Merge Sort

#include<stdlib.h>

#include<stdio.h>

void merge(int arr[], int l, int m, int r)

{

    int i, j, k;

    int n1 = m - l + 1;

    int n2 =  r - m;

    // create temp arrays

    int L[n1], R[n2];

    // Copy data to temp arrays L[] and R[]

    for (i = 0; i < n1; i++)

        L[i] = arr[l + i];

    for (j = 0; j < n2; j++)

        R[j] = arr[m + 1+ j];

     // Merge the temp arrays back into arr[l..r]

    i = 0; // Initial index of first subarray

    j = 0; // Initial index of second subarray

    k = l; // Initial index of merged subarray

    while (i < n1 && j < n2)

    {

        if (L[i] <= R[j])

        {

            arr[k] = L[i];

            i++;

        }

        else

        {

            arr[k] = R[j];

            j++;

        }

        k++;

    }

     // Copy the remaining elements of L[], if there are any

    while (i < n1)

    {

        arr[k] = L[i];

        i++;

        k++;

    }

    // Copy the remaining elements of R[], if there are any

    while (j < n2)

    {

        arr[k] = R[j];

        j++;

        k++;

    }

}

// l is for left index and r is right index of the sub-array of arr to be sorted

void merge_Sort(int arr[], int l, int r)

{

    if (l < r)

    {

        // Same as (l+r)/2, but avoids overflow for large l and h

        int m = l+(r-l)/2;

 

        // Sort first and second halves

        merge_Sort(arr, l, m);

        merge_Sort(arr, m+1, r);

 

        merge(arr, l, m, r);

    }

}

// Function to print an array

void print_Array(int A[], int size)

{

    int i;

    for (i=0; i < size; i++)

        printf("%d ", A[i]);

    printf("\n");

}

int main()

{

    int arr[] = {12, 11, 13, 5, 6, 7};

    int arr_size = sizeof(arr)/sizeof(arr[0]);

 

    printf("Given array is \n");

    print_Array(arr, arr_size);

 

    merge_Sort(arr, 0, arr_size - 1);

 

    printf("\nSorted array is \n");

    print_Array(arr, arr_size);

    return 0;

}

Insertion Sort

#include <stdio.h>
#include <math.h>
 Function to sort an array using insertion sort
void insertion_Sort(int arr[], int n)
{
   int i, key, j;
   for (i = 1; i < n; i++)
   {
       key = arr[i];
       j = i-1;
   Move elements of arr[0..i-1], that are  greater than key, to one position ahead of their current position 
       while (j >= 0 && arr[j] > key)
       {
           arr[j+1] = arr[j];
           j = j-1;
       }
       arr[j+1] = key;
   }
}
 A utility function ot print an array of size n
void print_Array(int arr[], int n)
{
   int i;
   for (i=0; i < n; i++)
       printf("%d ", arr[i]);
   printf("\n");
}

int main()
{
    int arr[] = {12, 11, 13, 5, 6};
    int n = sizeof(arr)/sizeof(arr[0]);
    insertion_Sort(arr, n);
    print_Array(arr, n);
    return 0;
}

Bubble Sort

#include <stdio.h>

void swap(int *xp, int *yp)
{
    int temp = *xp;
    *xp = *yp;
    *yp = temp;
}
 A function to implement bubble sort
void bubble_Sort(int arr[], int n)
{
   int i, j;
   for (i = 0; i < n-1; i++)      
        Last i elements are already in place   
       for (j = 0; j < n-i-1; j++) 
           if (arr[j] > arr[j+1])
              swap(&arr[j], &arr[j+1]);
}
Function to print an array 
void printArray(int arr[], int size)
{
    int i;
    for (i=0; i < size; i++)
        printf("%d ", arr[i]);
    printf("n");
}

int main()
{
    int arr[] = {64, 34, 25, 12, 22, 11, 90};
    int n = sizeof(arr)/sizeof(arr[0]);
    bubble_Sort(arr, n);
    printf("Sorted array: \n");
    printArray(arr, n);
    return 0;

Selection Sort

#include <stdio.h> 

void swap(int *xp, int *yp)

{

    int temp = *xp;

    *xp = *yp;

    *yp = temp;

}

void selectionSort(int arr[], int n)

{

    int i, j, min_index;

     One by one move boundary of unsorted subarray

    for (i = 0; i < n-1; i++)

    {

         Find the minimum element in unsorted array

        min_index = i;

        for (j = i+1; j < n; j++)

          if (arr[j] < arr[min_index])

            min_index = j;

         Swap the found minimum element with the first element

        swap(&arr[min_index], &arr[i]);

    }

}

 Function to print an array

void printArray(int arr[], int size)

{

    int i;

    for (i=0; i < size; i++)

        printf("%d ", arr[i]);

    printf("\n");

}

int main()

{

    int arr[] = {64, 25, 12, 22, 11};

    int n = sizeof(arr)/sizeof(arr[0]);

    selectionSort(arr, n);

    printf("Sorted array: \n");

    printArray(arr, n);

    return 0;

}

Write a C program to find whether a given matrix is an upper triangular matrix or not.

                                    UPPER TRIANGULAR MATRIX
                                        
                                              C-Solution

#include<stdio.h>
#include<stdlib.h>
int **create(int r,int c)
{
    int **mat,i;
    mat=(int **)malloc(r*sizeof(int *));
    for(i=0;i<r;i++)
    {
        *(mat+i)=(int *)malloc(c*sizeof(int ));
    }
    return mat;
}
int **getelement(int **m,int r,int c)
{
    int i,j;
    for(i=0;i<r;i++)
    {
        for(j=0;j<c;j++)
        {
            scanf("%d",*(m+i)+j);
        }
    }
    return m;
}
void exec(int **m,int r,int c)
{
    int i,j,c1=1;
    for(i=0;i<r;i++)
    {
        for(j=0;j<c;j++)
        {
            if((j<i)&&*(*(m+i)+j)!=0)
            {
                c1=0;
            }
        }
    }
    if(c1==1)
    {
        printf("yes");
    }
    else
    {
        printf("no");
    }
}
int main()
{
    int **m;
    int r;
    scanf("%d",&r);
    m=create(r,r);
    m=getelement(m,r,r);
    exec(m,r,r);
    return 0;
}