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
#668088#5576. Advertising ICPCenze114514AC ✓19ms4088kbC++204.7kb2024-10-23 11:13:042024-10-23 11:13:11

Judging History

你现在查看的是最新测评结果

  • [2024-10-23 11:13:11]
  • 评测
  • 测评结果:AC
  • 用时:19ms
  • 内存:4088kb
  • [2024-10-23 11:13:04]
  • 提交

answer

#include <bits/stdc++.h>
using namespace std;

typedef long long ll;

// Constants
const int MOD = 998244353;

// Structure to store mask_prev and mask_pc for each row assignment
struct RowAssignment {
    int mask_prev; // Mask for 'I C' positions
    int mask_pc;   // Mask for 'P C' positions
};

int main(){
    ios::sync_with_stdio(false);
    cin.tie(0);
    
    int n, m;
    cin >> n >> m;
    vector<string> grid(n);
    for(auto &s : grid) cin >> s;
    
    // Mapping characters to numerical values
    // 'C' = 0, 'I' = 1, 'P' = 2
    unordered_map<char, int> char_map = { {'C', 0}, {'I', 1}, {'P', 2} };
    
    // Precompute all possible row assignments
    // Total states per row: 3^m
    int total_states = pow(3, m);
    vector<RowAssignment> assignments(total_states);
    
    for(int s = 0; s < total_states; s++){
        int tmp = s;
        int mask_prev = 0;
        int mask_pc = 0;
        for(int j = 0; j < m; j++){
            int val = tmp % 3;
            tmp /=3;
            // Compute mask_prev: positions where 'I' followed by 'C'
            if(j < m-1){
                int next_val = tmp % 3;
                if(val == 1 && next_val == 0){
                    mask_prev |= (1 << j);
                }
            }
            // Compute mask_pc: positions where 'P' followed by 'C'
            if(j < m-1){
                int next_val = tmp % 3;
                if(val == 2 && next_val == 0){
                    mask_pc |= (1 << j);
                }
            }
        }
        assignments[s].mask_prev = mask_prev;
        assignments[s].mask_pc = mask_pc;
    }
    
    // Initialize DP
    // dp_prev[state] represents the number of ways to reach a given state
    // where state is the mask of 'I C' positions in the previous row
    vector<ll> dp_prev(128, 0); // 7-bit masks for m=8
    for(int s = 0; s < total_states; s++){
        // Only consider valid row assignments based on the grid
        bool valid = true;
        int tmp = s;
        for(int j = 0; j < m; j++){
            if(grid[0][j] != '?'){
                if(char_map.find(grid[0][j]) == char_map.end() || char_map[grid[0][j]] != (tmp % 3)){
                    valid = false;
                    break;
                }
            }
            tmp /=3;
        }
        if(valid){
            dp_prev[assignments[s].mask_prev]++;
            dp_prev[assignments[s].mask_prev] %= MOD;
        }
    }
    
    // Iterate through each row and update DP
    for(int r =1; r < n; r++){
        vector<ll> dp_curr(128, 0);
        for(int p =0; p < 128; p++){
            if(dp_prev[p]==0) continue;
            for(int s =0; s < total_states; s++){
                // Check if current row assignment is valid based on the grid
                bool valid = true;
                int tmp = s;
                for(int j =0; j < m; j++){
                    if(grid[r][j] != '?'){
                        if(char_map.find(grid[r][j]) == char_map.end() || char_map[grid[r][j]] != (tmp %3)){
                            valid = false;
                            break;
                        }
                    }
                    tmp /=3;
                }
                if(!valid) continue;
                
                // Check forbidden patterns
                // If previous row had 'I C' at position j, current row cannot have 'P C' at the same position
                if( (p & assignments[s].mask_pc) !=0 ) continue;
                
                // Update dp_curr with the new mask_prev
                dp_curr[assignments[s].mask_prev] += dp_prev[p];
                if(dp_curr[assignments[s].mask_prev] >= MOD){
                    dp_curr[assignments[s].mask_prev] -= MOD;
                }
            }
        }
        dp_prev = move(dp_curr);
    }
    
