# 24 - lexicographic permutations

A permutation is an ordered arrangement of objects. For example, 3124 is one possible per-mutation of the digits 1, 2, 3 and 4. If all of the permutations are listed numerically or alpha-betically, we call it lexicographic order. The lexicographic permutations of 0, 1 and 2 are:

``````012   021   102   120   201   210
``````

What is the millionth lexicographic permutation of the digits 0, 1, 2, 3, 4, 5, 6, 7, 8 and 9?

cevap : 2783915460

Derleme ortami Visual studio community c++

``````// project euler problem 24
// yasin tasan --> apr 2018
#include "stdafx.h"
#include <iostream>     // std::cout
#include <algorithm>    // std::next_permutation, std::sort
#include <string>

using namespace std;
void fact(unsigned int *n, unsigned int *fact);
void assign(unsigned int *j, unsigned int **matrix, unsigned int array, unsigned int *array_length);

int main() {
unsigned int array[] = { 0,1,2,3,4,5,6,7,8,9};
unsigned int array_length = (sizeof(array) / sizeof(*array));
unsigned int total_permutation = 1;

printf("list of digits = ");
for (size_t i = 0; i < array_length; i++)
{
printf("%d ", array[i]);
}
printf("\n");

fact(&array_length, &total_permutation); // factorial calculation for total permutation number

unsigned int **matrix = (unsigned int **)malloc(total_permutation * sizeof(unsigned int*)); // total_permutation aslinda matrix'in line sayisi

for (size_t i = 0; i < total_permutation; i++)
{
matrix[i] = (unsigned int*)malloc(array_length * sizeof(unsigned int)); // array_length aslinda matrix'in column sayisi
}

sort(array, array + array_length); // permutation list sorting

unsigned int j = 0;
do {
assign(&j, matrix, array, &array_length);
j++;
} while (next_permutation(array, array + array_length));

unsigned int counter = 0; // for line break

for (size_t i = 0; i < total_permutation; i++)
{
counter = 0;
printf("%d. permutation = ", i);
for (size_t j = 0; j < array_length; j++)
{
printf("%d", matrix[i][j]);
counter++;
if (counter % array_length == 0)
{
printf("\n");
if (i == 999999) // print 1000000. permutation
{
i=total_permutation; // break
}
}
}
}

return 0;
}

// factorial calculation for total permutation number
void fact(unsigned int *n, unsigned int *fact)
{
for (unsigned int i = 1; i <= *n; ++i)
{
*fact *= i; // factorial = factorial*i;
}
}

// array assign to matrix (matrix)
void assign(unsigned int *j, unsigned int **matrix, unsigned int array, unsigned int *array_length)
{
for (size_t i = 0; i < *array_length; i++)
{
matrix[*j][i] = array[i];
}
}
``````