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I was tring to solve this question, "You are given an integer N. Consider the sequence containing the integers {1, 2,....,N} in increasing order (each exactly once). Find the maximum length of its contiguous subsequence with an even sum.
This is the code that I came up with,
#include <stdio.h>
int Nsum(int n);
int main(void) {
int t, n;
scanf("%d", &t);
while(t--)
{
scanf("%d", &n);
int z = Nsum(n);
printf("%d\n", z);
// printf("%d\n", sum);
}
return 0;
}
int Nsum(int n) {
int count = 0;
int sum = 0;
for(int i = 1; i <= n; i++)
{
sum = sum + i;
count++;
}
if (sum % 2 == 0)
{
return count;
}
else (Nsum(n - 1));
}
Consider these cases:
N
Sequence
Sum of elements
A maximum subsequence with even sum
Its length
0
{ }
0
{ 0 }
0
1
{ 1 }
1
{ }
0
2
{ 1, 2 }
3
{ 2 }
1
3
{ 1, 2, 3 }
6
{ 1, 2, 3 }
3
4
{ 1, 2, 3, 4
10
{ 1, 2, 3, 4
4
5
{ 1, 2, 3, 4, 5 }
15
{ 2, 3, 4, 5 }
4
6
{ 1, 2, 3, 4, 5, 6 }
21
{ 2, 3, 4, 5, 6 }
5
7
{ 1, 2, 3, 4, 5, 6, 7 }
28
{ 1, 2, 3, 4, 5, 6, 7 }
7
We can easily see patterns here. One pattern is that when the sum is even, the whole sequence { 1,… N } is the maximum subsequence with an even sum, and, when the sum is odd, chopping off the 1 to make { 2,… N } gives a maximum subsequence with an even sum.
Another pattern is that whenever N is even, the parity (evenness/oddness) of the sum of { 1,… N } stays the same from the previous N, since adding an even number does not change it. Whenever N is odd, the parity changes. So, the pattern is:
N’s parity
Sum’s parity
even
stay the same
odd
changes
even
say the same
odd
changes
It takes two changes to bring parity back to what it was. Two changes occur every two odd numbers, so they occur every four steps. Therefore, the parity of the sum goes through a fully cycle as N goes through four values. So the remainder of N modulo four tells us where we are in the cycle:
N % 4
Parity of sum
Length of a maximum subsequence
0
even
N
1
odd
N−1
2
odd
N−1
3
even
N
Therefore, Nsum may be implemented:
int Nsum(int N)
{
switch (N % 4)
{
case 0: return N;
case 1: return N-1;
case 2: return N-1;
case 3: return N;
}
}
(Note that negative N are not handled.)
Declare an array containing these number and print the evens numbers and odd numbers
Now I initialized an array that containing 11 integers.
Here is my code
#include <stdio.h>
int main(void) {
int nums[11] = {11,3,9,7,6,10,13,17,2,8,3}; // create an variables that store integers
int evens[11] = {0}; // initialized an array to store even numbers
int odds[11] = {0}; // initialized an array to store even numbers
int length = sizeof(nums) / sizeof(nums[0]); // get the length of nums
int nums_index = 0;
int evens_index = 0;
int odds_index = 0;
for (nums_index; nums_index < length;nums_index++) {
if (nums[nums_index] % 2 == 0) {
evens[evens_index] = nums[nums_index];
evens_index++;
}
else if(nums[nums_index] % 2 != 0) {
odds[odds_index] = nums[nums_index];
odds_index++;
}
printf("%d\n",evens[evens_index]);
printf("%d\n",odds[odds_index]);
}
return 0;
}
The major question is whether the output has problems when I compile my code.
The output is ：0 11 0 3 0 9 0 7 6 0 10 0 0 13 0 17 2 0 8 0 0 3
Why it could happened?
Thank you all.
You need separate indexing for each array, advancing the index for evens and odds only when nums[i] value is one of the two.
Otherwise you would get sort of a copy of nums with zeroes in place of those numbers of the opposite type (odd/even).