    // Calculate A: Number of assignments without any forbidden pattern
    ll A =0;
    for(int p=0; p <128; p++) {
        A = (A + dp_prev[p]) % MOD;
    }
    
    // Calculate T = 3^(k) mod MOD, where k is the number of '?'
    int k=0;
    for(int r=0; r <n; r++) {
        for(int j=0; j <m; j++) {
            if(grid[r][j] == '?') k++;
        }
    }
    
    // Fast exponentiation to compute 3^k mod MOD
    auto powmod_func = [&](ll base_val, ll exp, ll mod_val) -> ll {
        ll res =1;
        base_val %= mod_val;
        while(exp >0){
            if(exp &1LL){
                res = res * base_val % mod_val;
            }
            base_val = base_val * base_val % mod_val;
            exp >>=1LL;
        }
        return res;
    };
    ll T = powmod_func(3, k, MOD);
    
    // The answer is (T - A) mod MOD
    ll answer = (T - A + MOD) % MOD;
    cout << answer;
}

详细

Test #1:

score: 100
Accepted
time: 0ms
memory: 3844kb

input:

3 3
???
?I?
???

output:

243

result:

ok single line: '243'

Test #2:

score: 0
Accepted
time: 0ms
memory: 3880kb

input:

2 2
IC
PC

output:

1

result:

ok single line: '1'

Test #3:

score: 0
Accepted
time: 19ms
memory: 3888kb

input:

8 8
????????
????????
????????
????????
????????
????????
????????
????????

output:

776529021

result:

ok single line: '776529021'

Test #4:

score: 0
Accepted
time: 0ms
memory: 3752kb

input:

2 2
??
??

output:

1

result:

ok single line: '1'

Test #5:

score: 0
Accepted
time: 0ms
memory: 3920kb

input:

2 2
CP
CI

output:

0

result:

ok single line: '0'

Test #6:

score: 0
Accepted
time: 0ms
memory: 3792kb

input:

2 2
IP
CC

output:

0

result:

ok single line: '0'

Test #7:

score: 0
Accepted
time: 0ms
memory: 3816kb

input:

2 2
PI
CC

output:

0

result:

ok single line: '0'

Test #8:

score: 0
Accepted
time: 0ms
memory: 4020kb

input:

2 2
CI
CP

output:

0

result:

ok single line: '0'

Test #9:

score: 0
Accepted
time: 2ms
memory: 3884kb

input:

2 8
???P????
???P??P?

output:

115443

result:

ok single line: '115443'

Test #10:

score: 0
Accepted
time: 0ms
memory: 3884kb

input:

2 8
IC???C??
?I?IC?I?

output:

0

result:

ok single line: '0'

Test #11:

score: 0
Accepted
time: 2ms
memory: 3936kb

input:

2 8
?????P??
I???C??I

output:

32562

result:

ok single line: '32562'

Test #12:

score: 0
Accepted
time: 1ms
memory: 3888kb

input:

2 8
?PIC?CP?
?CIPC?IC

output:

0

result:

ok single line: '0'

Test #13:

score: 0
Accepted
time: 1ms
memory: 3876kb

input:

2 8
CCCPICPP
PII?PCCP

output:

3

result:

ok single line: '3'

Test #14:

score: 0
Accepted
time: 0ms
memory: 3880kb

input:

8 2
P?
??
??
??
I?
??
?P
??

output:

96957

result:

ok single line: '96957'

Test #15:

score: 0
Accepted
time: 0ms
memory: 3884kb

input:

8 2
??
C?
??
??
??
??
??
I?

output:

234009

result:

ok single line: '234009'

Test #16:

score: 0
Accepted
time: 0ms
memory: 3896kb

input:

8 2
PI
CC
IC
CI
?I
P?
CP
CP

output:

