[POJ1050]To the Max（最大子矩阵，DP）

Posted 2020-07-26

题目链接：http://poj.org/problem?id=1050

发现这个题没有写过题解，现在补上吧，思路挺经典的。

思路就是枚举所有的连续的连续的行，比如1 2 3 4 12 23 34 45 123 234 345...然后把这些行对应列相加缩成一行，之后就是求最大子序列和了。

  1     /*
  2 ━━━━━┒ギリギリ♂ eye！
  3 ┓┏┓┏┓┃キリキリ♂ mind！
  4 ┛┗┛┗┛┃＼○／
  5 ┓┏┓┏┓┃ /
  6 ┛┗┛┗┛┃ノ)
  7 ┓┏┓┏┓┃
  8 ┛┗┛┗┛┃
  9 ┓┏┓┏┓┃
 10 ┛┗┛┗┛┃
 11 ┓┏┓┏┓┃
 12 ┛┗┛┗┛┃
 13 ┓┏┓┏┓┃
 14 ┃┃┃┃┃┃
 15 ┻┻┻┻┻┻
 16 */
 17 #include <algorithm>
 18 #include <iostream>
 19 #include <iomanip>
 20 #include <cstring>
 21 #include <climits>
 22 #include <complex>
 23 #include <fstream>
 24 #include <cassert>
 25 #include <cstdio>
 26 #include <bitset>
 27 #include <vector>
 28 #include <deque>
 29 #include <queue>
 30 #include <stack>
 31 #include <ctime>
 32 #include <set>
 33 #include <map>
 34 #include <cmath>
 35 using namespace std;
 36 #define fr first
 37 #define sc second
 38 #define cl clear
 39 #define BUG puts("here!!!")
 40 #define W(a) while(a--)
 41 #define pb(a) push_back(a)
 42 #define Rint(a) scanf("%d", &a)
 43 #define Rll(a) scanf("%lld", &a)
 44 #define Rs(a) scanf("%s", a)
 45 #define Cin(a) cin >> a
 46 #define FRead() freopen("in", "r", stdin)
 47 #define FWrite() freopen("out", "w", stdout)
 48 #define Rep(i, len) for(int i = 0; i < (len); i++)
 49 #define For(i, a, len) for(int i = (a); i < (len); i++)
 50 #define Cls(a) memset((a), 0, sizeof(a))
 51 #define Clr(a, x) memset((a), (x), sizeof(a))
 52 #define Full(a) memset((a), 0x7f7f7f, sizeof(a))
 53 #define lrt rt << 1
 54 #define rrt rt << 1 | 1
 55 #define pi 3.14159265359
 56 #define RT return
 57 #define lowbit(x) x & (-x)
 58 #define onenum(x) __builtin_popcount(x)
 59 typedef long long LL;
 60 typedef long double LD;
 61 typedef unsigned long long ULL;
 62 typedef pair<int, int> pii;
 63 typedef pair<string, int> psi;
 64 typedef pair<LL, LL> pll;
 65 typedef map<string, int> msi;
 66 typedef vector<int> vi;
 67 typedef vector<LL> vl;
 68 typedef vector<vl> vvl;
 69 typedef vector<bool> vb;
 70 
 71 const int maxn = 110;
 72 int G[maxn][maxn];
 73 int n;
 74 int dp[maxn];
 75 
 76 int lss() {
 77     int tmp = -0x7f7f7f, ret = -0x7f7f7f;
 78     For(i, 1, n+1) {
 79         if(tmp > 0) tmp += dp[i];
 80         else tmp = dp[i];
 81         ret = max(tmp, ret);
 82     }
 83     return ret;
 84 }
 85 
 86 int main() {
 87     // FRead();
 88     while(~Rint(n)) {
 89         For(i, 1, n+1) For(j, 1, n+1) Rint(G[i][j]);
 90         int ret = 0;
 91         For(i, 1, n+1) {
 92             Cls(dp);
 93             For(j, i, n+1) {
 94                 For(k, 1, n+1) dp[k] += G[j][k];
 95                 ret = max(ret, lss());
 96             }
 97         }
 98         printf("%d\n", ret);
 99     }
100     RT 0;
101 }