牛客表达式得到期望结果的组成种数

骑猪看日落 2023-06-04 14:55 16阅读 0赞

题目链接：[https://www.nowcoder.com/practice/9690bd908d5b4f9b91640fa835ef6f4f?tpId=101&tqId=33115&tPage=1&rp=1&ru=/ta/programmer-code-interview-guide&qru=/ta/programmer-code-interview-guide/question-ranking][https_www.nowcoder.com_practice_9690bd908d5b4f9b91640fa835ef6f4f_tpId_101_tqId_33115_tPage_1_rp_1_ru_ta_programmer-code-interview-guide_qru_ta_programmer-code-interview-guide_question-ranking]

### 题目大意： ###

略。

### 分析： ###

区间 dp，表达式可能不合法，此时要输出 0。

### 代码如下： ###

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1 #include <bits/stdc++.h>
      2 using namespace std;
      3  
      4 #define INIT() ios::sync_with_stdio(false);cin.tie(0);cout.tie(0);
      5 #define Rep(i,n) for (int i = 0; i < (int)(n); ++i)
      6 #define For(i,s,t) for (int i = (int)(s); i <= (int)(t); ++i)
      7 #define rFor(i,t,s) for (int i = (int)(t); i >= (int)(s); --i)
      8 #define ForLL(i, s, t) for (LL i = LL(s); i <= LL(t); ++i)
      9 #define rForLL(i, t, s) for (LL i = LL(t); i >= LL(s); --i)
     10 #define foreach(i,c) for (__typeof(c.begin()) i = c.begin(); i != c.end(); ++i)
     11 #define rforeach(i,c) for (__typeof(c.rbegin()) i = c.rbegin(); i != c.rend(); ++i)
     12  
     13 #define pr(x) cout << #x << " = " << x << "  "
     14 #define prln(x) cout << #x << " = " << x << endl
     15  
     16 #define LOWBIT(x) ((x)&(-x))
     17  
     18 #define ALL(x) x.begin(),x.end()
     19 #define INS(x) inserter(x,x.begin())
     20 #define UNIQUE(x) x.erase(unique(x.begin(), x.end()), x.end())
     21 #define REMOVE(x, c) x.erase(remove(x.begin(), x.end(), c), x.end()); // 删去 x 中所有 c 
     22 #define TOLOWER(x) transform(x.begin(), x.end(), x.begin(),::tolower);
     23 #define TOUPPER(x) transform(x.begin(), x.end(), x.begin(),::toupper);
     24  
     25 #define ms0(a) memset(a,0,sizeof(a))
     26 #define msI(a) memset(a,0x3f,sizeof(a))
     27 #define msM(a) memset(a,-1,sizeof(a))
     28 
     29 #define MP make_pair
     30 #define PB push_back
     31 #define ft first
     32 #define sd second
     33  
     34 template<typename T1, typename T2>
     35 istream &operator>>(istream &in, pair<T1, T2> &p) {
     36     in >> p.first >> p.second;
     37     return in;
     38 }
     39  
     40 template<typename T>
     41 istream &operator>>(istream &in, vector<T> &v) {
     42     for (auto &x: v)
     43         in >> x;
     44     return in;
     45 }
     46 
     47 template<typename T>
     48 ostream &operator<<(ostream &out, vector<T> &v) {
     49     Rep(i, v.size()) out << v[i] << " \n"[i == v.size() - 1];
     50     return out;
     51 }
     52  
     53 template<typename T1, typename T2>
     54 ostream &operator<<(ostream &out, const std::pair<T1, T2> &p) {
     55     out << "[" << p.first << ", " << p.second << "]" << "\n";
     56     return out;
     57 }
     58 
     59 inline int gc(){
     60     static const int BUF = 1e7;
     61     static char buf[BUF], *bg = buf + BUF, *ed = bg;
     62     
     63     if(bg == ed) fread(bg = buf, 1, BUF, stdin);
     64     return *bg++;
     65 } 
     66 
     67 inline int ri(){
     68     int x = 0, f = 1, c = gc();
     69     for(; c<48||c>57; f = c=='-'?-1:f, c=gc());
     70     for(; c>47&&c<58; x = x*10 + c - 48, c=gc());
     71     return x*f;
     72 }
     73 
     74 template<class T>
     75 inline string toString(T x) {
     76     ostringstream sout;
     77     sout << x;
     78     return sout.str();
     79 }
     80 
     81 inline int toInt(string s) {
     82     int v;
     83     istringstream sin(s);
     84     sin >> v;
     85     return v;
     86 }
     87 
     88 //min <= aim <= max
     89 template<typename T>
     90 inline bool BETWEEN(const T aim, const T min, const T max) {
     91     return min <= aim && aim <= max;
     92 }
     93 
     94 typedef unsigned int uI;
     95 typedef long long LL;
     96 typedef unsigned long long uLL;
     97 typedef vector< int > VI;
     98 typedef vector< bool > VB;
     99 typedef vector< char > VC;
    100 typedef vector< double > VD;
    101 typedef vector< string > VS;
    102 typedef vector< LL > VL;
    103 typedef vector< VI > VVI;
    104 typedef vector< VB > VVB;
    105 typedef vector< VS > VVS;
    106 typedef vector< VL > VVL;
    107 typedef vector< VVI > VVVI;
    108 typedef vector< VVL > VVVL;
    109 typedef pair< int, int > PII;
    110 typedef pair< LL, LL > PLL;
    111 typedef pair< int, string > PIS;