0

result:

ok single line: '0'

Test #17:

score: 0
Accepted
time: 0ms
memory: 3892kb

input:

8 2
?C
II
CC
IP
?C
C?
PP
?I

output:

0

result:

ok single line: '0'

Test #18:

score: 0
Accepted
time: 0ms
memory: 3992kb

input:

8 2
PP
PC
?I
?C
II
CC
I?
CI

output:

0

result:

ok single line: '0'

Test #19:

score: 0
Accepted
time: 4ms
memory: 3880kb

input:

3 8
????I???
???P????
??????P?

output:

598932682

result:

ok single line: '598932682'

Test #20:

score: 0
Accepted
time: 6ms
memory: 3800kb

input:

3 8
???C????
???????C
I???????

output:

176286317

result:

ok single line: '176286317'

Test #21:

score: 0
Accepted
time: 2ms
memory: 3976kb

input:

3 8
?IPCI??I
?C?CIIP?
?PCP?P?C

output:

0

result:

ok single line: '0'

Test #22:

score: 0
Accepted
time: 1ms
memory: 4060kb

input:

3 8
I?IPCCC?
?CPCC?P?
?CCPCC?I

output:

486

result:

ok single line: '486'

Test #23:

score: 0
Accepted
time: 1ms
memory: 3864kb

input:

3 8
CPICCCIP
CIP??CPC
CPPPCIPC

output:

4

result:

ok single line: '4'

Test #24:

score: 0
Accepted
time: 0ms
memory: 4064kb

input:

8 3
???
???
???
???
I??
???
?P?
???

output:

181529684

result:

ok single line: '181529684'

Test #25:

score: 0
Accepted
time: 0ms
memory: 3852kb

input:

8 3
I??
???
I??
?C?
??P
?I?
CII
C?C

output:

966654

result:

ok single line: '966654'

Test #26:

score: 0
Accepted
time: 0ms
memory: 3868kb

input:

8 3
CC?
??I
???
I?C
PCC
C?C
??C
??I

output:

241974

result:

ok single line: '241974'

Test #27:

score: 0
Accepted
time: 0ms
memory: 3832kb

input:

8 3
IIP
???
IPI
P?C
I?P
P?C
CPI
C?P

output:

243

result:

ok single line: '243'

Test #28:

score: 0
Accepted
time: 0ms
memory: 3816kb

input:

8 3
PCP
PPP
?CC
CPP
C?P
CP?
CPC
II?

output:

0

result:

ok single line: '0'

Test #29:

score: 0
Accepted
time: 15ms
memory: 4040kb

input:

8 8
????????
?P??C?P?
????????
????I???
?P????I?
???C????
????????
C??????I

output:

694454028

result:

ok single line: '694454028'

Test #30:

score: 0
Accepted
time: 9ms
memory: 3972kb

input:

8 8
????I?PI
???PC?I?
????IPC?
?????P??
PPIC????
?P????I?
???????C
C?????C?

output:

943439945

result:

ok single line: '943439945'

Test #31:

score: 0
Accepted
time: 5ms
memory: 3932kb

input:

8 8
PPPI????
??P??PIC
?PC??CCP
CPP????I
?II????C
CIPCI??C
C??PPC??
PI?PCCCC

output:

930881552

result:

ok single line: '930881552'

Test #32:

score: 0
Accepted
time: 2ms
memory: 4072kb

input:

8 8
IPPI?IPP
ICPC?II?
IICII??I
?PPCPPCC
?C??I?II
?ICCCCCI
PIIP?IIP
?P??II?C

output:

4782969

result:

ok single line: '4782969'

Test #33:

score: 0
Accepted
time: 2ms
memory: 3868kb

input:

8 8
PCPICCPP
IIICIICI
PCCPIC?P
IIPICIIC
CPIC?ICI
PCCI?C??
C?CC?IIC
CCPIPICP

output:

0

result:

ok single line: '0'

