Divide and Conquer

Merge Sort

Quick Sort

Maximum and Minimum

MERGE SORT#include<stdio.h>#include<conio.h>void mergesort(int a[],int i,int j);void merge(int a[],int i1,int j1,int i2,int j2);void main(){int a[30],n,i;clrscr();printf("enter the no.of elements:");scanf("%d",&n);printf("enter array elements:");for(i=0;i<n;i++)scanf("%d",&a[i]);mergesort(a,0,n-1);printf("\n sorted array is:");for(i=0;i<n;i++)printf("%d",a[i]);getch();}

void mergesort(int a[],int i,int j){int mid;if(i<j){mid=(i+j)/2;mergesort(a,i,mid);mergesort(a,mid+1,j);merge(a,i,mid,mid+1,j);}}

void merge(int a[],int i1,int j1,int i2,int j2){int temp[50];int i,j,k;i=i1;j=i2;k=0;while(i<=j1&&j<=j2){if(a[i]<a[j])temp[k++]=a[i++];elsetemp[k++]=a[j++];}while(i<=j1)temp[k++]=a[j++];while(j<=j2)temp[k++]=a[j++];for(i=i1,j=0;i<=j2;i++,j++)a[i]=temp[j];}

Output:Enter the no. Of elements: 5

Enter array elements:1005902030

Sorted array is:5203090100

Quick Sort#include<stdio.h>

#include<conio.h>

void quicksort(int array[20],int first,int last);

void main()

{

int array[30];

int i,size;

clrscr();

printf("enter the total number of elements:");

scanf("%d",&size);

printf("enter the total %d elements:\n",size);

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

scanf("%d",&array[i]);

quicksort(array,0,size-1);

printf("quicksorted elements are as:\n");

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

printf("%d\t",array[i]);

getch();

}

void quicksort(int array[20],int first,int last)

{

int i,j,pivot,temp;

if(first<last)

{

pivot=first;

i=first;

j=last;

while(i<j)

{

while(array[i]<=array[pivot]&&i<last)

i++;

while(array[j]>array[pivot])

j--;

if(i<j)

{

temp=array[i];

array[i]=array[j];

array[j]=temp;

}

}

temp=array[pivot];

array[pivot]=array[j];

array[j]=temp;

quicksort(array,first,j-1);

quicksort(array,j+1,last);

}

}

MAXIMUM AND MINIMUM#include<stdio.h>#include<conio.h>void main(){int a[10],i,n,max,min;clrscr();printf("enter the value of n:");scanf("%d",&n);printf("\n");for(i=0;i<n;i++){printf("enter the %delements",i+1);scanf("%d",&a[i]);}max=a[0];min=a[0];for(i=0;i<n;i++){if(a[i]>max)max=a[i];if(a[i]<min)min=a[i];}printf("\n the maximum number is %d\n",max);printf("\n the minimum number is %d\n",min);getch();}

Greedy Method

Knap sack Problem

Tree Vertex Splitting

Job Sequencing

KNAPSACK PROBLEM#include<stdio.h>#include<conio.h>void knapsack(int n,float weight[],float profit[],float capacity){float x[20],tp=0;int i,j,u;u=capacity;for(i=0;i<n;i++)x[i]=0.0;for(i=0;i<n;i++){if(weight[i]>u)break;else{x[i]=1.0;tp=tp+profit[i];u=u-weight[i];}}if(i<n)x[i]=u/weight[i];tp=tp+(x[i]*profit[i]);printf("\nthe result vector is:");for(i=0;i<n;i++)printf("%f\t",x[i]);printf("\nmaximum profit is:%f",tp);}int main(){float weight[20],profit[20],capacity;int num,i,j;float ratio[20],temp;clrscr();

printf("\nenter the no of objects:");scanf("%d",&num);printf("\nenter the wts and profit of each object:");for(i=0;i<num;i++){scanf("%f%f",&weight[i],&profit[i]);}printf("\nenter the capacity of knapsack:");scanf("%f",&capacity);for(i=0;i<num;i++){ratio[i]=profit[i]/weight[i];}for(i=0;i<num;i++){for(j=i+1;j<num;j++){if(ratio[i]<ratio[j]){temp=ratio[j];ratio[j]=ratio[i];ratio[i]=temp;temp=weight[j];weight[j]=temp;temp=profit[j];profit[j]=profit[i];profit[i]=temp;}}}knapsack(num,weight,profit,capacity);return(0);}

TREE VERTEX SPLITTING#include <stdio.h>#include <stdlib.h> int min(int x, int y) { return ( (x < y)? x: y);)} struct node{ int data; int vc; struct node *left, *right;}; int vCover(struct node *root){ if (root == NULL) return 0; if (root->left == NULL && root->right == NULL) return 0; if (root->vc != 0) return root->vc; int size_incl = 1 + vCover(root->left) + vCover(root->right); int size_excl = 0; if (root->left) size_excl += 1 + vCover(root->left->left) + vCover(root->left->right); if (root->right) size_excl += 1 + vCover(root->right->left) + vCover(root->right->right); root->vc = min(size_incl, size_excl); return root->vc;} struct node* newNode( int data ){ struct node* temp = (struct node *) malloc( sizeof(struct node) ); temp->data = data;

temp->left = temp->right = NULL; temp->vc = 0; return temp;} int main(){struct node *root = newNode(20);root->left = newNode(8);root->left->left = newNode(4);root->left->right = newNode(12);root->left->right->left = newNode(10);root->left->right->right = newNode(14);root->right = newNode(22);root->right->right = newNode(25); printf ("Size of the smallest vertex cover is %d ", vCover(root)); return 0;}