**Beautiful 3 Set**

### Problem Statement :

You are given an integer n. A set, S, of triples (xi,yi,zi) is beautiful if and only if: 0 <= xi,yi,zi xi+yi+zi = n, for all i : 1 <= i <= |S| Let X be the set of different xi's in S, Y be the set of different yi's in S, and Z be the set of different zi in S. Then |X| = |Y| = |Z| = |S|. The third condition means that all xi's are pairwise distinct. The same goes for yi and zi. Given , find any beautiful set having a maximum number of elements. Then print the cardinality of (i.e., ) on a new line, followed by lines where each line contains space-separated integers describing the respective values of , , and . Input Format A single integer, n. Constraints 1 <= n <= 300 Output Format On the first line, print the cardinality of S (i.e., |S|). For each of the |S| subsequent lines, print three space-separated numbers per line describing the respective values of xi, yi, and zi for triple i in S.

### Solution :

` ````
Solution in C :
In C++ :
#include <cmath>
#include <cstdio>
#include <vector>
#include <iostream>
#include <algorithm>
using namespace std;
int main() {
int N;
cin >> N;
if (N == 1){
cout << "1\n0 0 1\n";
} else if (N == 2){
cout << "2\n0 0 2\n1 1 0\n";
} else if (N == 3){
cout << "3\n0 1 2\n2 0 1\n1 2 0\n";
} else if (N == 4){
cout << "3\n0 0 4\n1 1 2\n2 2 0\n";
} else {
if (N % 3 == 0){
int h = N/3*2+1;
cout << h << "\n";
for (int i=0; i<h; i++){
cout << i << ' ' << (N/3+i)%h << ' ' << (N - i - (N/3+i)%h) << '\n';
}
} else if (N % 3 == 2){
int h = N-N/3;
cout << h << "\n0 0 " << N << "\n";
for (int i=1; i<h; i++){
int m = i <= h/2 ? (i + N/3) : (i - N/3 - 1);
cout << i << ' ' << m << ' ' << (N-i-m) << "\n";
}
} else {
int h = N-N/3;
cout << h << "\n0 0 " << N << "\n1 1 " << N-2 << "\n";
for (int i=1; i<=N/3; i++){
cout << i+1 << ' ' << i+N/3 << ' ' << N - (i+1) - (i+N/3) << '\n';
}
for (int i=1; i<N/3; i++){
cout << i+N/3+1 << ' ' << i+1 << ' ' << N - (i+N/3+1) - (i+1) << '\n';
}
}
}
return 0;
}
In Java :
import java.io.*;
import java.util.*;
import java.text.*;
import java.math.*;
import java.util.regex.*;
public class Solution {
public static void main(String[] args) {
Scanner sc = new Scanner(System.in);
int n = sc.nextInt();
int max = n/3*2;
if (n%3==2)
max++;
int sn = n;
if (n%3==1)
sn--;
System.out.println(max+1);
int first = max;
for (int i = (max+1)/2; i >= 0; i--) {
System.out.println(first+" "+i+" "+(n-i-first));
first--;
}
for (int i = sn-first-1; first >= 0; i--) {
System.out.println(first+" "+i+" "+(n-i-first));
first--;
}
}
}
In C :
#include <stdio.h>
#include <stdlib.h>
int main() {
int n, k, r, **S, i, q;
scanf("%d",&n);
k = (2*n)/3;
r = (2*n)%3;
S = malloc(sizeof(int*)*k);
switch ( r ) {
case 0:
for (i=0; i<=k/2; i++) {
S[i] = malloc(sizeof(int)*3);
S[i][0] = i;
S[i][1] = k-2*i;
S[i][2] = k/2+i;
}
for (i=k/2+1; i<=k; i++) {
S[i] = malloc(sizeof(int)*3);
S[i][0] = i;
S[i][1] = 2*(k-i)+1;
S[i][2] = i-k/2-1;
}
break;
case 2:
for (i=0; i<=k/2; i++) {
S[i] = malloc(sizeof(int)*3);
S[i][0] = i;
S[i][1] = k-2*i;
S[i][2] = k/2+i+1;
}
for (i=k/2+1; i<=k; i++) {
S[i] = malloc(sizeof(int)*3);
S[i][0] = i;
S[i][1] = 2*(k-i)+1;
S[i][2] = i-k/2;
}
break;
case 1:
q = k/2;
for (i=0; i<=q; i++) {
S[i] = malloc(sizeof(int)*3);
S[i][0] = i;
S[i][1] = k-2*i;
S[i][2] = q+i+1;
}
for (i=q+1; i<=k; i++) {
S[i] = malloc(sizeof(int)*3);
S[i][0] = i+1;
S[i][1] = 2*(k-i);
S[i][2] = i-q-1;
}
break;
default:
break;
}
printf("%d\n",k+1);
for (i=0; i<=k; i++)
printf("%d %d %d\n", S[i][0], S[i][1], S[i][2]);
return 0;
}
In Python3 :
n = int(input().strip())
low = n // 3
high = 2 * n // 3
print(high + 1)
for i in range(low+1):
print(i, 2*(low-i), n+i-2*low)
for j in range(low+1, high+1):
print(j, 2*(high-j)+1, n+j-1-2*high)
```

## View More Similar Problems

## Counting On a Tree

Taylor loves trees, and this new challenge has him stumped! Consider a tree, t, consisting of n nodes. Each node is numbered from 1 to n, and each node i has an integer, ci, attached to it. A query on tree t takes the form w x y z. To process a query, you must print the count of ordered pairs of integers ( i , j ) such that the following four conditions are all satisfied: the path from n

View Solution →## Polynomial Division

Consider a sequence, c0, c1, . . . , cn-1 , and a polynomial of degree 1 defined as Q(x ) = a * x + b. You must perform q queries on the sequence, where each query is one of the following two types: 1 i x: Replace ci with x. 2 l r: Consider the polynomial and determine whether is divisible by over the field , where . In other words, check if there exists a polynomial with integer coefficie

View Solution →## Costly Intervals

Given an array, your goal is to find, for each element, the largest subarray containing it whose cost is at least k. Specifically, let A = [A1, A2, . . . , An ] be an array of length n, and let be the subarray from index l to index r. Also, Let MAX( l, r ) be the largest number in Al. . . r. Let MIN( l, r ) be the smallest number in Al . . .r . Let OR( l , r ) be the bitwise OR of the

View Solution →## The Strange Function

One of the most important skills a programmer needs to learn early on is the ability to pose a problem in an abstract way. This skill is important not just for researchers but also in applied fields like software engineering and web development. You are able to solve most of a problem, except for one last subproblem, which you have posed in an abstract way as follows: Given an array consisting

View Solution →## Self-Driving Bus

Treeland is a country with n cities and n - 1 roads. There is exactly one path between any two cities. The ruler of Treeland wants to implement a self-driving bus system and asks tree-loving Alex to plan the bus routes. Alex decides that each route must contain a subset of connected cities; a subset of cities is connected if the following two conditions are true: There is a path between ever

View Solution →## Unique Colors

You are given an unrooted tree of n nodes numbered from 1 to n . Each node i has a color, ci. Let d( i , j ) be the number of different colors in the path between node i and node j. For each node i, calculate the value of sum, defined as follows: Your task is to print the value of sumi for each node 1 <= i <= n. Input Format The first line contains a single integer, n, denoti

View Solution →