QOJ.ac
QOJ
ID | Problem | Submitter | Result | Time | Memory | Language | File size | Submit time | Judge time |
---|---|---|---|---|---|---|---|---|---|
#912861 | #10111. Dividing Chains | 呆呆鸟 (Weicheng Wang, Anyi Xu, Xiangwen Wang) | AC ✓ | 54ms | 8948kb | C++23 | 3.7kb | 2025-02-24 00:20:59 | 2025-02-24 00:21:00 |
Judging History
This is a historical verdict posted at 2025-02-24 00:21:00.
- [2025-02-25 03:27:21]
- hack成功,自动添加数据
- (/hack/1576)
- [2025-02-24 00:20:59]
- Submitted
answer
#include <bits/stdc++.h>
using namespace std;
const int md = 998244353;
inline int add(int x, int y) {
if (x + y >= md) return x + y - md;
return x + y;
}
inline void addx(int &x, int y) {
x += y;
if (x >= md) x -= md;
}
inline int sub(int x, int y) {
if (x < y) return x - y + md;
return x - y;
}
inline void subx(int &x, int y) {
x -= y;
if (x < 0) x += md;
}
inline int mul(int x, int y) { return 1ull * x * y % md; }
inline int fpow(int x, int y) {
int ans = 1;
while (y) {
if (y & 1) ans = mul(ans, x);
y >>= 1; x = mul(x, x);
}
return ans;
}
const int N = 505;
int dp[N][N], tmpl[N][N], tmpr[N][N], ans[N][N], dp0[N][N];
// dp[l][r] 这个区间不能被划分成若干个上升的段, 能被划分成若干个下降的段的方案数
// 是否等价于 l 不是最小值 && r 不是最大值?
// 如果划分后 l 可能是最小值, 说明右边全是最小值
// 如果划分后 r 可能是最大值, 说明左边全是最大值
int a[N];
int n;
int main() {
scanf("%d", &n);
for (int i = 1; i <= n; i++) {
scanf("%d", &a[i]);
}
if (a[1] == a[n]) {
printf("1\n");
return 0;
}
for (int i = 1; i <= n + 1; i++) {
dp[i][i] = dp[i][i - 1] = 1;
ans[i][i] = 1;
dp0[i][i] = 1;
}
for (int len = 2; len <= n; len++) {
for (int l = 1; l <= n - len + 1; l++) {
int r = l + len - 1;
if (a[l] == a[r]) {
dp[l][r] = 0; // 肯定能再分
ans[l][r] = 1;
dp0[l][r] = 1;
continue;
}
for (int i = l; i <= r - 1; i++) {
dp0[l][r] = add(dp0[l][r], mul(dp[l][i], dp0[i + 1][r]));
}
dp[l][r] = dp0[l][r];
// fprintf(stderr, "dp[%d][%d] = %d\n", l, r, dp[l][r]);
ans[l][r] = dp[l][r];
for (int i = l; i <= r - 1; i++) {
if (a[i] == a[r]) {
int val;
if (a[i] == a[i - 1]) val = sub(ans[l][i - 1], ans[l][i - 2]);
else val = ans[l][i - 1];
// fprintf(stderr, "bad r [%d, %d] = %d\n", l, i, val);
tmpr[l][r] = add(tmpr[l][r], val);
dp[l][r] = sub(dp[l][r], val);
}
}
// 3 4 5 3 3 3 非法
// 4 3 5 3 3 3 合法
// 枚举第一段 [i, r], 后面全是 3, [i, r] 是一个上升, [i, r] 不能以 3 作为开头
for (int i = l + 1; i <= r; i++) {
if (a[l] == a[i]) {
int val;
if (a[i] == a[i + 1]) val = sub(ans[i + 1][r], ans[i + 2][r]);
else val = ans[i + 1][r];
// fprintf(stderr, "bad l [%d, %d] = %d\n", i, r, val);
tmpl[l][r] = add(tmpl[l][r], val);
dp[l][r] = sub(dp[l][r], val);
// fprintf(stderr, "dpr[%d][%d] = %d\n", i, r, dpr[i][r]);
// fprintf(stderr, "l = %d, r = %d, i = %d, (%d, %d), dp = %d\n", l, r, i, dp[i][r], dpr[i][r], dp[l][r]);
}
}
ans[l][r] = add(ans[l][r], dp[l][r]);
dp0[l][r] = add(dp0[l][r], dp[l][r]);
// fprintf(stderr, "l = %d, r = %d, dp = %d\n", l, r, dp[l][r]);
}
}
printf("%d\n", ans[1][n]);
return 0;
}
// (1 3 3) 1
// dp[2][4] : (1 3 3 排成下降, 3 3 1)
// 3 (1, 3)
/*
l = 1, r = 2, dp = 998244351, dpl = 0, dpr = 0
l = 1, r = 3, dp = 998244351, dpl = 0, dpr = 0
*/
// 1+1, 1+2, 1+3, 2+1, 2+2, 3+1
// 1 1 2 3
// 3 2 1 1
// 3 1 2 1
// 2 3 1 1
// 2 1 3 1
这程序好像有点Bug,我给组数据试试?