For instance:
int j = 0;
int k = 0;
for (int i = 0; i < length; i++) {
if (nums[i] % 2 == 0) {
evens[j] = nums[i];
j++;
}
else if(nums[i] % 2 != 0) {
odds[k] = nums[i];
k++;
}
printf("%d\n",evens[i]);
printf("%d\n",odds[i]);
}
This will compose the arrays like:
11 3 9 7 13 17 3 0 0 0 0 --- for odds
6 10 2 8 0 0 0 0 0 0 0 0 --- for evens
The second problem is that you are printing inside the loop, firstly a value from evens and immediately after a value for odds.
So if you want to display them nice and separate, you can move both printf outside the first loop, then looping again on each result array for displaying it completely, before proceding to the other.
#include <stdio.h>
void PrintNumbers(int*, int);
int main(void) {
int nums[11] = {11,3,9,7,6,10,13,17,2,8,3}; // create an variables that store integers
int evens[11] = {0}; // initialized an array to store even numbers
int odds[11] = {0}; // initialized an array to store even numbers
int length = sizeof(nums) / sizeof(nums[0]); // get the length of nums
int nums_index = 0;
int evens_index = 0;
int odds_index = 0;
for (nums_index; nums_index < length; nums_index++)
{
if (nums[nums_index] % 2 == 0)
{
evens[evens_index] = nums[nums_index];
evens_index++;
}
else if(nums[nums_index] % 2 != 0)
{
odds[odds_index] = nums[nums_index];
odds_index++;
}
}
printf("Original List: ");
PrintNumbers(nums, length);
printf("Even numbers: ");
PrintNumbers(evens, length);
printf("Odd numbers: ");
PrintNumbers(odds, length);
return 0;
}
void PrintNumbers(int* numbers, int n)
{
for (int i = 0; i < n; i++)
{
printf("%d, ", numbers[i]);
}
printf("\n");
}
Output:
Original List: 11, 3, 9, 7, 6, 10, 13, 17, 2, 8, 3,
Even numbers: 6, 10, 2, 8, 0, 0, 0, 0, 0, 0, 0,
Odd numbers: 11, 3, 9, 7, 13, 17, 3, 0, 0, 0, 0,
Let's suppose I have this array
int diml = 3;
int dims = 3;
int time [diml][dims] ={
(10, 3, 5),
( 4, 7, 2),
( 2, 8, 1)
};
How can I get every combination like:
(10, 3, 5)
(10, 3, 2)
(10, 3, 1)
(10, 7, 5)
(10, 7, 2)
(10, 7, 1)
...
(2, 8, 5)
(2, 8, 2)
(2, 8, 1)
*Is this possible without saving all the combinations in a new array, but just a 1D local array that can store the current combination on every cycle?
*I'd prefer cycles over recursion. And at the end of each cycle I need the pattern (like 10, 3, 2) so I can elaborate it.
*The dimensions of the 2D array are MxN (3x3 is just an example).
*A solution with binary trees is accepted (but I want to save the indexes too).
I should do this in C. I have found similar solutions in StackOverflow but they work by column and they save the data in a 2D array, but that's not what I need.
Thanks in advance! (:
For this example codes, The first one was built so it would be easier to understand example 2. Example 1 was built for only 3x3 matrixes. Example 2 was built so that it can accommodate a matrix with 8 columns at maximum. I didn't use malloc or return an array. It will print back all the possible combinations for you. It doesn't deal with returning the data but it wouldn't be hard to incorporate that into the code.
For the method of calculation all the possible combination, I would use a 3x3 matrix as an example.
In a 3x3 matrix, there are 3 rows and 3 columns. I treated each column as a set of number that I can pick and the rows as the possible of numbers that I can pick from. So in that example, I can pick 012 for my first, second, and third set of number.
So to get all the possible combinations, I have 3 arrays, [0] [1] [2]. They all start at 0. I first save the possible combination of 0 0 0. Then I increase array 2 by 1. Then I would get 0 0 1. I then save that combination. I will keep on doing that and one the [2] array == 2. I turn that to 0 and add a 1 to the array to the left of it. So it become 0 1 0. When I reach a loop where my values of my arrays are 0 2 2, the loop after that, I will get 1 0 0. I will keep on doing that until all the value turn to zero then I am done.
For how the data is store, I store them continually in an array. To read back the value properly. Say for example in a 2x5 matrix. Each combination will have 5 numbers. Thus, the first combination is the first five indexes, the next combination, is the next five numbers after that one.
