【CF】259 Div.1 B Little Pony and Harmony Chest

还蛮有趣的一道状态DP的题目。

  1 /* 435B */
  2 #include <iostream>
  3 #include <string>
  4 #include <map>
  5 #include <queue>
  6 #include <set>
  7 #include <stack>
  8 #include <vector>
  9 #include <deque>
 10 #include <algorithm>
 11 #include <cstdio>
 12 #include <cmath>
 13 #include <ctime>
 14 #include <cstring>
 15 #include <climits>
 16 #include <cctype>
 17 #include <cassert>
 18 #include <functional>
 19 #include <iterator>
 20 #include <iomanip>
 21 using namespace std;
 22 //#pragma comment(linker,"/STACK:102400000,1024000")
 23
 24 #define sti                set<int>
 25 #define stpii            set<pair<int, int> >
 26 #define mpii            map<int,int>
 27 #define vi                vector<int>
 28 #define pii                pair<int,int>
 29 #define vpii            vector<pair<int,int> >
 30 #define rep(i, a, n)     for (int i=a;i<n;++i)
 31 #define per(i, a, n)     for (int i=n-1;i>=a;--i)
 32 #define clr                clear
 33 #define pb                 push_back
 34 #define mp                 make_pair
 35 #define fir                first
 36 #define sec                second
 37 #define all(x)             (x).begin(),(x).end()
 38 #define SZ(x)             ((int)(x).size())
 39 #define lson            l, mid, rt<<1
 40 #define rson            mid+1, r, rt<<1|1
 41
 42 const int maxn = 65;
 43 int mask[maxn];
 44 bool visit[maxn];
 45 int P[maxn];
 46 const int m = 16;
 47 const int N = (1<<m)+5;
 48 const int INF = 0x1f1f1f1f;
 49 int dp[105][N];
 50 int path[105][N];
 51 int a[105];
 52
 53 void init() {
 54     int i, j, k = 0;
 55
 56     for (i=2; i<maxn; ++i) {
 57         if (!visit[i]) {
 58             P[k++] = i;
 59             for (j=i*i; j<maxn; j+=i)
 60                 visit[j] = true;
 61         }
 62     }
 63
 64     for (i=1; i<maxn; ++i) {
 65         for (j=0; j<m; ++j) {
 66             if (i%P[j] == 0) {
 67                 mask[i] |= (1<<j);
 68             }
 69         }
 70     }
 71
 72     #ifndef ONLINE_JUDGE
 73         printf("P[%d] = %d\n", m, P[m]);
 74     #endif
 75 }
 76
 77 int main() {
 78     ios::sync_with_stdio(false);
 79     #ifndef ONLINE_JUDGE
 80         freopen("data.in", "r", stdin);
 81         freopen("data.out", "w", stdout);
 82     #endif
 83
 84     init();
 85     int n;
 86
 87     scanf("%d", &n);
 88     rep(i, 1, n+1)
 89         scanf("%d", &a[i]);
 90
 91     int i, j, k;
 92     int st, tmp;
 93     int mxs = 1<<16;
 94
 95     memset(dp, 0x1f, sizeof(dp));
 96     memset(dp[0], 0, sizeof(int)*N);
 97     for (i=1; i<=n; ++i) {
 98         for (j=0; j<mxs; ++j) {
 99             for (k=1; k<=60; ++k) {
100                 if (j & mask[k])
101                     continue;
102                 tmp = dp[i-1][j] + abs(a[i] - k);
103                 st = j | mask[k];
104                 if (dp[i][st] > tmp) {
105                     dp[i][st] = tmp;
106                     path[i][st] = k;
107                 }
108             }
109         }
110     }
111
112     int mn = INT_MAX, v;
113
114     for (j=0; j<mxs; ++j) {
115         if (dp[n][j] < mn) {
116             mn = dp[n][j];
117             v = j;
118         }
119     }
120
121     vi ans;
122
123     for (i=n; i>0; --i) {
124         k = path[i][v];
125         ans.pb(k);
126         v ^= mask[k];
127     }
128
129     for (i=n-1; i>=0; --i)
130         printf("%d ", ans[i]);
131     putchar(‘\n‘);
132
133     #ifndef ONLINE_JUDGE
134         printf("time = %d.\n", (int)clock());
135     #endif
136
137     return 0;
138 }