    112 typedef pair< string, int > PSI;
    113 typedef pair< string, string > PSS;
    114 typedef pair< double, double > PDD;
    115 typedef vector< PII > VPII;
    116 typedef vector< PLL > VPLL;
    117 typedef vector< VPII > VVPII;
    118 typedef vector< VPLL > VVPLL;
    119 typedef vector< VS > VVS;
    120 typedef map< int, int > MII;
    121 typedef unordered_map< int, int > uMII;
    122 typedef map< LL, LL > MLL;
    123 typedef map< string, int > MSI;
    124 typedef map< int, string > MIS;
    125 typedef multiset< int > mSI;
    126 typedef multiset< char > mSC;
    127 typedef set< int > SI;
    128 typedef stack< int > SKI;
    129 typedef deque< int > DQI;
    130 typedef queue< int > QI;
    131 typedef priority_queue< int > PQIMax;
    132 typedef priority_queue< int, VI, greater< int > > PQIMin;
    133 const double EPS = 1e-8;
    134 const LL inf = 0x7fffffff;
    135 const LL infLL = 0x7fffffffffffffffLL;
    136 const LL mod = 1e9 + 7;
    137 const int maxN = 3e2 + 7;
    138 const LL ONE = 1;
    139 const LL evenBits = 0xaaaaaaaaaaaaaaaa;
    140 const LL oddBits = 0x5555555555555555;
    141 
    142 int N;
    143 string str, tmp;
    144 bool tar;
    145 // dp[L][R][0/1] 表示区间[2*L, 2*R]上答案为假（真）有多少种可能 
    146 LL dp[maxN][maxN][2];
    147 
    148 bool check(string &s) {
    149     if(s.size() % 2 == 0) return false;
    150     Rep(i, s.size()) {
    151         if(i % 2) {
    152             if(s[i] != '^' && s[i] != '|' && s[i] != '&') return false;
    153         }
    154         else {
    155             if(s[i] != '0' && s[i] != '1') return false;
    156         }
    157     }
    158     return true;
    159 }
    160 
    161 int main() {
    162     //freopen("MyOutput.txt","w",stdout);
    163     //freopen("input.txt","r",stdin);
    164     INIT();
    165     cin >> str >> tmp;
    166     tar = (tmp == "true" ? 1 : 0);
    167     N = str.size();
    168     
    169     if(!check(str)) {
    170         cout << 0 << endl;
    171         return 0;
    172     }
    173     
    174     For(i, 0, N >> 1) {
    175         dp[i][i][0] = (str[i << 1] == '0');
    176         dp[i][i][1] = (str[i << 1] == '1');
    177     } 
    178     
    179     For(len, 2, (N >> 1) + 1) {
    180         For(L, 0, (N >> 1) - len + 1) {
    181             int R = L + len - 1;
    182             
    183             For(M, L, R - 1) { // 枚举 [L, M]和[M+1, R]对答案的贡献 
    184                 char op =  str[(M << 1) + 1];
    185                 
    186                 LL ZeroZero = (dp[L][M][0] * dp[M + 1][R][0]) % mod;
    187                 LL ZeroOne = (dp[L][M][0] * dp[M + 1][R][1]) % mod;
    188                 LL OneZero = (dp[L][M][1] * dp[M + 1][R][0]) % mod;
    189                 LL OneOne = (dp[L][M][1] * dp[M + 1][R][1]) % mod;
    190                 
    191                 switch(op) {
    192                     case '^':{
    193                         dp[L][R][0] = (dp[L][R][0] + ZeroZero + OneOne) % mod;
    194                         dp[L][R][1] = (dp[L][R][1] + ZeroOne + OneZero) % mod;
    195                         break;
    196                     }
    197                     case '|':{
    198                         dp[L][R][0] = (dp[L][R][0] + ZeroZero) % mod;
    199                         dp[L][R][1] = (dp[L][R][1] + OneOne + ZeroOne + OneZero) % mod;
    200                         break;
    201                     }
    202                     case '&':{
    203                         dp[L][R][0] = (dp[L][R][0] + ZeroZero + ZeroOne + OneZero) % mod;
    204                         dp[L][R][1] = (dp[L][R][1] + OneOne) % mod;
    205                         break;
    206                     }
    207                     default:{
    208                         assert(false);
    209                     }
    210                 }
    211             }
    212         }
    213     }
    214     
    215     cout << dp[0][N >> 1][tar] << endl;
    216     return 0;
    217 }

转载于:https://www.cnblogs.com/zaq19970105/p/11402873.html

[https_www.nowcoder.com_practice_9690bd908d5b4f9b91640fa835ef6f4f_tpId_101_tqId_33115_tPage_1_rp_1_ru_ta_programmer-code-interview-guide_qru_ta_programmer-code-interview-guide_question-ranking]: https://www.nowcoder.com/practice/9690bd908d5b4f9b91640fa835ef6f4f?tpId=101&tqId=33115&tPage=1&rp=1&ru=/ta/programmer-code-interview-guide&qru=/ta/programmer-code-interview-guide/question-ranking
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