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Submission #728089

# Submission time Handle Problem Language Result Execution time Memory
728089 2023-04-22T01:05:55 Z thomas_li Bowling (BOI15_bow) C++17
100 / 100
 90 ms 12896 KB 
#include <bits/stdc++.h>
using namespace std;
string rk = "x-"; vector<string> spstr,rgstr;
string c1 = "xxx";
vector<string> c2,c3,c4,c5,c6,c7;
int n,a[11]; int64_t dp[11][22][22][301]; // first i frames, carry amount from previous i, carry amount from i, score after i
                                          // carry is -1 if we don't add
string s;

void solve(){
    memset(dp,0,sizeof dp);
    cin >> n >> s; s = ' ' + s;
    for(int i = 1; i <= n; i++) cin >> a[i];
    auto can = [&](int i, string& t){
        assert(t.size() == 2);
        for(int j = 0; j < 2; j++){
            char c = s[i+j]; if(c == '?') continue;
            if(c != t[j]) return false;
        }
        return true;
    };
    auto can1 = [&](int i, string& t){
        assert(t.size() == 3);
        for(int j = 0; j < 3; j++){
            char c = s[i+j];
            if(c == '?') continue;
            if(c != t[j]) return false;
        }
        return true;
    };
    dp[0][0][0][0] = 1;
    auto add = [&](int64_t& x, int64_t y){
        x = (x+y);
    };
    // solve normal
    for(int i = 1; i <= n-1; i++){
        // generate good strings
        bool grk = can(2*i-1,rk);
        vector<string> gsp,grg;  
        for(auto& t : spstr) if(can(2*i-1,t)) gsp.push_back(t);
        for(auto& t : rgstr) if(can(2*i-1,t)) grg.push_back(t);
        swap(gsp,spstr);
        swap(grg,rgstr);
        int lo = 0, hi = 30*i;
        if(a[i] != -1) lo = hi = a[i];           
        for(int j = -1; j <= 10; j++) for(int k = -1; k <= 20; k++){ // previous previous, previous carries
            // strike
            // our shot needs to make j zero, k non negative
            if(grk && (j == -1 || j-10 == 0) && (k == -1 || (k-10 >= 0 && k-10 <= 10))){
                int nk = (k == -1 ? -1 : k-10);
                // we can gain some more from carries if needed 
                for(int gain = 0; gain <= 20; gain++){
                    // l >= gain+10
                    //if(l-gain-10 < 0) break;
                    for(int l = max(lo,gain+10); l <= hi; l++) add(dp[i][nk+1][gain+1][l],dp[i-1][j+1][k+1][l-gain-10]);
                }
            }     
            // spare
            if(k == -1 || k-10 == 0){
                // TODO: opt break
                for(auto& t : spstr){
                    // previous previous gets subtracted by fs, previous gets subtracted by 10
                    // both are gone after this frame, so need to become 0
                    int fs = t[0]-'0';
                    if(j != -1 && j-fs != 0) continue;
                    for(int gain = 0; gain <= 10; gain++){
                        //if(l-gain-10 < 0) break;
                        // add to previous slot to satisfy one bonus feature
                        for(int l = max(lo,gain+10); l <= hi; l++) add(dp[i][gain+1][0][l],dp[i-1][j+1][k+1][l-gain-10]);
                    }
                }
            }
            // regular
            for(auto& t : rgstr){
                // previous previous gets subtracted by fs, previous gets subtracted by sn+fs
                // both are gone after this frame, so need to become 0
                int fs = t[0]-'0',sn = t[1]-'0';
                if(j != -1 && j-fs != 0) continue;
                if(k != -1 && k-fs-sn != 0) continue;
                //if(l-fs-sn < 0) continue;
                for(int l = max(lo,fs+sn); l <= hi; l++) add(dp[i][0][0][l],dp[i-1][j+1][k+1][l-fs-sn]);
            }
                /*
                bool good = 0;
                for(int z = 0; z <= 20 && !good; z++) for(int w = 0; w <= 20; w++) if(dp[i][z][w][l]){
                    good = 1;
                    break;
                }
                if(good) cout << l << " " << i << "\n";  */
        }
        swap(gsp,spstr);
        swap(grg,rgstr);
    }
    // solve last
    // preprocess equalities
    vector<string> gc2,gc3,gc4,gc5,gc6,gc7;
    for(auto& t : c2) if(can1(2*n-1,t)) gc2.push_back(t);
    for(auto& t : c3) if(can1(2*n-1,t)) gc3.push_back(t);
    for(auto& t : c4) if(can1(2*n-1,t)) gc4.push_back(t);
    for(auto& t : c5) if(can1(2*n-1,t)) gc5.push_back(t);
    for(auto& t : c6) if(can1(2*n-1,t)) gc6.push_back(t);
    for(auto& t : c7) if(can1(2*n-1,t)) gc7.push_back(t);
    bool gc1 = can1(2*n-1,c1);
    swap(gc2,c2);
    swap(gc3,c3);
    swap(gc4,c4);
    swap(gc5,c5);
    swap(gc6,c6);
    swap(gc7,c7);
    int64_t res = 0;
    int lo = 0, hi = 300;
    if(a[n] != -1) lo = hi = a[n];
    for(int j = -1; j <= 10; j++) for(int k = -1; k <= 20; k++){ // previous previous, previous carries


