QOJ.ac
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 |
---|---|---|---|---|---|---|---|---|---|
#563740 | #7954. Special Numbers | sentheta# | AC ✓ | 7ms | 310840kb | C++20 | 3.4kb | 2024-09-14 15:35:53 | 2024-09-14 15:35:53 |
Judging History
answer
#include<bits/stdc++.h>
using namespace std;
#define rep(i,a,b) for(int i=(int)a; i<(int)b; i++)
#define Int long long
#define int long long
#define V vector
void solve();
signed main(){
solve();
}
const int MOD = 1e9+7;
int k;
int two, tri, fiv, svn;
V<int> fac;
int dp[22][68][43][30][25];
// #nonzero integer with nonzero digit product divisible by k
int f(string s){
bool allZero = 1;
for(char ch : s) allZero &= ch=='0';
if(allZero) return 0;
rep(i,0,s.size())
rep(a,0,two+1) rep(b,0,tri+1) rep(c,0,fiv+1) rep(d,0,svn+1)
dp[i][a][b][c][d] = 0;
int sa=0, sb=0, sc=0, sd=0, zro=0;
for(int i=0; i<s.size(); i++){
// cerr << "i " << i << endl;
int x = s[i]-'0';
// prv(nonzero) + y
// cerr << "prv + y" << endl;
if(i>0) for(int y=1; y<=9; y++){
rep(a,0,two+1) rep(b,0,tri+1) rep(c,0,fiv+1) rep(d,0,svn+1)
(dp[i]
[min(two,a+(y%2==0)+(y%4==0)+(y%8==0))]
[min(tri,b+(y%3==0)+(y%9==0))]
[min(fiv,c+(y%5==0))]
[min(svn,d+(y%7==0))]
+= dp[i-1][a][b][c][d] )%=MOD;
}
// pref(s) + y
// cerr << "prefix + y" << endl;
if(!zro) for(int y=1; y<x; y++){
dp[i]
[min(two,sa+(y%2==0)+(y%4==0)+(y%8==0))]
[min(tri,sb+(y%3==0)+(y%9==0))]
[min(fiv,sc+(y%5==0))]
[min(svn,sd+(y%7==0))]
+= 1;
}
zro |= x==0;
sa += (x%2==0) + (x%4==0) + (x%8==0);
sb += (x%3==0) + (x%9==0);
sc += (x%5==0);
sd += (x%7==0);
// zeroes + y
// cerr << "zeroes + y" << endl;
if(i>0) for(int y=1; y<=9; y++){
dp[i]
[min(two,(int)(y%2==0)+(y%4==0)+(y%8==0))]
[min(tri,(int)(y%3==0)+(y%9==0))]
[min(fiv,(int)(y%5==0))]
[min(svn,(int)(y%7==0))]
++;
}
}
// check s itself
// cerr << "dp[last][last]... " << dp[s.size()-1][two][tri][fiv][svn] << '\n';
int ret = dp[s.size()-1][two][tri][fiv][svn] + (!zro)*(sa>=two)*(sb>=tri)*(sc>=fiv)*(sd>=svn);
return ret;
}
int dpg[22][2];
// #nonzero integer with zero digit product
int g(string s){
bool allZero = 1;
for(char ch : s) allZero &= ch=='0';
if(allZero) return 0;
rep(i,0,s.size())
dpg[i][0] = dpg[i][1] = 0;
int prod = 1;
for(int i=0; i<s.size(); i++){
int x = s[i]-'0';
// cerr << "x: " << x << endl;
// prv(nonzero) + y
if(i>0) for(int y=0; y<=9; y++){
(dpg[i][0] += dpg[i-1][0] )%=MOD;
(dpg[i][(bool)(y)] += dpg[i-1][1] )%=MOD;
}
// pref(s) + y
for(int y=(i==0?1:0); y<x; y++){
dpg[i][prod&(bool)y]++;
}
prod &= (bool)x;
// zeroes + y
if(i>0) for(int y=1; y<=9; y++){
dpg[i][1]++;
}
}
// cerr << "g: dpg[last][0]: " << dpg[s.size()-1][0] << endl;
// cerr << "prod " << prod << endl;
int ret = dpg[s.size()-1][0] + (prod==0);
return ret;
}
void solve(){
string l, r;
cin >> k >> l >> r;
// substract 1 from l
l.back()--;
for(int i=l.size()-1; i>=0 && l[i]=='0'-1; i--){
l[i] += 10;
l[i-1]--;
}
while(l[0]=='0'){
l = l.substr(1);
}
// cerr << l << " " << r << endl;
// factorize k
while(k%2==0){
k/=2; two++;
}
while(k%3==0){
k/=3; tri++;
}
while(k%5==0){
k/=5; fiv++;
}
while(k%7==0){
k/=7; svn++;
}
// cerr << k << endl;
int ans = 0;
if(k==1){
// nonzero product
(ans += f(r) )%=MOD;
(ans -= f(l) )%=MOD;
}
// cerr << "f: " << ans << '\n';
// zero product
(ans += g(r) )%=MOD;
(ans -= g(l) )%=MOD;
// cerr << "f+g: " << ans << '\n';
ans = (ans%MOD+MOD)%MOD;
cout << ans << '\n';
}
详细
Test #1:
score: 100
Accepted
time: 1ms
memory: 5676kb
input:
5 1 20
output:
4
result:
ok single line: '4'
Test #2:
score: 0
Accepted
time: 1ms
memory: 7668kb
input:
5 50 100
output:
19
result:
ok single line: '19'
Test #3:
score: 0
Accepted
time: 1ms
memory: 5908kb
input:
15 11 19
output:
0
result:
ok single line: '0'
Test #4:
score: 0
Accepted
time: 0ms
memory: 14100kb
input:
1 100 100000
output:
99901
result:
ok single line: '99901'
Test #5:
score: 0
Accepted
time: 0ms
memory: 3568kb
input:
1 1 1
output:
1
result:
ok single line: '1'
Test #6:
score: 0