To calculate how much array length you would need before calculating the combinations, you can just base the calculation on rows and columns. Think of this like the lottery. If there are 3 columns, it like you can pick 3 numbers. Each column have 3 rows, so that mean for each time you pick a number there are 3 possible numbers to pick from. For you to hit a jackpot the chances are 1:3 x 1:3 x 1:3 or 1:27 because there are 27 possibilities if picking 3 numbers like this (123 123 123) and matching them in the correct order. Thus, for a 3x3 matrix, it is 3x3x3, 4x4 = 4x4x4x4, 1x3 = 1, 3x1 = 3, 2x5 = 2x2x2x2x2 = 32.
Thus, the amount of possible combinations is "the amount of rows" to the power of "the amount of columns".
The size is the amount of possible combinations multiply by the amount of numbers per combination. Of which would be "possibilities multiply column count = array size needed.
Example 1:
#include <stdio.h>
void printMatrixCombo(int row, int col, int matrix[row][col]);
int main(){
const int m1 = 3;
const int m2 = 3;
int matrix[m1][m2] = {
{10, 3, 5},
{4, 7, 2},
{2, 8, 1}
};
printMatrixCombo(m1, m2, matrix);
return 0;
}
// Only use this for a 3x3
void printMatrixCombo(int row, int col, int matrix[row][col]){
int oi = 0;
int output[81] = {0};
for (int group1 = 0; group1 < 3; group1++){
for (int group2 = 0; group2 < 3; group2++ ){
for (int group3 = 0; group3 < 3; group3++ ){
output[oi++] = matrix[group1][0];
output[oi++] = matrix[group2][1];
output[oi++] = matrix[group3][2];
}
}
}
printf("There were %d combination in the matrix of %d x %d\n", oi / col, row, col );
for ( int i = 0; i < oi ; ){
printf("(");
for ( int j = 0; j < col; j++ ){
printf("%d", output[i+j]);
if ( j != col - 1 ) printf(", ");
}
printf(")\n");
i = i + col;
}
}
Example 2:
#include <stdio.h>
void printMatrixCombo(int row, int col, int matrix[row][col]);
int main(){
const int row = 4;
const int col = 4;
/*// 3x3
int matrix[row][col] = {
{10, 3, 5},
{4, 7, 2},
{2, 8, 1}
};//*/
// 4 x 4
int matrix[row][col] = {
{10, 3, 5, 7},
{4, 7, 2, 3},
{2, 8, 1, 9},
{9, 4, 8, 11}
};//*/
/*// 5 x 5
int matrix[row][col] = {
{10, 3, 5, 7, 25},
{4, 7, 2, 87, 42},
{2, 8, 1, 85, 39},
{9, 4, 8, 94, 57},
{10, 3, 5, 7, 93},
};//*/
/*// 2 x 2
int matrix[row][col] = {
{10, 3},
{4, 7},
};//*/
/*// 1 x 1
int matrix[row][col] = {
{10},
};//*/
/* // 3 x 1
int matrix[row][col] = {
{10},
{4},
{1}
}; //*/
/*// 1 x 3
int matrix[row][col] = {
{10, 4, 1},
};// */
printMatrixCombo(row, col, matrix);
return 0;
}
void printMatrixCombo(int row, int col, int matrix[row][col]){
int oi = 0;
int allZ = 0;
// This is the maximum for a 5x5
// Change to fit usage case
int output[15625] = {0};
int colCount[8] = {0};
int lastCol = col - 1;
int lastRow = row - 1;
while (1){
for ( int i = 0; i < col; i++ )
output[oi++] = matrix[colCount[i]][i];
if ( colCount[lastCol] == lastRow ){
colCount[lastCol] = 0;
for (int i = lastCol - 1; i > -1; i--){
if ( colCount[i] == lastRow ){
colCount[i] = 0;
} else {
colCount[i]++;
break;
}
}
} else {
colCount[lastCol]++;
}
allZ = 1;
for ( int i = 0; i < col; i++ ){
if ( colCount[i] != 0 ){
allZ = 0;
break;
}
}
if (allZ == 1) break;
}
printf("There were %d combination in the matrix of %d x %d\n", oi / col, row, col );
printf("Array's length(indexes) is %d\n", oi );
for ( int i = 0; i < oi ; ){
printf("(");
for ( int j = 0; j < col; j++ ){
printf("%d", output[i+j]);
if ( j != col - 1 ) printf(", ");
}
printf(")\n");
i = i + col;
}
}
I am trying to make a program that will count the number of even numbers in the provided arrays. When I run the program now, it will return the amount of numbers in the array, but not the amount of even numbers. For some reason my count_even function doesn't work. Can anyone help?
