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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
#912861#10111. Dividing Chains呆呆鸟 (Weicheng Wang, Anyi Xu, Xiangwen Wang)AC ✓51ms8840kbC++233.7kb2025-02-24 00:20:592025-02-25 03:28:07

Judging History

This is the latest submission verdict.

  • [2025-02-25 03:28:07]
  • 自动重测本题所有获得100分的提交记录
  • Verdict: AC
  • Time: 51ms
  • Memory: 8840kb
  • [2025-02-25 03:27:21]
  • hack成功,自动添加数据
  • (/hack/1576)
  • [2025-02-24 00:21:00]
  • Judged
  • Verdict: 100
  • Time: 54ms
  • Memory: 8948kb
  • [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?

詳細信息

Test #1:

score: 100
Accepted
time: 0ms
memory: 8008kb

input:

3
2 3 3

output:

3

result:

ok "3"

Test #2:

score: 0
Accepted
time: 1ms
memory: 3840kb

input:

5
1 1 3 3 5

output:

29

result:

ok "29"

Test #3:

score: 0
Accepted
time: 0ms
memory: 8008kb

input:

9
1 2 3 5 5 6 7 8 9

output:

26276

result:

ok "26276"

Test #4:

score: 0
Accepted
time: 0ms
memory: 8004kb

input:

10
1 2 2 3 4 5 8 10 10 10

output:

42088

result:

ok "42088"

Test #5:

score: 0
Accepted
time: 1ms
memory: 3968kb

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: 8008kb

input:

10
1 2 3 5 6 6 6 8 9 9

output:

41826

result:

ok "41826"

Test #7:

score: 0
Accepted
time: 0ms
memory: 8012kb

input:

10
2 6 6 7 7 8 9 10 10 10

output:

26684

result:

ok "26684"

Test #8:

score: 0
Accepted
time: 0ms
memory: 3840kb

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: 3968kb

input:

10
1 1 2 3 4 4 9 9 10 10

output:

33348

result:

ok "33348"

Test #10:

score: 0
Accepted
time: 1ms
memory: 3968kb

input:

10
1 3 4 4 5 5 8 8 10 10

output:

32826

result:

ok "32826"

Test #11:

score: 0
Accepted
time: 0ms
memory: 3968kb

input:

10
1 3 3 4 5 6 9 9 9 10

output:

42136

result:

ok "42136"

Test #12:

score: 0
Accepted
time: 0ms
memory: 8004kb

input:

10
1 1 1 2 2 4 4 5 5 6

output:

16274

result:

ok "16274"

Test #13:

score: 0
Accepted
time: 0ms
memory: 8012kb

input:

10
1 3 5 5 5 6 7 8 8 9

output:

42088

result:

ok "42088"

Test #14:

score: 0
Accepted
time: 50ms
memory: 8588kb

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: 51ms
memory: 8840kb

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: 50ms
memory: 8564kb

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: 49ms
memory: 8772kb

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: 48ms
memory: 8688kb

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: 48ms
memory: 8776kb

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: 48ms
memory: 8608kb

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: 49ms
memory: 8660kb

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: 51ms
memory: 8772kb

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: 47ms
memory: 8576kb

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: 0ms
memory: 3840kb

input:

1
1

output:

1

result:

ok "1"

Test #25:

score: 0
Accepted
time: 47ms
memory: 8812kb

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: 3840kb

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