Details
Tip: Click on the bar to expand more detailed information
Test #1:
score: 100
Accepted
time: 1ms
memory: 3960kb
input:
3 2 3 3
output:
3
result:
ok "3"
Test #2:
score: 0
Accepted
time: 0ms
memory: 7952kb
input:
5 1 1 3 3 5
output:
29
result:
ok "29"
Test #3:
score: 0
Accepted
time: 0ms
memory: 8044kb
input:
9 1 2 3 5 5 6 7 8 9
output:
26276
result:
ok "26276"
Test #4:
score: 0
Accepted
time: 2ms
memory: 8048kb
input:
10 1 2 2 3 4 5 8 10 10 10
output:
42088
result:
ok "42088"
Test #5:
score: 0
Accepted
time: 2ms
memory: 7904kb
input:
10 1 2 4 5 5 5 5 6 10 10
output:
17210
result:
ok "17210"
Test #6:
score: 0
Accepted
time: 0ms
memory: 8048kb
input:
10 1 2 3 5 6 6 6 8 9 9
output:
41826
result:
ok "41826"
Test #7:
score: 0
Accepted
time: 1ms
memory: 6068kb
input:
10 2 6 6 7 7 8 9 10 10 10
output:
26684
result:
ok "26684"
Test #8:
score: 0
Accepted
time: 1ms
memory: 4064kb
input:
10 1 1 3 3 4 5 9 9 10 10
output:
33378
result:
ok "33378"
Test #9:
score: 0
Accepted
time: 1ms
memory: 4012kb
input:
10 1 1 2 3 4 4 9 9 10 10
output:
33348
result:
ok "33348"
Test #10:
score: 0
Accepted
time: 0ms
memory: 7904kb
input:
10 1 3 4 4 5 5 8 8 10 10
output:
32826
result:
ok "32826"
Test #11:
score: 0
Accepted
time: 1ms
memory: 4060kb
input:
10 1 3 3 4 5 6 9 9 9 10
output:
42136
result:
ok "42136"
Test #12:
score: 0
Accepted
time: 2ms
memory: 7984kb
input:
10 1 1 1 2 2 4 4 5 5 6
output:
16274
result:
ok "16274"
Test #13:
score: 0
Accepted
time: 1ms
memory: 4024kb
input:
10 1 3 5 5 5 6 7 8 8 9
output:
42088
result:
ok "42088"
Test #14:
score: 0
Accepted
time: 49ms
memory: 8812kb
input:
500 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 2 2 2 2 2 2 2 2 2 2 2 3 3 3 3 3 3 3 3 3 3 3 4 4 4 4 4 4 4 4 4 4 4 4 4 5 5 5 5 5 5 5 5 5 6 6 6 6 6 6 6 6 6 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 8 8 8 8 8 8 8 8 8 8 9 9 9 9 9 9 9 9 9 9 10 10 10 10 10 10 10 10 11 11 11 11 11 11 11 11 11 11 12 12 12 12 12 12 12 12 12...
output:
316934967
result:
ok "316934967"
Test #15:
score: 0
Accepted
time: 54ms
memory: 8756kb
input:
500 1 1 1 1 1 1 1 2 2 2 2 2 2 2 3 3 3 3 3 4 4 4 4 5 5 5 5 5 5 5 5 5 6 6 7 7 7 7 7 8 8 9 9 10 10 10 10 10 11 11 11 11 12 12 12 12 12 13 13 14 14 14 14 15 15 15 16 16 16 17 17 17 17 17 17 17 18 18 18 18 18 18 19 19 19 19 19 19 19 19 20 21 21 21 21 21 21 22 22 22 22 22 22 22 22 22 23 23 23 23 23 23 23 ...
output:
211204090
result:
ok "211204090"
Test #16:
score: 0
Accepted
time: 51ms
memory: 8828kb
input:
500 1 1 1 2 3 4 4 4 4 4 4 4 4 5 5 5 6 7 7 7 7 8 8 9 9 10 10 10 10 10 10 11 11 11 11 11 11 12 12 12 12 12 12 13 13 13 14 14 14 14 15 15 15 16 16 16 16 18 19 19 19 19 19 20 20 21 21 21 22 22 22 22 22 22 23 23 24 24 24 24 24 24 24 25 26 26 27 27 27 28 28 29 29 29 30 30 31 31 31 31 31 32 32 32 32 33 33 ...
output:
66910402
result:
ok "66910402"
Test #17:
score: 0
Accepted
time: 47ms
memory: 8760kb
input:
500 1 1 2 2 2 2 3 4 4 4 4 4 5 6 6 7 8 8 8 9 9 9 9 9 10 10 11 12 12 13 13 14 14 15 15 15 16 16 17 17 17 17 17 17 18 18 18 19 19 19 19 19 20 20 21 21 21 21 22 22 22 23 23 24 24 25 25 25 25 26 26 26 27 27 27 28 28 28 28 29 30 30 31 31 32 32 33 33 34 34 34 35 35 35 36 36 36 36 37 37 37 37 37 37 38 38 39...