#include <stdio.h>
int main()
{
int data_array_1[] = { 1, 3, 5, 7, 9, 11 };
int data_array_2[] = { 2, -4, 6, -8, 10, -12, 14, -16 };
int data_array_3[] = { 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 0 };
int data_array_4[] = { 6, 2, 4, 5, 1, -9 };
int data_array_5[] = { 1, 3, 9, 23, 5, -2, 4 };
int result_1 = count_even(data_array_1, 6);
printf("data_array_1 has %d even numbers.\n", result_1);
int result_2 = count_even(data_array_2, 8);
printf("data_array_2 has %d even numbers.\n", result_2);
int result_3 = count_even(data_array_3, 11);
printf("data_array_3 has %d even numbers.\n", result_3);
int result_4 = count_even(data_array_4, 6);
printf("data_array_4 has %d even numbers.\n", result_4);
int result_5 = count_even(data_array_5, 7);
printf("data_array_5 has %d even numbers.\n", result_5);
return 0;
}
int count_even(int* data_array, int size)
{
int even_num = 0;
for (int i = 0; i == size; i++)
{
if (data_array[size] % 2 == 0)
{
even_num++;
}
}
return even_num;
}
The condition in your for loop is wrong.
The correct condition should say "as long as the index is smaller than size", but yours say "as long as the index equal to to size".
The condition should be i < size.
As for the result, it seems like it should return 0 (for the non-working code), not size.
Also, you are using size as an index, when you should use i.
In your count_even function, you are using the size attribute as the array index, when it should be i
int count_even(int* data_array, int size)
{
int even_num = 0
for(int i = 0; i <= size, ++i)
{
if(data_array[i] % 2 == 0)
{
even_num++;
}
}
return even_num;
}
these two lines are the root of the problems in the code:
for (int i = 0; i == size; i++)
{
if (data_array[size] % 2 == 0)
the for() statement, should be:
for (int i = 0; i < size; i++)
so the loop exits when reaching the end of the array
the if() statement is always looking at the same entry beyond the end of the array, This is undefined behaviour
The if() statement should be:
if (data_array[i] % 2 == 0)
However, the modulo operator & is not a good choice for negative numbers
a better choice would be:
if ( !(data_array[i] & 1 ) )
I am programming in C. What is the best method (I mean in linear time) to spit array on elements less, equals and greater than some value x.
For example if I have array
{1, 4, 6, 7, 13, 1, 7, 3, 5, 11}
and x = 7 then it should be
{1, 4, 6, 1, 3, 5, 7, 7, 13, 11 }
I don't want to sort elements because I need more efficient way. Of course in this example in could be any permutation of {1, 4, 6, 1, 3, 5} and {13, 11}.
My thougt: less or grater than some element in array... In this example it is 7.
