HDU 2859 Phalanx DP

题目链接：http://acm.hdu.edu.cn/showproblem.php?pid=2859

题目大意：求一个矩阵的按反对角线对称的子矩阵的行最大值。

解题思路：dp[i][j]:=以(i,j)为左下角起点的满足条件的矩阵的行最大值，那么将第一行和最后一列初始化为1之后从第0行第n-1列倒着初始化即可。

代码：

const int maxn = 1e3 + 100;
int n;
char maze[maxn][maxn];
int dp[maxn][maxn]; 

void init(){
    memset(dp, 0, sizeof(dp));
    for(int i = 0; i < n; i++){
        dp[0][i] = 1;
        dp[i][n - 1] = 1;
    }
}
void solve(){
    int ans = 1;
    for(int i = 1; i < n; i++){
        for(int j = n - 2; j >= 0; j--){
            int tmp = dp[i - 1][j + 1], cnt = 1;
            for(int k = 1; k <= tmp; k++)
                if(maze[i - k][j] == maze[i][j + k]) cnt++;
                else break;
            dp[i][j] = cnt;
            ans = max(ans, dp[i][j]);
        }
    }
    printf("%d
", ans);
}

int main(){
    while(scanf("%d", &n) && n){
        for(int i = 0; i < n; i++)
            scanf("%s", maze[i]);
        init();
        solve();
    }
}

题目：

Phalanx

Time Limit: 10000/5000 MS (Java/Others)    Memory Limit: 32768/32768 K (Java/Others)
Total Submission(s): 1988    Accepted Submission(s): 988

Problem Description

Today is army day, but the servicemen are busy with the phalanx for the celebration of the 60th anniversary of the PRC.
A phalanx is a matrix of size n*n, each element is a character (a~z or A~Z), standing for the military branch of the servicemen on that position.
For some special requirement it has to find out the size of the max symmetrical sub-array. And with no doubt, the Central Military Committee gave this task to ALPCs.
A symmetrical matrix is such a matrix that it is symmetrical by the “left-down to right-up” line. The element on the corresponding place should be the same. For example, here is a 3*3 symmetrical matrix:
cbx
cpb
zcc

 

Input

There are several test cases in the input file. Each case starts with an integer n (0<n<=1000), followed by n lines which has n character. There won’t be any blank spaces between characters or the end of line. The input file is ended with a 0.

 

Output

Each test case output one line, the size of the maximum symmetrical sub- matrix.

 

Sample Input

3 abx cyb zca 4 zaba cbab abbc cacq 0

 

Sample Output

3 3

 

Source

2009 Multi-University Training Contest 5 - Host by NUDT