output:
778673575
result:
ok "778673575"
Test #18:
score: 0
Accepted
time: 49ms
memory: 8872kb
input:
500 1 1 1 2 4 4 4 5 6 6 6 7 7 8 8 8 8 9 9 13 14 14 14 15 15 16 16 16 16 16 17 18 19 20 21 21 21 22 22 22 22 23 23 24 24 24 25 25 26 26 26 27 27 28 28 28 28 28 28 30 30 30 31 31 32 32 33 34 34 34 35 36 36 36 37 37 39 39 39 40 40 40 41 42 42 42 43 43 43 44 44 45 45 45 46 47 48 48 48 49 49 49 49 50 51 ...
output:
626585352
result:
ok "626585352"
Test #19:
score: 0
Accepted
time: 50ms
memory: 8772kb
input:
500 1 2 3 3 4 5 5 5 6 6 8 8 8 10 11 12 13 13 13 13 13 13 14 14 15 15 17 18 18 18 18 19 19 20 20 20 21 21 21 25 25 26 26 27 27 29 30 30 30 32 33 33 33 34 34 34 35 36 36 37 37 37 38 38 38 39 40 40 40 42 42 43 44 44 45 45 46 47 47 48 50 54 54 55 55 57 57 57 58 59 59 60 61 62 63 63 63 64 65 65 66 66 66 ...
output:
918943801
result:
ok "918943801"
Test #20:
score: 0
Accepted
time: 53ms
memory: 8768kb
input:
500 1 1 2 3 3 3 4 4 5 6 7 9 9 9 11 12 13 13 14 14 14 14 15 15 16 19 19 20 22 23 24 25 25 26 26 27 30 31 32 33 33 33 34 35 35 36 37 38 38 39 43 43 45 45 46 46 47 47 48 48 50 51 51 52 52 52 52 53 54 57 58 58 58 59 60 60 61 62 62 63 63 64 64 64 65 66 66 66 68 68 70 70 70 72 72 73 73 73 75 75 75 76 78 7...
output:
593100090
result:
ok "593100090"
Test #21:
score: 0
Accepted
time: 46ms
memory: 8884kb
input:
500 1 2 2 3 4 4 5 5 6 6 7 8 9 11 11 12 12 13 14 14 14 14 16 17 19 19 20 21 22 22 24 26 26 26 27 27 28 28 29 29 35 39 40 41 42 43 46 47 48 49 49 50 50 51 52 52 52 56 56 56 56 57 59 59 59 60 61 61 65 66 68 69 69 71 71 72 72 73 73 74 74 75 75 76 76 76 79 80 82 82 84 85 87 87 88 88 89 90 91 91 91 94 95 ...
output:
51077903
result:
ok "51077903"
Test #22:
score: 0
Accepted
time: 47ms
memory: 8940kb
input:
500 1 2 3 3 4 4 4 5 6 6 7 9 10 11 11 12 14 14 15 15 15 16 16 17 17 17 18 18 18 18 18 19 19 20 20 21 22 23 24 25 25 25 31 32 32 32 32 33 33 34 35 36 36 37 37 38 38 45 46 47 48 50 50 51 52 52 53 56 58 60 61 61 61 61 62 62 62 62 63 63 63 63 63 64 64 65 67 67 68 71 72 73 74 74 75 75 76 77 77 77 77 77 77...
output:
645029056
result:
ok "645029056"
Test #23:
score: 0
Accepted
time: 52ms
memory: 8752kb
input:
500 1 1 2 2 2 6 8 8 9 9 11 11 11 12 13 13 13 13 15 16 16 19 19 19 20 20 20 20 22 23 24 25 25 26 27 29 31 31 33 33 33 35 35 39 39 39 40 40 40 45 46 46 47 47 47 48 49 50 52 53 53 53 54 55 57 57 58 59 61 62 64 64 66 66 66 68 69 70 71 72 74 74 75 75 76 76 78 80 81 83 83 84 85 85 85 86 88 89 90 90 91 92 ...
output:
799979293
result:
ok "799979293"
Test #24:
score: 0
Accepted
time: 1ms
memory: 3844kb
input:
1 1
output:
1
result:
ok "1"
Test #25:
score: 0
Accepted
time: 49ms
memory: 8948kb
input:
500 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 ...
output:
903664836
result:
ok "903664836"
Test #26:
score: 0
Accepted
time: 1ms
memory: 3864kb
input:
500 500 500 500 500 500 500 500 500 500 500 500 500 500 500 500 500 500 500 500 500 500 500 500 500 500 500 500 500 500 500 500 500 500 500 500 500 500 500 500 500 500 500 500 500 500 500 500 500 500 500 500 500 500 500 500 500 500 500 500 500 500 500 500 500 500 500 500 500 500 500 500 500 500 500 ...
output:
1
result:
ok "1"
Extra Test:
score: 0
Extra Test Passed