Accepted
time: 0ms
memory: 13880kb
input:
10 800 43021
output:
23570
result:
ok single line: '23570'
Test #7:
score: 0
Accepted
time: 3ms
memory: 310840kb
input:
1125899906842624 1 100000000000000000000
output:
555058180
result:
ok single line: '555058180'
Test #8:
score: 0
Accepted
time: 0ms
memory: 67048kb
input:
187500000 5941554024261918062 17356601866920567143
output:
679191360
result:
ok single line: '679191360'
Test #9:
score: 0
Accepted
time: 0ms
memory: 56884kb
input:
1555848 157165614890794026 49792374427566422833
output:
588832126
result:
ok single line: '588832126'
Test #10:
score: 0
Accepted
time: 3ms
memory: 77460kb
input:
53814924637488000 8378901287491856069 46225409092942057365
output:
964965504
result:
ok single line: '964965504'
Test #11:
score: 0
Accepted
time: 4ms
memory: 79460kb
input:
11814720750000000 8152927138245188051 35351923956338524619
output:
183963359
result:
ok single line: '183963359'
Test #12:
score: 0
Accepted
time: 3ms
memory: 108136kb
input:
6453888000000 4334845344448208535 35982793193772682339
output:
570114022
result:
ok single line: '570114022'
Test #13:
score: 0
Accepted
time: 0ms
memory: 61220kb
input:
90071357282285400 7893548167754114409 27099084703937108974
output:
869822186
result:
ok single line: '869822186'
Test #14:
score: 0
Accepted
time: 0ms
memory: 65196kb
input:
45571065750000 177160749596350425 98884377930460959454
output:
607698665
result:
ok single line: '607698665'
Test #15:
score: 0
Accepted
time: 0ms
memory: 147204kb
input:
1128443962982400 6338876482181492537 40931938533793596007
output:
881168270
result:
ok single line: '881168270'
Test #16:
score: 0
Accepted
time: 0ms
memory: 3624kb
input:
1 1 1
output:
1
result:
ok single line: '1'
Test #17:
score: 0
Accepted
time: 0ms
memory: 48816kb
input:
1412793457031250 2410155470167050095 99063185266833009818
output:
399813226
result:
ok single line: '399813226'
Test #18:
score: 0
Accepted
time: 4ms
memory: 132684kb
input:
67722117120000 8909573534349989418 73129289758235281558
output:
898227227
result:
ok single line: '898227227'
Test #19:
score: 0
Accepted
time: 3ms
memory: 138800kb
input:
472055808000 6809917603531307093 27494416416722163137
output:
379198478
result:
ok single line: '379198478'
Test #20:
score: 0
Accepted
time: 4ms
memory: 116404kb
input:
19353600000 8687492345912514346 24058039408337150852
output:
250715555
result:
ok single line: '250715555'
Test #21:
score: 0
Accepted
time: 0ms
memory: 65372kb
input:
47855420020225440 6150828649270625443 84863934988301168136
output:
665186711
result:
ok single line: '665186711'
Test #22:
score: 0
Accepted
time: 0ms
memory: 112308kb
input:
1382400000 9545797804645162278 70441077437727026904
output:
278230087
result:
ok single line: '278230087'
Test #23:
score: 0
Accepted
time: 0ms
memory: 90128kb
input:
816293376 2952089614708276156 10939708785225040670
output:
120954190
result:
ok single line: '120954190'
Test #24:
score: 0
Accepted
time: 3ms
memory: 44692kb
input:
4185097875 1348426133484952253 56617823359794500344
output:
773995224
result:
ok single line: '773995224'
Test #25:
score: 0
Accepted
time: 0ms
memory: 132600kb
input:
5828945117184 7777082394971366991 63470232991138132969
output:
678496908
result:
ok single line: '678496908'
Test #26:
score: 0
Accepted
time: 0ms
memory: 144956kb
input:
16184770560 3869053219872876321 94590086601168840932
output:
168181821
result:
ok single line: '168181821'
Test #27:
score: 0
Accepted
time: 1ms
memory: 5848kb
input:
2 1 12
output:
6
result:
ok single line: '6'
Test #28:
score: 0
Accepted
time: 0ms
memory: 42552kb
input:
30146484375 290228705524339176 51853415145287716863
output:
229436627
result:
ok single line: '229436627'
Test #29:
score: 0
Accepted
time: 0ms
memory: 167400kb
input:
2072513819443200 3726664558969607832 42501102605103061370
output:
947952932
result:
ok single line: '947952932'
Test #30:
score: 0
Accepted
time: 7ms
