GRIDXOR - Editorial

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PROBLEM LINK:

Practice
Div-3 Contest
Div-2 Contest
Div-1 Contest

Author: Vishesh Saraswat
Tester: Istvan Nagy
Editorialist: Harshikaa Agrawal

Difficulty:

Simple

Prerequisites:

Bitwise operations

Problem:

Given an integer N, print an N \times N matrix such that the bitwise XOR of each row, column and diagonal is the same.

Explanation:

The bitwise XOR for each row, column and diagonal would be the same if all elements of the N \times N matrix are the same.

image
image992Ă—283 6 KB

Given that 0\oplus0 is 0 and 1\oplus1 is 0, when N is even the value would be 0 if all values are the same.

Example: N = 4
We choose 5 as the number we output.

image
image967Ă—290 8.47 KB

When N is odd, it means that N-1 is even and thus, the value for (N-1)+1 times is the number itself.

Example: N = 5
We choose 5 as the number we output.

image
image982Ă—341 9.19 KB

Thus, output the same number (which is ≤ 10^9) in the entire N \times N grid.

Time Complexity:

O(N^2) for each test case

Setter’s Solution

Setter's Solution 
#include "bits/stdc++.h"
using namespace std;
/*
#include <ext/pb_ds/assoc_container.hpp>
using namespace __gnu_pbds;
using ordered_set = tree<int, null_type, less<int>, rb_tree_tag, tree_order_statistics_node_update>;
*/

#define all(x) begin(x), end(x)
#define rall(x) rbegin(x), rend(x)
#define sz(x) (int)(x).size()

using ll = long long;
const int mod = 1e9+7;

void solve(int tc) {
    int n;
    cin >> n;
    for (int i = 0; i < n; ++i) {
        for (int j = 0; j < n; ++j) {
            cout << 1;
            if (j < n-1)
                cout << " ";
        }
        cout << '\n';
    }
}

signed main() {
    cin.tie(0)->sync_with_stdio(0);
    int tc = 1;
    cin >> tc;
    for (int i = 1; i <= tc; ++i) solve(i);
    return 0;
}

Tester’s Solution

Tester's Solution 
#include <iostream>
#include <algorithm>
#include <string>
#include <assert.h>
using namespace std;
 
long long readInt(long long l,long long r,char endd){
	long long x=0;
	int cnt=0;
	int fi=-1;
	bool is_neg=false;
	while(true){
		char g=getchar();
		if(g=='-'){
			assert(fi==-1);
			is_neg=true;
			continue;
		}
		if('0'<=g && g<='9'){
			x*=10;
			x+=g-'0';
			if(cnt==0){
				fi=g-'0';
			}
			cnt++;
			assert(fi!=0 || cnt==1);
			assert(fi!=0 || is_neg==false);
			
			assert(!(cnt>19 || ( cnt==19 && fi>1) ));
		} else if(g==endd){
			assert(cnt>0);
			if(is_neg){
				x= -x;
			}
			assert(l<=x && x<=r);
			return x;
		} else {
			assert(false);
		}
	}
}

string readString(int l,int r,char endd){
	string ret="";
	int cnt=0;
	while(true){
		char g=getchar();
		assert(g!=-1);
		if(g==endd){
			break;
		}
		cnt++;
		ret+=g;
	}
	assert(l<=cnt && cnt<=r);
	return ret;
}
long long readIntSp(long long l,long long r){
	return readInt(l,r,' ');
}
long long readIntLn(long long l,long long r){
	return readInt(l,r,'\n');
}
string readStringLn(int l,int r){
	return readString(l,r,'\n');
}
string readStringSp(int l,int r){
	return readString(l,r,' ');
}

int main(){
	int T = readIntLn(1, 100);
	for(int tc = 0; tc < T; ++tc)
	{
		int N = readIntLn(1, 100);
		for (int i = 0; i < N; ++i)
		{
			for (int j = 0; j < N; ++j)
			{
				printf("1 ");
			}
			printf("\n");
		}
	}
	assert(getchar()==-1);
}

Editorialist’s solution:

Editorialist's Solution 
#include <bits/stdc++.h>
using namespace std;

int main() {
    int t;
    cin>>t;
    while(t--)
    {
        int n; 
        cin>>n;
        for(int i = 0; i < n; i++)
        {
            for(int j = 0; j < n; j++)
            {
                cout<<1<<" ";
            }
            cout<<"\n";
        }
    }
    return 0;
}

The event is a part of our annual tech symposium Exun 2021-22, powered by Athena Education.

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