My function is:
int x = 7;
int u =0, z = 0;
for(int i=0; i<size-1; i++) // size - 1 because the last element will be choosen value
{
if(A[i] == x)
swap(A[i], A[u]);
else if(A[i] == x)
{
swap(A[i], A[n-(++z)]);
continue;
}
i++
}
for(int i = 0; i<z; i++)
swap(A[u+i],A[size-(++z)];
where u is number of current less elements, and z is the number of equals element
But if I have every elements in array equals there it doesn't work (size-(++z)) is going under 0
This is the so-called Dutch national flag problem, named after the three-striped Dutch flag. (It was named that by E.W. Dijkstra, who was Dutch.) It's similar to the partition function needed to implement quicksort, but in most explanations of quicksort a two-way partitioning algorithm is presented whereas here we are looking for a three-way partition. The classic quicksort partitioning algorithms divide the vector into two parts, one consisting of elements no greater than the pivot and the other consisting of elements strictly greater. [See note 1]
The wikipedia article gives pseudocode for Dijkstra's solution, which (unlike the classic partition algorithm usually presented in discussions of quicksort) moves left to right through the vector:
void dutchflag(int* v, size_t n, int x) {
for (size_t lo = 0, hi = n, j = 0; j < hi; ) {
if (v[j] < x) {
swap(v, lo, j); ++lo; ++j;
} else if (v[j] > x) {
--hi; swap(v, j, hi);
} else {
++j;
}
}
There is another algorithm, discovered in 1993 by Bentley and McIlroy and published in their paper "Engineering a Sort Function" which has some nice diagrams illustrating how various partitioning functions work, as well as some discussion about why partitioning algorithms matter. The Bentley & McIlroy algorithm is better in the case that the pivot element occurs infrequently in the list while Dijkstra's is better if it appears often, so you have to know something about your data in order to choose between them. I believe that most modern quicksort algorithms use Bentley & McIlroy, because the common case is that the array to be sorted has few duplicates.
Notes
The Hoare algorithm as presented in the Wikipedia Quicksort article, does not rearrange values equal to the pivot, so they can end up being present in both partitions. Consequently, it is not a true partitioning algorithm.
You can do this:
1) Loop through the array, if element is less than x then put in new array1.
2)If element is greater than x then put in new array2.
This is linear time O(n)
I tried something like this below which I think is O(n). Took me a little bit to work the kinks out but I think it's pretty similar to the dutchflag answer above.
My ouptput
a.exe
1 4 6 5 3 1 7 7 11 13
1 4 5 6 3 1 7 7 7 11 13
code:
#define ARRAY_SIZE(x) (sizeof(x)/sizeof(x[0]))
void order(int * list, int size, int orderVal)
{
int firstIdx, lastIdx, currVal, tempVal;
firstIdx = 0;
lastIdx = size-1;
for ( ;lastIdx>firstIdx;firstIdx++)
{
currVal = list[firstIdx];
if (currVal >= orderVal)
{
tempVal = list[lastIdx];
list[lastIdx] = currVal;
lastIdx--;
list[firstIdx] = tempVal;
if (tempVal >= orderVal)
firstIdx--;
}
}
lastIdx = size-1;
for( ;lastIdx>firstIdx && middleNum>0;lastIdx--)
{
currVal = list[lastIdx];
if (currVal == orderVal)
{
tempVal = list[firstIdx];
list[firstIdx] = currVal;
firstIdx++;
list[lastIdx] = tempVal;
if (tempVal == orderVal)
lastIdx++;
}
}
}
int main(int argc, char * argv[])
{
int i;
int list[] = {1, 4, 6, 7, 13, 1, 7, 3, 5, 11};
int list2[] = {1, 4, 7, 6, 7, 13, 1, 7, 3, 5, 11};
order(list, ARRAY_SIZE(list), 7);
for (i=0; i<ARRAY_SIZE(list); i++)
printf("%d ", list[i]);
printf("\n");
order(list2, ARRAY_SIZE(list2), 7);
for (i=0; i<ARRAY_SIZE(list2); i++)
printf("%d ", list2[i]);
}
Here is an example using a bubble sort. Which type of sort algorithm is best, is up to you, this is just to demonstrate. Here, I treat values < x as -1, values == x as 0, values > x as 1.
Note that the elements < x and those > x are still in the same sequence.
#include <stdio.h>
int main(void)
{
int array[] = { 1, 4, 6, 7, 13, 1, 7, 3, 5, 11 };
int x = 7;
int len = sizeof array / sizeof array[0];
int i, j, m, n, tmp;
for (i=0; i<len-1; i++) {
m = array[i] < x ? -1 : array[i] == x ? 0 : 1;
for (j=i+1; j<len; j++) {
n = array[j] < x ? -1 : array[j] == x ? 0 : 1;
if (m > n) {
tmp = array[i]; // swap the array element
array[i] = array[j];
array[j] = tmp;
m = n; // and replace alias
}
}
}
for(i=0; i<len; i++)
printf("%d ", array[i]);
printf("\n");
return 0;
}
Program output:
1 4 6 1 3 5 7 7 13 11