Problem:
Largest Square

Given a matrix (H × W) which contains only 1 and 0, find the area of the largest square matrix which only contains 0s.

Input

H W
c1,1 c1,2 ... c1,W
c2,1 c2,2 ... c2,W
:
cH,1 cH,2 ... cH,W

In the first line, two integers H and W separated by a space character are given. In the following H lines, ci,j, elements of the H × W matrix, are given.

Output

Print the area (the number of 0s) of the largest square.

Constraints

1 ≤ H, W ≤ 1,400

Sample Input

4 5
0 0 1 0 0
1 0 0 0 0
0 0 0 1 0
0 0 0 1 0

Sample Output

4

Solution in JAVA (judge verdict: Time Limit Exceeded)


import java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStream;
import java.io.InputStreamReader;
import java.io.OutputStream;
import java.io.PrintWriter;
import java.util.InputMismatchException;
import java.util.StringTokenizer;

public class Main {

	public static void main(String[] args) throws IOException {
		InputStream inputStream = System.in;
		OutputStream outputStream = System.out;
		InputReader in = new InputReader(inputStream);
		PrintWriter out = new PrintWriter(outputStream);
		TaskX solver = new TaskX();
		solver.solve(1, in, out);
		out.close();
	}

	static int INF = 1 << 30;
	static int MOD = 1000000007;
	static int[] mh4 = { 0, -1, 1, 0 };
	static int[] mw4 = { -1, 0, 0, 1 };
	static int[] mh8 = { -1, -1, -1, 0, 0, 1, 1, 1 };
	static int[] mw8 = { -1, 0, 1, -1, 1, -1, 0, 1 };

	static class TaskX {

		int[][] sum;
		public void solve(int testNumber, InputReader in, PrintWriter out) {

			int h = in.nextInt();
			int w = in.nextInt();

			int[][] mat = new int[h+1][w+1];
			for (int i = 0; i < h; i++) {
				for (int j = 0; j < w; j++) {
					mat[i][j] = in.nextInt();
				}
			}

			sum = new int[h+1][w+1];
			for (int i = 0; i <= h; i++) {
				for (int j = 0; j <= w; j++) {
					sum[i][j] = mat[i][j];
					if (j - 1 >= 0) sum[i][j] += sum[i][j - 1];
					if (i - 1 >= 0) sum[i][j] += sum[i - 1][j];
					if (i - 1 >= 0 && j - 1 >= 0) sum[i][j] -= sum[i - 1][j - 1];
				}
			}

			int k = Math.min(h, w)-1;
			while (k >= 0) {
				for (int i = 0; i+k < h; i++) {
					for (int j = 0; j+k < w; j++) {
						if (get(i, j, i+k, j+k) == 0) {
							out.println((k+1)*(k+1));
							return;
						}
					}
				}
				k--;
			}

			out.println(0);
		}

		int get(int x1, int y1, int x2, int y2) {

			int res = sum[x2][y2];
			if (x1 > 0) res -= sum[x1 - 1][y2];
			if (y1 > 0) res -= sum[x2][y1 - 1];
			if (x1 > 0 && y1 > 0) res += sum[x1 - 1][y1 - 1];

			return res;
		}
	}

	static class InputReader {
		BufferedReader in;
		StringTokenizer tok;

		public String nextString() {
			while (!tok.hasMoreTokens()) {
				try {
					tok = new StringTokenizer(in.readLine(), " ");
				} catch (IOException e) {
					throw new InputMismatchException();
				}
			}
			return tok.nextToken();
		}

		public int nextInt() {
			return Integer.parseInt(nextString());
		}

		public long nextLong() {
			return Long.parseLong(nextString());
		}

		public double nextDouble() {
			return Double.parseDouble(nextString());
		}

		public int[] nextIntArray(int n) {
			int[] res = new int[n];
			for (int i = 0; i < n; i++) {
				res[i] = nextInt();
			}
			return res;
		}

		public long[] nextLongArray(int n) {
			long[] res = new long[n];
			for (int i = 0; i < n; i++) {
				res[i] = nextLong();
			}
			return res;
		}

		public InputReader(InputStream inputStream) {
			in = new BufferedReader(new InputStreamReader(inputStream));
			tok = new StringTokenizer("");
		}
	}

}