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Codeforces 486B OR in Matrix【水题】

2016-10-02 19:21 260 查看
B. OR in Matrix

time limit per test
1 second

memory limit per test
256 megabytes

input
standard input

output
standard output

Let's define logical OR as an operation on two logical values (i. e. values that belong to the set {0, 1})
that is equal to 1 if either or both of the logical values is set to 1,
otherwise it is 0. We can define logical OR of
three or more logical values in the same manner:


 where 

 is
equal to 1 if some ai = 1,
otherwise it is equal to 0.

Nam has a matrix A consisting of m rows
and n columns. The rows are numbered from 1 to m,
columns are numbered from 1 to n.
Element at row i (1 ≤ i ≤ m)
and column j (1 ≤ j ≤ n)
is denoted as Aij.
All elements of A are either 0 or 1. From matrix A,
Nam creates another matrix B of the same size using formula:


.

(Bij is OR of
all elements in row i and column j of
matrix A)

Nam gives you matrix B and challenges you to guess matrix A.
Although Nam is smart, he could probably make a mistake while calculating matrix B, since size of A can
be large.

Input

The first line contains two integer m and n (1 ≤ m, n ≤ 100),
number of rows and number of columns of matrices respectively.

The next m lines each contain n integers
separated by spaces describing rows of matrix B (each element of B is
either 0 or 1).

Output

In the first line, print "NO" if Nam has made a mistake when calculating B,
otherwise print "YES". If the first line is "YES", then
also print mrows consisting of n integers
representing matrix A that can produce given matrix B.
If there are several solutions print any one.

Examples

input
2 2
1 0
0 0


output
NO


input
2 3
1 1 1
1 1 1


output
YES
1 1 1
1 1 1


input
2 3
0 1 0
1 1 1


output
YES
0 0 0
0 1 0


 题意:

一个新的矩阵的元素Bij为 矩阵A的第i行和A的第j列的元素相互按位与运算的结果。现在给你一个矩阵B,求矩阵A。如果存在输出YES,就把矩阵打印出来,否则输出NO。

思路:

当矩阵元素是0的时候最为特殊,现将储存答案的矩阵置为1,遇到交叉点是0的情况就把矩阵交叉点所在的行列全部置为0。处理结束后再查一遍1的位置是否合法。

#include <map>
#include <set>
#include <cstdio>
#include <cstring>
#include <algorithm>
#include <queue>
#include <iostream>
#include <stack>
#include <cmath>
#include <string>
#include <vector>
#include <cstdlib>
//#include <bits/stdc++.h>
//#define LOACL
#define space " "
using namespace std;
//typedef long long LL;
//typedef __int64 Int;
typedef pair<int, int> paii;
const int INF = 0x3f3f3f3f;
const double ESP = 1e-5;
const double PI = acos(-1.0);
const int MOD = 1e9 + 7;
const int MAXN = 1e5;
int c[110][110], b[110][110];
int main() {
int n, m;
while (scanf("%d%d", &n, &m) != EOF) {
for (int i = 0; i < n; i++) {
for (int j = 0; j < m; j++) {
scanf("%d", &b[i][j]);
c[i][j] = 1;
}
}
for (int i = 0; i < n; i++) {
for (int j = 0; j < m; j++) {
if (!b[i][j]) {
for (int k = 0; k < m; k++) {
c[i][k] = 0;
}
for (int k = 0; k < n; k++) {
c[k][j] = 0;
}
}
}
}
bool flag;
for (int i = 0; i < n; i++) {
for (int j = 0; j < m; j++) {
flag = false;
if (b[i][j]) {
flag = true;
for (int k = 0; k < m; k++) {
if (c[i][k]) flag = false;
}
for (int k = 0; k < n; k++) {
if (c[k][j]) flag = false;
}
}
if (flag) break;
}
if (flag) break;
}
if (flag) printf("NO\n");
else {
printf("YES\n");
for (int i = 0; i < n; i++) {
for (int j = 0; j < m - 1; j++) {
printf("%d ", c[i][j]);
}
printf("%d\n", c[i][m - 1]);
}
}
}
return 0;
}
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