(self,key):
        v=self.root
        while v!=None:
            if key<v.key:
                v=v.left
            elif v.key<key:
                v=v.right
            else:
                return True
        return False
    def Bisect_Right(self,key):
        retu=None
        v=self.root
        while v!=None:
            if v.key>key:
                if retu==None or retu[0]>v.key:
                    retu=(v.key,v.value)
                v=v.left
            else:
                v=v.right
        return retu
    def Bisect_Left(self,key):
        retu=None
        v=self.root
        while v!=None:
            if v.key<key:
                if retu==None or retu[0]<v.key:
                    retu=(v.key,v.value)
                v=v.right
            else:
                v=v.left
        return retu
    def Find_Kth_Element(self,K):
        v=self.root
        s=0
        while v!=None:
            t=s+v.left.size if v.left!=None else s
            if t==K:
                return v.key,v.value
            elif t<K:
                s=t+1
                v=v.right
            else:
                v=v.left
        return None
    def keys(self):
        stack=[(self.root,True)]
        while stack:
            node,subtree=stack.pop()
            if subtree:
                if node.right!=None:
                    stack.append((node.right,True))
                stack.append((node,False))
                if node.left!=None:
                    stack.append((node.left,True))
            else:
                yield node.key
    def values(self):
        stack=[(self.root,True)]
        while stack:
            node,subtree=stack.pop()
            if subtree:
                if node.right!=None:
                    stack.append((node.right,True))
                stack.append((node,False))
                if node.left!=None:
                    stack.append((node.left,True))
            else:
                yield node.value
    def items(self):
        stack=[(self.root,True)]
        while stack:
            node,subtree=stack.pop()
            if subtree:
                if node.right!=None:
                    stack.append((node.right,True))
                stack.append((node,False))
                if node.left!=None:
                    stack.append((node.left,True))
            else:
                yield (node.key,node.value)
    def __bool__(self):
        return self.root!=None
    def __len__(self):
        return 0 if self.root==None else self.root.size
    def __iter__(self):
        return iter(self.keys())
    def __str__(self):
        if self.root==None:
            retu="{}"
        else:
            retu="{"+", ".join(f"{r}: {m}" for r,m in self.items())+"}"
        return retu
class Convex_Hull_Trick:
    def __init__(self):
      self.lines=AVLTree_dict()
    def is_removed(self,line0,line1,line2):
        if line0==None:
            return False
        if line2==None:
            return False
        a0,b0=line0
        a1,b1=line1
        a2,b2=line2
        return (a1-a0)*(b2-b1)<=(b1-b0)*(a2-a1)
    def add_line(self,a,b):
        bb=self.lines[a]
        if bb!=None and bb<=b:
            return
        line0=self.lines.Bisect_Left(a)
        line1=(a,b)
        line2=self.lines.Bisect_Right(a)
        if self.is_removed(line0,line1,line2):
            return
        
        self.lines[a]=b
        line2=(a,b)
        line1=self.lines.Bisect_Left(line2[0])
        line0=None if line1==None else self.lines.Bisect_Left(line1[0])
        while self.is_removed(line0,line1,line2):
            del self.lines[line1[0]]
            line1=line0
            line0=None if line1==None else self.lines.Bisect_Left(line1[0])
        
        line0=(a,b)
        line1=self.lines.Bisect_Right(line0[0])
        line2=None if line1==None else self.lines.Bisect_Right(line1[0])
        while self.is_removed(line0,line1,line2):
            del self.lines[line1[0]]
            line1=line2
            line2=None if line1==None else self.lines.Bisect_Right(line1[0])
        
    def __call__(self,x):
        size=len(self.lines)
        if not size:
            return None
        ok,ng=-1,size-1
        while ng-ok>1:
            mid=(ok+ng)//2
            a0,b0=self.lines.Find_Kth_Element(mid)
            a1,b1=self.lines.Find_Kth_Element(mid+1)
            if a0*x+b0>a1*x+b1:
                ok=mid
            else:
                ng=mid
        a,b=self.lines.Find_Kth_Element(ok+1)
        return a*x+b
    def __getitem__(self,a):
        return self.lines[a]
    
    def __setitem__(self,a,b):
        self.add_line(a,b)
N=int(readline())
A=list(map(int,readline().split()))
X=list(map(int,readline().split()))
Y=list(map(int,readline().split()))
dp=Convex_Hull_Trick()
cost=0
for i in range(N):
    dp.add_line(-2*X[i],cost+X[i]**2+Y[i]**2)
    cost=dp(A[i])+A[i]**2
ans=cost
print(ans)
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