[luoguP1005] 矩阵取数游戏（DP + 高精度）

  1 #include <cstdio>
  2 #include <cstring>
  3 #include <iostream>
  4 
  5 struct Big_int
  6 {
  7     int s[35], idx;
  8     Big_int()
  9     {
 10         idx = 0;
 11         memset(s, 0, sizeof(s));
 12     }
 13 };
 14 
 15 int n, m;
 16 Big_int ans, a[81], f[81][81];
 17 
 18 inline void clear(Big_int &x)
 19 {
 20     x.idx = 0;
 21     memset(x.s, 0, sizeof(x.s));
 22 }
 23 
 24 inline Big_int Big(int x)
 25 {
 26     Big_int ret;
 27     while(x)
 28     {
 29         ret.s[ret.idx] = x % 10;
 30         x /= 10;
 31         ret.idx++;
 32     }
 33     return ret;
 34 }
 35 
 36 inline bool operator > (const Big_int x, const Big_int y)
 37 {
 38     int i;
 39     if(x.idx > y.idx) return 1;
 40     else if(x.idx < y.idx) return 0;
 41     else for(i = x.idx - 1; i >= 0; i--)
 42         if(x.s[i] > y.s[i]) return 1;
 43         else if(x.s[i] < y.s[i]) return 0;
 44 }
 45 
 46 inline Big_int Max(const Big_int x, const Big_int y)
 47 {
 48     return x > y ? x : y;
 49 }
 50 
 51 inline int max(int x, int y)
 52 {
 53     return x > y ? x : y;
 54 }
 55 
 56 inline Big_int operator + (const Big_int x, const Big_int y)
 57 {
 58     int i;
 59     Big_int ret;
 60     ret.idx = max(x.idx, y.idx) + 1;
 61     for(i = 0; i < ret.idx; i++)
 62     {
 63         ret.s[i] += x.s[i] + y.s[i];
 64         ret.s[i + 1] += ret.s[i] / 10;
 65         ret.s[i] %= 10;
 66     }
 67     while(!ret.s[ret.idx - 1] && ret.idx > 1) ret.idx--;
 68     return ret;
 69 }
 70 
 71 inline Big_int operator * (const Big_int x, const Big_int y)
 72 {
 73     int i, j;
 74     Big_int ret;
 75     ret.idx = x.idx + y.idx;
 76     for(i = 0; i < x.idx; i++)
 77         for(j = 0; j < y.idx; j++)
 78         {
 79             ret.s[i + j] += x.s[i] * y.s[j];
 80             ret.s[i + j + 1] += ret.s[i + j] / 10;
 81             ret.s[i + j] %= 10;
 82         }
 83     while(!ret.s[ret.idx - 1] && ret.idx > 1) ret.idx--;
 84     return ret;
 85 }
 86 
 87 inline void print(const Big_int x)
 88 {
 89     int i;
 90     if(!x.idx) printf("0");
 91     else for(i = x.idx - 1; i >= 0; i--) printf("%d", x.s[i]);
 92     puts("");
 93 }
 94 
 95 inline int read()
 96 {
 97     int x = 0, f = 1;
 98     char ch = getchar();
 99     for(; !isdigit(ch); ch = getchar()) if(ch == ‘-‘) f = -1;
100     for(; isdigit(ch); ch = getchar()) x = (x << 1) + (x << 3) + ch - ‘0‘;
101     return x * f;
102 }
103 
104 inline Big_int dp(int x, int y, Big_int z)
105 {
106     if(f[x][y].idx) return f[x][y];
107     if(x == y) return f[x][y] = a[x] * z;
108     else return f[x][y] = Max(dp(x + 1, y, z * Big(2)) + a[x] * z, dp(x, y - 1, z * Big(2)) + a[y] * z);
109 }
110 
111 int main()
112 {
113     int i, j;
114     n = read();
115     m = read();
116     while(n--)
117     {
118         for(i = 1; i <= m; i++) a[i] = Big(read());
119         for(i = 1; i <= m; i++)
120             for(j = 1; j <= m; j++)
121                 clear(f[i][j]);
122         ans = ans + dp(1, m, Big(2));
123     }
124     print(ans);
125     return 0;
126 }