Test #34:

score: 0
Accepted
time: 4ms
memory: 4048kb

input:

8 7
???????
???????
??????C
???????
???????
???????
???????
???????

output:

407572405

result:

ok single line: '407572405'

Test #35:

score: 0
Accepted
time: 2ms
memory: 3856kb

input:

8 7
??????P
????P??
PC???C?
P?P????
?CI?P??
?????PI
????C??
C?PCI?P

output:

299705028

result:

ok single line: '299705028'

Test #36:

score: 0
Accepted
time: 2ms
memory: 3916kb

input:

8 7
IP?I?I?
??C??C?
IPC????
P???C??
??IP???
IPI???C
P??PPI?
?PPICCC

output:

945285612

result:

ok single line: '945285612'

Test #37:

score: 0
Accepted
time: 1ms
memory: 3900kb

input:

8 7
?PCPC?C
P?IC?P?
P?ICPPC
?C??P??
P?PICPI
I?CCC?I
I??PCPI
PCIIIPP

output:

24011073

result:

ok single line: '24011073'

Test #38:

score: 0
Accepted
time: 1ms
memory: 3812kb

input:

8 7
CIC??II
CCIIPPC
IPCIPCP
IC?IPPI
PPCCPP?
ICPPIIP
PPPCI?I
CIICI??

output:

0

result:

ok single line: '0'

Test #39:

score: 0
Accepted
time: 14ms
memory: 3828kb

input:

7 8
????????
????????
?P??????
????????
????????
????????
????????

output:

335862381

result:

ok single line: '335862381'

Test #40:

score: 0
Accepted
time: 7ms
memory: 3808kb

input:

7 8
CI?P?P??
I?P?I???
??????I?
???PP???
?C????P?
?P??????
?PI?I??I

output:

371435886

result:

ok single line: '371435886'

Test #41:

score: 0
Accepted
time: 3ms
memory: 4040kb

input:

7 8
ICI?II?C
???C????
I?IC??I?
??CC????
C????CCI
P??I??II
C??I?PCP

output:

220669500

result:

ok single line: '220669500'

Test #42:

score: 0
Accepted
time: 2ms
memory: 4076kb

input:

7 8
CPI?CP?C
I?P??PPI
P?CCCPP?
PIC?I?PP
IPII?PII
CIPCCP??
IIC???IP

output:

3483891

result:

ok single line: '3483891'

Test #43:

score: 0
Accepted
time: 1ms
memory: 4044kb

input:

7 8
IIICICII
IIPPPCIP
ICCP?C?C
CPIP??IC
IIICICII
C?CPPPII
CIPPCPCC

output:

243

result:

ok single line: '243'

Test #44:

score: 0
Accepted
time: 3ms
memory: 3900kb

input:

7 7
???C???
???????
???????
P?????P
???????
I?????C
???????

output:

45031736

result:

ok single line: '45031736'

Test #45:

score: 0
Accepted
time: 1ms
memory: 3904kb

input:

7 7
?P?C?I?
?????C?
??I?P??
?CICPCC
???P??I
IIPP?I?
???P???

output:

414440826

result:

ok single line: '414440826'

Test #46:

score: 0
Accepted
time: 1ms
memory: 3916kb

input:

7 7
??I?P?C
?I?PIPC
C???PPI
I????PI
PP?I?PC
P?IIC??
IPC??CC

output:

623536432

result:

ok single line: '623536432'

Test #47:

score: 0
Accepted
time: 1ms
memory: 4088kb

input:

7 7
I??PCP?
IPP?CCP
IPIP?II
P?CCPP?
?CP???P
PPIC??C
??IPCPP

output:

1751787

result:

ok single line: '1751787'

Test #48:

score: 0
Accepted
time: 1ms
memory: 3936kb

input:

7 7
I?PPPPC
CIIICPP
CCCPPPP
PP?PCIP
IIIIIPI
ICIPCII
?ICPPCI

output:

0

result:

ok single line: '0'