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QOJ
ID | 题目 | 提交者 | 结果 | 用时 | 内存 | 语言 | 文件大小 | 提交时间 | 测评时间 |
---|---|---|---|---|---|---|---|---|---|
#555904 | #5981. Costly Binary Search | yz_ly | 27 ✓ | 11581ms | 86796kb | C++14 | 1.9kb | 2024-09-10 12:01:25 | 2024-09-10 12:01:26 |
Judging History
answer
#include<bits/stdc++.h>
using namespace std;
inline int read(){
int f=1,x=0;
char ch=getchar();
while(ch<'0'||ch>'9'){
if(ch=='-')
f=-f;
ch=getchar();
}
while(ch>='0'&&ch<='9'){
x=x*10+ch-'0';
ch=getchar();
}
return f*x;
}
inline void work(int k){
if(k<0){
putchar('-');
k=-k;
}
if(k>9)
work(k/10);
putchar(k%10+'0');
}
/*
首先有暴力dp
定义dp[l][r]表示在[l,r]的最坏情况最小代价
dp[l][r]=min(c[k]+max(dp[l][k-1],dp[k+1][r]))
因为c[i]<=9,所以dp中的值最多就是clogn的,并且观察式子对于同一个l,当l<=r<=r'的时候dp[l][r]<=dp[l][r'],因为不同区间是取max
对于这种值域很小并且dp值有单调性就可以通过维护每个值域的端点值来维护状态
定义L[c][i]表示右端点为i是,最小的l使得dp[l][i]<=c,R[c][i]同理,维护最大的r
每次转移枚举端点,x=L[c-a[k]][k-1],y=R[c-a[k]][k+1]
L[c][y]=min(x),R[c][x]=max(y)
因为dp值的单调性,再做一个前/后缀,min/max就行了,dp[l][r]<=dp[l][r']->L[v][r]<=L[v][r'],L同理
滚动数组
*/
int t,val[1000005],L[10][1000005],R[10][1000005];
char s[1000005];
int solve(){
int n=strlen(s+1);
for(int i=1;i<=n;i++){
val[i]=s[i]-'0';
}
for(int v=0;;v++){
for(int i=0;i<=n+1;i++){
L[v%10][i]=i+1;
R[v%10][i]=i-1;
}
for(int i=1;i<=n;i++){
if(val[i]<=v){
int l=L[(v-val[i])%10][i-1],r=R[(v-val[i])%10][i+1];
L[v%10][r]=min(L[v%10][r],l);
R[v%10][l]=max(R[v%10][l],r);
}
}
for(int i=2;i<=n;i++){
R[v%10][i]=max(R[v%10][i],R[v%10][i-1]);/*dp[l][r]<=dp[l'][r],l'<=l<=r*/
}
for(int i=n-1;i;i--){
L[v%10][i]=min(L[v%10][i],L[v%10][i+1]);/*dp[l][r]<=dp[l][r'],l<=r<=r'*/
}
if(R[v%10][1]>=n)
return v;
}
}
int main(){
t=read();
for(int i=1;i<=t;i++){
scanf("%s",s+1);
printf("Case #%d: %d\n",i,solve());
}
return 0;
}
详细
Subtask #1:
score: 8
Accepted
Test #1:
score: 8
Accepted
time: 79ms
memory: 47012kb
input:
50 8 5128831164925953487661279378526736416489768154389124821528467927357884749642747626797857463132866343496157991453139582295398452863172464853698678624523849653538713928372648295734165346972222781179687541337591976277864785653638476127839556323849395641196246971351933655287441377531627938395427487...
output:
Case #1: 8 Case #2: 37 Case #3: 34 Case #4: 37 Case #5: 34 Case #6: 114 Case #7: 126 Case #8: 24 Case #9: 37 Case #10: 103 Case #11: 36 Case #12: 64 Case #13: 37 Case #14: 117 Case #15: 37 Case #16: 35 Case #17: 14 Case #18: 34 Case #19: 36 Case #20: 37 Case #21: 38 Case #22: 39 Case #23: 14 Case #2...
result:
ok 50 lines
Subtask #2:
score: 19
Accepted
Test #2:
score: 19
Accepted
time: 11581ms
memory: 86796kb
input:
50 647322722753778843259213887674615134214258235986992692879314555957455541351526284343217116351733247781713552149464672262787737941588358671583528664757823365936975517145283412965139791726299864122725212222496898855627124979178341548651669956711341742838725446489235961853391195148929571712449139335...
output:
Case #1: 42 Case #2: 43 Case #3: 120 Case #4: 42 Case #5: 43 Case #6: 43 Case #7: 31 Case #8: 43 Case #9: 171 Case #10: 42 Case #11: 39 Case #12: 42 Case #13: 42 Case #14: 44 Case #15: 39 Case #16: 20 Case #17: 180 Case #18: 30 Case #19: 45 Case #20: 43 Case #21: 44 Case #22: 31 Case #23: 83 Case #2...
result:
ok 50 lines
Extra Test:
score: 0
Extra Test Passed