        if((j == -1 || j-10 == 0) && (k == -1 || k-20 == 0)){
            // xxx 
            if(gc1) for(int l = max(lo,30); l <= hi; l++) add(res,dp[n-1][j+1][k+1][l-30]);
            // xxA  
            // condition is same since bonus is only contributed in the first two shots
            for(auto& t : c2) {
                int ls = t[2]-'0'; 
                for(int l = max(lo,20+ls); l <= hi; l++) add(res,dp[n-1][j+1][k+1][l-20-ls]);
            }
        }
        if((j == -1 || j-10 == 0)){
            // xA/
            for(auto& t : c3) {
                int fs = t[1]-'0';
                if(k != -1 && k-10-fs != 0) continue; 
                for(int l = max(lo,20); l <= hi; l++) add(res,dp[n-1][j+1][k+1][l-20]);
            }
        }
        // xAB
        for(auto& t : c4){
            int fs = t[1]-'0',sn = t[2]-'0';
            if(j != -1 && j-10 != 0) continue; 
            if(k != -1 && k-10-fs != 0) continue; 
            for(int l = max(lo,10+fs+sn); l <= hi; l++) add(res,dp[n-1][j+1][k+1][l-10-fs-sn]);
        }

        if(k == -1 || k-10 == 0){
            // A/x
            for(auto& t : c5) {
                int fs = t[0]-'0'; 
                if(j != -1 && j-fs != 0) continue;
                for(int l = max(lo,20); l <= hi; l++) add(res,dp[n-1][j+1][k+1][l-20]);
            }
            // A/B
            for(auto& t : c6) if(k == -1 || k-10 == 0){
                int fs = t[0]-'0',ls = t[2]-'0'; 
                if(j != -1 && j-fs != 0) continue;
                for(int l = max(lo,10+ls); l <= hi; l++) add(res,dp[n-1][j+1][k+1][l-10-ls]);
            }
        }
        // AB-
        for(auto& t : c7){
            int fs = t[0]-'0',sn = t[1]-'0'; 
            if(j != -1 && j-fs != 0) continue;
            if(k != -1 && k-fs-sn != 0) continue;
            for(int l = max(lo,fs+sn); l <= hi; l++) add(res,dp[n-1][j+1][k+1][l-fs-sn]);
        }
    }
    swap(gc2,c2);
    swap(gc3,c3);
    swap(gc4,c4);
    swap(gc5,c5);
    swap(gc6,c6);
    swap(gc7,c7);
    cout << res << "\n";
}
int main(){
    cin.tie(0)->sync_with_stdio(0);
    for(int i = 0; i <= 9; i++){
        spstr.push_back(to_string(i) + "/");
        c2.push_back("xx"+to_string(i));
        c3.push_back("x"+to_string(i)+"/");
        for(int j = 0; i+j < 10; j++){
            rgstr.push_back(to_string(i)+to_string(j));
            c4.push_back("x"+to_string(i)+to_string(j));
            c7.push_back(to_string(i)+to_string(j)+"-");
        }
        c5.push_back(to_string(i)+"/x");
        for(int j = 0; j <= 9; j++){
            c6.push_back(to_string(i)+"/"+to_string(j));
        }
    }
    int t; cin >> t; while(t--) solve();
}
// number of strs for frame: 10 + 1 + 10
// 5726805883325784576

Subtask #1
16.0 / 16.0

# Verdict Execution time Memory Grader output
1 Correct 39 ms 12884 KB Output is correct
2 Correct 39 ms 12888 KB Output is correct
3 Correct 40 ms 12884 KB Output is correct
4 Correct 37 ms 12884 KB Output is correct
5 Correct 45 ms 12884 KB Output is correct
6 Correct 42 ms 12884 KB Output is correct
7 Correct 41 ms 12820 KB Output is correct
8 Correct 38 ms 12880 KB Output is correct
9 Correct 39 ms 12836 KB Output is correct
10 Correct 40 ms 12884 KB Output is correct
11 Correct 42 ms 12884 KB Output is correct
12 Correct 44 ms 12884 KB Output is correct
13 Correct 12 ms 12892 KB Output is correct
14 Correct 41 ms 12884 KB Output is correct
15 Correct 16 ms 12892 KB Output is correct

