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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 ICPC | enze114514 | AC ✓ | 19ms | 4088kb | C++20 | 4.7kb | 2024-10-23 11:13:04 | 2024-10-23 11:13:11 |
Judging History
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;
}
詳細信息
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'