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QOJ
ID | Problem | Submitter | Result | Time | Memory | Language | File size | Submit time | Judge time |
---|---|---|---|---|---|---|---|---|---|
#711253 | #9158. 分数 | Qwerty1232 | 95 | 5214ms | 3932kb | C++23 | 2.6kb | 2024-11-05 08:08:59 | 2024-11-05 08:09:00 |
Judging History
answer
#include <bits/stdc++.h>
struct Frac {
int64_t a, b, c, d;
// (ax + b) / (cx + d)
Frac() {
a = d = 1;
b = c = 0;
}
Frac(int64_t a, int64_t b, int64_t c, int64_t d) : a(a), b(b), c(c), d(d) { ; }
std::pair<int64_t, int64_t> get(int x, int y) const {
return {a * x + b * y, c * x + d * y};
}
int64_t get_max(int x, int y) const {
auto [a, b] = get(x, y);
return std::max(a, b);
}
};
Frac comp(const Frac& l, const Frac& r) {
Frac res = {
int(l.a) * 1LL * int(r.a) + int(l.b) * 1LL * int(r.c),
int(l.a) * 1LL * int(r.b) + int(l.b) * 1LL * int(r.d),
int(l.c) * 1LL * int(r.a) + int(l.d) * 1LL * int(r.c),
int(l.c) * 1LL * int(r.b) + int(l.d) * 1LL * int(r.d)};
return res;
}
int n, m, N;
int64_t ans;
int64_t dfs2_calls = 0;
bool dfs2(int p, int q, int x, const Frac& f) {
dfs2_calls++;
if (p + 2LL * x * q > N) {
return false;
}
auto [a0, b0] = f.get(p + 2 * x * q, q);
{
if (std::max(a0, b0) > N || std::min(a0, b0) > std::min(n, m)) {
return false;
}
}
int p1 = f.a * q, p2 = f.a * p + f.b * q;
int q1 = f.c * q, q2 = f.c * p + f.d * q;
int64_t dlt = 0;
for (auto [n, m] : std::array{std::pair{::n, ::m}, std::pair{::m, ::n}}) {
int r1 = n - p2 - p1 * 2 * x;
int r2 = m - q2 - q1 * 2 * x;
if (std::min(r1, r2) >= 0) {
r1 = p1 == 0 ? int(1e9) : r1 / (2 * p1) + 1;
r2 = q1 == 0 ? int(1e9) : r2 / (2 * q1) + 1;
int dt = std::min(r1, r2);
dlt += dt;
}
}
// std::cerr << dlt << " ";
ans += dlt;
for (int k = 1; a0 + 2 * k * b0 <= N; k++) {
int x2 = std::max(x, k);
if (!dfs2(p, q, std::max(x, k), comp(Frac(0, 1, 1, 2 * k), f))) {
break;
}
}
return true;
}
bool dfs1(int a, int b, int x = 0) {
if (std::max(a, b) > N) {
return false;
}
// if (a + 2LL * (x + 1) * b > N) {
// return false;
// }
if (!dfs2(a, b, x + 1, Frac(0, 1, 1, 0))) {
return false;
}
for (int k = 1; a + 2 * k * b <= N && b + 2LL * (std::max(x, k) + 1) * (a + 2 * k * b) <= N; k++) {
if (!dfs1(b, a + 2 * k * b, std::max(x, k))) {
break;
}
}
return true;
}
int32_t main() {
n = m = 3e7;
std::cin >> n >> m;
N = std::max(n, m);
dfs1(0, 1, 0);
std::cout << ans << "\n";
std::cerr << dfs2_calls / 1e6 << " M\n";
return 0;
}
Details
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Pretests
Pretest #1:
score: 5
Accepted
time: 0ms
memory: 3844kb
input:
99 99
output:
406
result:
ok 1 number(s): "406"
Pretest #2:
score: 5
Accepted
time: 0ms
memory: 3896kb
input:
98 97
output:
405
result:
ok 1 number(s): "405"
Pretest #3:
score: 5
Accepted
time: 0ms
memory: 3848kb
input:
99 96
output:
396
result:
ok 1 number(s): "396"
Pretest #4:
score: 5
Accepted
time: 0ms
memory: 3844kb
input:
995 977
output:
11153
result:
ok 1 number(s): "11153"
Pretest #5:
score: 5
Accepted
time: 0ms
memory: 3832kb
input:
991 990
output:
11220
result:
ok 1 number(s): "11220"
Pretest #6:
score: 5
Accepted
time: 0ms
memory: 3888kb
input:
976 968
output:
10900
result:
ok 1 number(s): "10900"
Pretest #7:
score: 5
Accepted
time: 1ms
memory: 3848kb
input:
7602 7864
output:
215706
result:
ok 1 number(s): "215706"
Pretest #8:
score: 5
Accepted
time: 1ms
memory: 3888kb
input:
7959 7735
output:
220256
result:
ok 1 number(s): "220256"
Pretest #9:
score: 5
Accepted
time: 1ms
memory: 3836kb
input:
7878 7863
output:
221162
result:
ok 1 number(s): "221162"
Pretest #10:
score: 5
Accepted
time: 0ms
memory: 3840kb
input:
7788 7658
output:
215323
result:
ok 1 number(s): "215323"
Pretest #11:
score: 5
Accepted
time: 4ms
memory: 3816kb
input:
95399 99767
output:
8285295
result:
ok 1 number(s): "8285295"
Pretest #12:
score: 5
Accepted
time: 4ms
memory: 3892kb
input:
98051 99642
output:
8439713
result:
ok 1 number(s): "8439713"
Pretest #13:
score: 5
Accepted
time: 4ms
memory: 3932kb
input:
95624 96007
output:
8068127
result:
ok 1 number(s): "8068127"
Pretest #14:
score: 5
Accepted
time: 4ms
memory: 3848kb
input:
99208 98047
output:
8412610
result:
ok 1 number(s): "8412610"
Pretest #15:
score: 5
Accepted
time: 71ms
memory: 3884kb
input:
997417 967722
output:
229917323
result:
ok 1 number(s): "229917323"
Pretest #16:
score: 5
Accepted
time: 68ms
memory: 3836kb
input:
987807 956529
output:
226426912
result:
ok 1 number(s): "226426912"
Pretest #17:
score: 5
Accepted
time: 70ms
memory: 3892kb
input:
971654 984345
output:
228363805
result:
ok 1 number(s): "228363805"
Pretest #18:
score: 5
Accepted
time: 1110ms
memory: 3932kb
input:
7892259 7983727
output:
4647501224
result:
ok 1 number(s): "4647501224"
Pretest #19:
score: 5
Accepted
time: 5214ms
memory: 3836kb
input:
7937869 29796968
output:
15197555613
result:
ok 1 number(s): "15197555613"
Pretest #20:
score: 0
Time Limit Exceeded
input:
29717543 29510173
output:
result:
Final Tests
Test #1:
score: 5
Accepted
time: 0ms
memory: 3756kb
input:
96 98
output:
396
result:
ok 1 number(s): "396"
Test #2:
score: 5
Accepted
time: 0ms
memory: 3896kb
input:
100 99
output:
408
result:
ok 1 number(s): "408"
Test #3:
score: 5
Accepted
time: 0ms
memory: 3824kb
input:
99 99
output:
406
result:
ok 1 number(s): "406"
Test #4:
score: 5
Accepted
time: 0ms
memory: 3836kb
input:
963 951
output:
10634
result:
ok 1 number(s): "10634"
Test #5:
score: 5
Accepted
time: 0ms
memory: 3848kb
input:
958 974
output:
10795
result:
ok 1 number(s): "10795"
Test #6:
score: 5
Accepted
time: 0ms
memory: 3892kb
input:
966 990
output:
11003
result:
ok 1 number(s): "11003"
Test #7:
score: 5
Accepted
time: 1ms
memory: 3888kb
input:
7958 7947
output:
224482
result:
ok 1 number(s): "224482"
Test #8:
score: 5
Accepted
time: 1ms
memory: 3848kb
input:
7623 7730
output:
213444
result:
ok 1 number(s): "213444"
Test #9:
score: 5
Accepted
time: 0ms
memory: 3888kb
input:
7845 7783
output:
218916
result:
ok 1 number(s): "218916"
Test #10:
score: 5
Accepted
time: 0ms
memory: 3840kb
input:
7881 7773
output:
219451
result:
ok 1 number(s): "219451"
Test #11:
score: 5
Accepted
time: 4ms
memory: 3752kb
input:
99414 98698
output:
8465217
result:
ok 1 number(s): "8465217"
Test #12:
score: 5
Accepted
time: 4ms
memory: 3932kb
input:
98249 96148
output:
8237486
result:
ok 1 number(s): "8237486"
Test #13:
score: 5
Accepted
time: 4ms
memory: 3832kb
input:
99003 96832
output:
8324931
result:
ok 1 number(s): "8324931"
Test #14:
score: 5
Accepted
time: 0ms
memory: 3840kb
input:
98266 96030
output:
8231065
result:
ok 1 number(s): "8231065"
Test #15:
score: 5
Accepted
time: 68ms
memory: 3892kb
input:
968207 958885
output:
223522215
result:
ok 1 number(s): "223522215"
Test #16:
score: 5
Accepted
time: 72ms
memory: 3888kb
input:
959846 998397
output:
228770873
result:
ok 1 number(s): "228770873"
Test #17:
score: 5
Accepted
time: 68ms
memory: 3836kb
input:
965821 972280
output:
225359210
result:
ok 1 number(s): "225359210"
Test #18:
score: 5
Accepted
time: 1104ms
memory: 3808kb
input:
7855098 7962479
output:
4622947400
result:
ok 1 number(s): "4622947400"
Test #19:
score: 5
Accepted
time: 5156ms
memory: 3896kb
input:
7841076 29648718
output:
15040798710
result:
ok 1 number(s): "15040798710"
Test #20:
score: 0
Time Limit Exceeded
input:
29365129 29012208