UVA1228 整数传输（贪心思维 dp）

╰半橙微兮° 2021-12-14 06:07 288阅读 0赞

## 题意：紫书P300。 ##

## 分析：紫书P300-301。 ##

## 代码： ##

#include<bits/stdc++.h>
    using namespace std;
    
    const int maxn = 64;
    
    int n, d, K[maxn];
    unsigned long long f[maxn+1][maxn+1];
    
    int zcnt = 0, ocnt = 0;
    int Z[maxn], O[maxn]; // z[i] is the i-th zero from left (0-based)
    
    // now we received i zeros and j ones. Can we receive another zero at the next time?
    bool can_receive_zero(int i, int j) {
      return i+1 <= zcnt && (j == ocnt || O[j]+d >= Z[i]);
    }
    
    bool can_receive_one(int i, int j) {
      return j+1 <= ocnt && (i == zcnt || Z[i]+d >= O[j]);
    }
    
    unsigned long long minv, maxv;
    
    void greedy() {
      minv = maxv = 0;
      int i = 0, j = 0;
      while(i < zcnt || j < ocnt) {
        if(can_receive_zero(i, j)) { i++; minv = minv * 2; }
        else { j++; minv = minv * 2 + 1; }
      }
      i = j = 0;
      while(i < zcnt || j < ocnt) {
        if(can_receive_one(i, j)) { j++; maxv = maxv * 2 + 1; }
        else { i++; maxv = maxv * 2; }
      }
    }
    
    void solve() {
      // compute Z and O
      ocnt = zcnt = 0;
      for(int i = 0; i < n; i++)
        if(K[i] == 1) O[ocnt++] = i;
        else Z[zcnt++] = i;
    
      // greedy to get minv, maxv
      greedy();
    
      // dp
      memset(f, 0, sizeof(f));
      f[0][0] = 1;
      for(int i = 0; i <= zcnt; i++)
        for(int j = 0; j <= ocnt; j++) {
          if(can_receive_zero(i, j)) f[i+1][j] += f[i][j];
          if(can_receive_one(i, j)) f[i][j+1] += f[i][j];
        }
      cout << f[zcnt][ocnt] << " " << minv << " " << maxv << "\n";
    }
    
    int main() {
      int kase = 0;
      unsigned long long k;
      while(cin >> n >> d >> k) {
        for(int i = 0; i < n; i++) {
          K[n-i-1] = k % 2; k /= 2;
        }
        cout << "Case " << ++kase << ": ";
        solve();
      }
      return 0;
    }