2666. Half

Fill an array n × n in the next way: secondary diagonal contains zeros, all cells above it contains twos and all cells below it contains ones.

Input. One positive integer n (n ≤ 20).

Output. Print the array filled like described above.

Sample input	Sample output
3	220 201 011

SOLUTION

arrays

Algorithm analysis

Fill a two dimensional array using a double loop as indicated in the problem statement.

The cell (i, j) lies:

· on the secondary diagonal, if i + j = n – 1;

· below the secondary diagonal, if i + j > n – 1;

· above the secondary diagonal, if i + j < n – 1;

Algorithm realization

Declare the two dimentional array.

#define MAX 30

int m[MAX][MAX];

Read the input data. Fill the array.

scanf("%d",&n);

for(i = 0; i < n; i++)

for(j = 0; j < n; j++)

if (i + j == n - 1) m[i][j] = 0; else

if (i + j < n - 1) m[i][j] = 2; else m[i][j] = 1;

Print the two dimensional array.

for(i = 0; i < n; i++)

{

for(j = 0; j < n; j++)

printf("%d",m[i][j]);

printf("\n");

}

Algorithm realization – double pointer

#include <stdio.h>

int **m;

int i, j, n;

int main(void)

{

scanf("%d", &n);

m = new int* [n];

for (i = 0; i < n; i++)

m[i] = new int[n];

for (i = 0; i < n; i++)

for (j = 0; j < n; j++)

if (i + j == n - 1) m[i][j] = 0; else

if (i + j < n - 1) m[i][j] = 2; else m[i][j] = 1;

for (i = 0; i < n; i++)

{

for (j = 0; j < n; j++)

printf("%d", m[i][j]);

printf("\n");

}

delete[] m;

return 0;

}

Algorithm realization – calloc

#include <stdio.h>

#include <malloc.h>

int **m;

int i, j, n;

int main(void)

{

scanf("%d", &n);

m = (int**)calloc(n, sizeof(int*));

for (i = 0; i < n; i++)

m[i] = (int*)calloc(n, sizeof(int));

for (i = 0; i < n; i++)

for (j = 0; j < n; j++)

if (i + j == n - 1) m[i][j] = 0; else

if (i + j < n - 1) m[i][j] = 2; else m[i][j] = 1;

for (i = 0; i < n; i++)

{

for (j = 0; j < n; j++)

printf("%d", m[i][j]);

printf("\n");

}

for (i = 0; i < n; i++)

free(m[i]);

free(m);

return 0;

}

Java realization

import java.util.*;

public class Main

{

public static void main(String[] args)

{

Scanner con = new Scanner(System.in);

int n = con.nextInt();

int m[][] = new int[n][n];

for(int i = 0; i < n; i++)

for(int j = 0; j < n; j++)

if (i + j == n - 1) m[i][j] = 0; else

if (i + j < n - 1) m[i][j] = 2; else m[i][j] = 1;

for(int i = 0; i < n; i++)

{

for(int j = 0; j < n; j++)

System.out.print(m[i][j]);

System.out.println();

}

con.close();

}

}

Java realization – two dimensional ArrayList

import java.util.*;

public class Main

{

public static void main(String[] args)

{

Scanner con = new Scanner(System.in);

int n = con.nextInt();

ArrayList<ArrayList<Integer>> m =

new ArrayList<ArrayList<Integer>>();

for(int i = 0; i < n; i++)

m.add(new ArrayList<Integer>());

for(int i = 0; i < n; i++)

for(int j = 0; j < n; j++)

if (i + j == n - 1) m.get(i).add(0); else

if (i + j < n - 1) m.get(i).add(2); else m.get(i).add(1);

for(int i = 0; i < n; i++)

{

for(int j = 0; j < n; j++)

System.out.print(m.get(i).get(j));

System.out.println();

}

con.close();

}

}

Java realization – array of ArrayList

import java.util.*;

public class Main

{

public static void main(String[] args)

{

Scanner con = new Scanner(System.in);

int n = con.nextInt();

ArrayList<Integer>[] m = new ArrayList[n];

for(int i = 0; i < n; i++)

m[i] = new ArrayList<Integer>();

for(int i = 0; i < n; i++)

for(int j = 0; j < n; j++)

if (i + j == n - 1) m[i].add(0); else

if (i + j < n - 1) m[i].add(2); else m[i].add(1);

for(int i = 0; i < n; i++)

{

for(int j = 0; j < n; j++)

System.out.print(m[i].get(j));

System.out.println();

}

con.close();

}

}

Python realization

n = int(input())

def char(i, j):

if i < j:

return '2'

if i == j:

return '0'

return '1'

for i in range(n):

print (''.join(reversed([char(i,j) for j in range(n)])))

Python realization – build a matrix

n = int(input())

def char(i, j):

if i + j < n - 1:

return '2'

elif i + j == n - 1:

return '0'

else: return '1'

a = []

for i in range(n):

a.append(''.join([char(i,j) for j in range(n)]))

for i in range(n):

print(a[i])