Subtask #2
17.0 / 17.0

# Verdict Execution time Memory Grader output
1 Correct 29 ms 12828 KB Output is correct
2 Correct 42 ms 12884 KB Output is correct
3 Correct 44 ms 12884 KB Output is correct
4 Correct 44 ms 12852 KB Output is correct
5 Correct 54 ms 12884 KB Output is correct
6 Correct 54 ms 12884 KB Output is correct
7 Correct 54 ms 12884 KB Output is correct
8 Correct 45 ms 12892 KB Output is correct
9 Correct 46 ms 12884 KB Output is correct
10 Correct 59 ms 12840 KB Output is correct
11 Correct 57 ms 12884 KB Output is correct
12 Correct 56 ms 12884 KB Output is correct
13 Correct 63 ms 12884 KB Output is correct
14 Correct 56 ms 12892 KB Output is correct
15 Correct 56 ms 12884 KB Output is correct
16 Correct 50 ms 12884 KB Output is correct
17 Correct 51 ms 12884 KB Output is correct
18 Correct 62 ms 12888 KB Output is correct
19 Correct 63 ms 12884 KB Output is correct
20 Correct 68 ms 12892 KB Output is correct
21 Correct 56 ms 12884 KB Output is correct

Subtask #3
26.0 / 26.0

# Verdict Execution time Memory Grader output
1 Correct 20 ms 12804 KB Output is correct
2 Correct 44 ms 12884 KB Output is correct
3 Correct 47 ms 12884 KB Output is correct
4 Correct 50 ms 12884 KB Output is correct
5 Correct 46 ms 12884 KB Output is correct
6 Correct 55 ms 12884 KB Output is correct
7 Correct 55 ms 12884 KB Output is correct
8 Correct 49 ms 12884 KB Output is correct
9 Correct 52 ms 12844 KB Output is correct
10 Correct 53 ms 12836 KB Output is correct
11 Correct 63 ms 12868 KB Output is correct
12 Correct 48 ms 12884 KB Output is correct
13 Correct 48 ms 12756 KB Output is correct
14 Correct 49 ms 12884 KB Output is correct
15 Correct 46 ms 12884 KB Output is correct
16 Correct 49 ms 12888 KB Output is correct
17 Correct 63 ms 12896 KB Output is correct
18 Correct 42 ms 12880 KB Output is correct
19 Correct 40 ms 12816 KB Output is correct
20 Correct 39 ms 12872 KB Output is correct
21 Correct 41 ms 12864 KB Output is correct

Subtask #4
23.0 / 23.0

# Verdict Execution time Memory Grader output
1 Correct 38 ms 12756 KB Output is correct
2 Correct 50 ms 12756 KB Output is correct
3 Correct 50 ms 12884 KB Output is correct
4 Correct 46 ms 12884 KB Output is correct
5 Correct 42 ms 12884 KB Output is correct
6 Correct 44 ms 12756 KB Output is correct
7 Correct 50 ms 12864 KB Output is correct
8 Correct 46 ms 12884 KB Output is correct
9 Correct 49 ms 12872 KB Output is correct
10 Correct 56 ms 12884 KB Output is correct
11 Correct 52 ms 12784 KB Output is correct
12 Correct 51 ms 12884 KB Output is correct
13 Correct 54 ms 12756 KB Output is correct
14 Correct 55 ms 12864 KB Output is correct
15 Correct 54 ms 12864 KB Output is correct
16 Correct 44 ms 12884 KB Output is correct
17 Correct 48 ms 12884 KB Output is correct
18 Correct 44 ms 12884 KB Output is correct
19 Correct 44 ms 12888 KB Output is correct
20 Correct 42 ms 12756 KB Output is correct
21 Correct 42 ms 12756 KB Output is correct