memory: 102632kb
input:
9920232000000000 4602219263214498291 80783137037024823899
output:
846877519
result:
ok single line: '846877519'
Test #31:
score: 0
Accepted
time: 0ms
memory: 124564kb
input:
97200000000000000 9310820760839688870 35322929083473756214
output:
936587432
result:
ok single line: '936587432'
Test #32:
score: 0
Accepted
time: 0ms
memory: 42484kb
input:
45209390625 5752361069878044328 64635325028527078951
output:
578047592
result:
ok single line: '578047592'
Test #33:
score: 0
Accepted
time: 0ms
memory: 95844kb
input:
54442233216000 2452030574225118723 90982734056131320662
output:
417646585
result:
ok single line: '417646585'
Test #34:
score: 0
Accepted
time: 0ms
memory: 87808kb
input:
1530550080000 7431421026778839808 84825282227911272129
output:
600103842
result:
ok single line: '600103842'
Test #35:
score: 0
Accepted
time: 0ms
memory: 136872kb
input:
13765147361280 4924477486471254843 10002324705150566233
output:
951883713
result:
ok single line: '951883713'
Test #36:
score: 0
Accepted
time: 6ms
memory: 53148kb
input:
59825698242187500 6303744363677706767 91410210495502213963
output:
774734375
result:
ok single line: '774734375'
Test #37:
score: 0
Accepted
time: 3ms
memory: 106228kb
input:
110658879959040 2133591391458550040 48494371567095341228
output:
103505650
result:
ok single line: '103505650'
Test #38:
score: 0
Accepted
time: 1ms
memory: 7888kb
input:
1 3 100
output:
98
result:
ok single line: '98'
Test #39:
score: 0
Accepted
time: 0ms
memory: 128844kb
input:
3160365465600 8968721517098518892 78444481529635953131
output:
364620926
result:
ok single line: '364620926'
Test #40:
score: 0
Accepted
time: 0ms
memory: 3628kb
input:
54838448056132899 4242999884713464056 92948071680698209741
output:
922087167
result:
ok single line: '922087167'
Test #41:
score: 0
Accepted
time: 0ms
memory: 3572kb
input:
78183771565555182 7823307199080715671 93466469990450000599
output:
635073629
result:
ok single line: '635073629'
Test #42:
score: 0
Accepted
time: 0ms
memory: 3512kb
input:
56555532446322947 2952925229100796893 35926880503684324113
output:
663547216
result:
ok single line: '663547216'
Test #43:
score: 0
Accepted
time: 0ms
memory: 3516kb
input:
15701121272683095 8633703383009071570 55273589042372583668
output:
253996413
result:
ok single line: '253996413'
Test #44:
score: 0
Accepted
time: 0ms
memory: 3628kb
input:
11914467542453704 2857068399817941722 83230805830740136213
output:
956698341
result:
ok single line: '956698341'
Test #45:
score: 0
Accepted
time: 0ms
memory: 3616kb
input:
28181999963152819 7948365158338416594 87742700746768593189
output:
720016372
result:
ok single line: '720016372'
Test #46:
score: 0
Accepted
time: 0ms
memory: 3600kb
input:
85409868208332321 3921672860136397259 55474188860042435613
output:
622329181
result:
ok single line: '622329181'
Test #47:
score: 0
Accepted
time: 0ms
memory: 3600kb
input:
14748052718175068 9293071633738211123 85443373435217434149
output:
38392129
result:
ok single line: '38392129'
Test #48:
score: 0
Accepted
time: 0ms
memory: 3572kb
input:
41002058985303228 6141335647135876923 78910335860595680506
output:
665823537
result:
ok single line: '665823537'
Test #49:
score: 0
Accepted
time: 0ms
memory: 9608kb
input:
4 3 123
output:
62
result:
ok single line: '62'
Test #50:
score: 0
Accepted
time: 3ms
memory: 134724kb
input:
100000000000000000 3 100000000000000000000
output:
302574822
result:
ok single line: '302574822'
Test #51:
score: 0
Accepted
time: 2ms
memory: 11996kb
input:
6 7 12034
output:
9505
result:
ok single line: '9505'
Test #52:
score: 0
Accepted
time: 2ms
memory: 12056kb
input:
7 8 43021
output:
25028
result:
ok single line: '25028'
Test #53:
score: 0
Accepted
time: 0ms
memory: 13812kb
input:
8 8 43021
output:
32619
result:
ok single line: '32619'
Test #54:
score: 0
Accepted
time: 0ms
memory: 11768kb
input:
9 800 43021
output:
30930
result:
ok single line: '30930'