Subtask #5
18.0 / 18.0

# Verdict Execution time Memory Grader output
1 Correct 39 ms 12884 KB Output is correct
2 Correct 39 ms 12888 KB Output is correct
3 Correct 40 ms 12884 KB Output is correct
4 Correct 37 ms 12884 KB Output is correct
5 Correct 45 ms 12884 KB Output is correct
6 Correct 42 ms 12884 KB Output is correct
7 Correct 41 ms 12820 KB Output is correct
8 Correct 38 ms 12880 KB Output is correct
9 Correct 39 ms 12836 KB Output is correct
10 Correct 40 ms 12884 KB Output is correct
11 Correct 42 ms 12884 KB Output is correct
12 Correct 44 ms 12884 KB Output is correct
13 Correct 12 ms 12892 KB Output is correct
14 Correct 41 ms 12884 KB Output is correct
15 Correct 16 ms 12892 KB Output is correct
16 Correct 29 ms 12828 KB Output is correct
17 Correct 42 ms 12884 KB Output is correct
18 Correct 44 ms 12884 KB Output is correct
19 Correct 44 ms 12852 KB Output is correct
20 Correct 54 ms 12884 KB Output is correct
21 Correct 54 ms 12884 KB Output is correct
22 Correct 54 ms 12884 KB Output is correct
23 Correct 45 ms 12892 KB Output is correct
24 Correct 46 ms 12884 KB Output is correct
25 Correct 59 ms 12840 KB Output is correct
26 Correct 57 ms 12884 KB Output is correct
27 Correct 56 ms 12884 KB Output is correct
28 Correct 63 ms 12884 KB Output is correct
29 Correct 56 ms 12892 KB Output is correct
30 Correct 56 ms 12884 KB Output is correct
31 Correct 50 ms 12884 KB Output is correct
32 Correct 51 ms 12884 KB Output is correct
33 Correct 62 ms 12888 KB Output is correct
34 Correct 63 ms 12884 KB Output is correct
35 Correct 68 ms 12892 KB Output is correct
36 Correct 56 ms 12884 KB Output is correct
37 Correct 20 ms 12804 KB Output is correct
38 Correct 44 ms 12884 KB Output is correct
39 Correct 47 ms 12884 KB Output is correct
40 Correct 50 ms 12884 KB Output is correct
41 Correct 46 ms 12884 KB Output is correct
42 Correct 55 ms 12884 KB Output is correct
43 Correct 55 ms 12884 KB Output is correct
44 Correct 49 ms 12884 KB Output is correct
45 Correct 52 ms 12844 KB Output is correct
46 Correct 53 ms 12836 KB Output is correct
47 Correct 63 ms 12868 KB Output is correct
48 Correct 48 ms 12884 KB Output is correct
49 Correct 48 ms 12756 KB Output is correct
50 Correct 49 ms 12884 KB Output is correct
51 Correct 46 ms 12884 KB Output is correct
52 Correct 49 ms 12888 KB Output is correct
53 Correct 63 ms 12896 KB Output is correct
54 Correct 42 ms 12880 KB Output is correct
55 Correct 40 ms 12816 KB Output is correct
56 Correct 39 ms 12872 KB Output is correct
57 Correct 41 ms 12864 KB Output is correct
58 Correct 38 ms 12756 KB Output is correct
59 Correct 50 ms 12756 KB Output is correct
60 Correct 50 ms 12884 KB Output is correct
61 Correct 46 ms 12884 KB Output is correct
62 Correct 42 ms 12884 KB Output is correct
63 Correct 44 ms 12756 KB Output is correct
64 Correct 50 ms 12864 KB Output is correct
65 Correct 46 ms 12884 KB Output is correct
66 Correct 49 ms 12872 KB Output is correct
67 Correct 56 ms 12884 KB Output is correct
68 Correct 52 ms 12784 KB Output is correct
69 Correct 51 ms 12884 KB Output is correct
70 Correct 54 ms 12756 KB Output is correct
71 Correct 55 ms 12864 KB Output is correct
72 Correct 54 ms 12864 KB Output is correct
73 Correct 44 ms 12884 KB Output is correct
74 Correct 48 ms 12884 KB Output is correct
75 Correct 44 ms 12884 KB Output is correct
76 Correct 44 ms 12888 KB Output is correct
77 Correct 42 ms 12756 KB Output is correct
78 Correct 42 ms 12756 KB Output is correct
79 Correct 25 ms 12884 KB Output is correct
80 Correct 47 ms 12884 KB Output is correct
81 Correct 52 ms 12884 KB Output is correct
82 Correct 45 ms 12864 KB Output is correct
83 Correct 42 ms 12884 KB Output is correct
84 Correct 45 ms 12884 KB Output is correct
85 Correct 51 ms 12892 KB Output is correct
86 Correct 46 ms 12884 KB Output is correct
87 Correct 48 ms 12884 KB Output is correct
88 Correct 58 ms 12884 KB Output is correct
89 Correct 59 ms 12844 KB Output is correct
90 Correct 66 ms 12884 KB Output is correct
91 Correct 61 ms 12884 KB Output is correct
92 Correct 45 ms 12864 KB Output is correct
93 Correct 67 ms 12884 KB Output is correct
94 Correct 81 ms 12884 KB Output is correct
95 Correct 74 ms 12884 KB Output is correct
96 Correct 90 ms 12892 KB Output is correct
97 Correct 77 ms 12884 KB Output is correct
98 Correct 72 ms 12888 KB Output is correct
99 Correct 69 ms 12756 KB Output is correct
100 Correct 75 ms 12884 KB Output is correct