CODEMASTER
Never
psProgram 1
Given an array of nonnegative integers, design a linear algorithm and implement it using a program to find whether a given key element is present in the array or not. Also, find the total number of comparisons for each input case.
Code:
#include<iostream>
using namespace std;
int main(void){
int t;
cin>>t;
while(t--){
int n;
cin>>n;
int A[n];
for(int i = 0;i < n;i++)
cin>>A[i];
int key;
cin>>key;
int count = 0,flag = 0;
for(int i = 0;i < n;i++){
if(key == A[i]){
count++;
flag = 1;
break;
}
count++;
}
if(flag == 1)
cout<<"Present"<<" "<<count<<endl;
else
cout<<"Not Present"<<" "<<count<<endl;
}
}
OUTPUT
psProgram 2
Given an already sorted array of positive integers, design an algorithm and implement it using a program to find whether given key element is present in the array or not. Also, find total number of comparisons for each input case. (Time Complexity = O(nlogn), where n is the size of input).
Code:
#include<iostream>
using namespace std;
int main(void){
int t;
cin>>t;
while(t--){
int n;
cin>>n;
int A[n];
for(int i = 0;i < n;i++)
cin>>A[i];
int key;
cin>>key;
int count = 0,flag = 0;int low = 0,high = n-1,mid = (low + high)/2;
while(low <= high){
if(key == A[mid]){
count++;
flag = 1;
break;
}
else if(key < A[mid]){
high = mid - 1;
mid = (low + high)/2;
count++;
}
else if(key > A[mid]){
low = mid + 1;
mid = (low + high)/2;
count++;
}}
if(flag == 1)
cout<<"Present"<<" "<<count<<endl;
else
cout<<"Not Present"<<" "<<count<<endl;
} }
OUTPUT
ps
Program 3
Given an already sorted array of positive integers, design an algorithm and implement it using a program to find whether a given key element is present in the sorted array or not. For an array arr[n], search at the indexes arr[0], arr[2], arr[4],. ,arr[2k] and so on. Once the interval (arr[2k] < key < arr[ 2k+1] ) is found, perform a linear search operation from the index 2k to find the element key. (Complexity < O(n), where n is the number of elements need to be scanned for searching)
Code:
#include<iostream>
#include<cmath>
using namespace std;
int main(void){
int t;
cin>>t;
while(t--){
int n;
cin>>n;
int A[n];
for(int i = 0;i < n;i++)
cin>>A[i];
int key;
cin>>key;
int count = 0,flag = 0; int m = sqrt(n);int start = 0;
while(A[m] <= key && m < n){
count++;
start = m;
m += sqrt(n);
if(m > n - 1)
m = n;
}
for(int i = start;i < m;i++){
if(A[i] == key){
count++;
flag = 1;
break;
}
count++;
}
if(flag == 1)
cout<<"Present"<<" "<<count<<endl;
else
cout<<"Not Present"<<" "<<count<<endl;
}
}
OUTPUT
ps
Program 4
Given a sorted array of positive integers containing few duplicate elements, design an algorithm and implement it using a program to find whether the given key element is present in the array or not. If present, then also find the number of copies of given key. (Time Complexity = O(log n))
Code:
#include<iostream>
using namespace std;
int binarySearch(int arr[],int n,int key){
int start = 0,end = n-1;
while(start <= end){
int mid = start + (end - start)/2;
if(arr[mid] == key)
return mid;
else if(arr[mid] > key)
end = mid - 1;
else
start = mid + 1;
}
return -1;
}
int main(void){
int t;
cin>>t;
while(t--){
int n;
cin>>n;
int arr[n];
for(int i = 0;i < n;i++)
cin>>arr[i];
int key;
cin>>key;
int index = binarySearch(arr,n,key); int count = 0;
if(index == -1)
cout<<"Key Not present"<<endl;
else{
for(int i = 0;i < n;i++){
if(arr[i] == key)
count++; }
cout<<arr[index]<<" - "<<count<<endl;
} } }
OUTPUT
psProgram 5
Given a sorted array of positive integers, design an algorithm and implement it using a program to find three indices i, j, k such that arr[i] + arr[j] =
arr[k].
Code:
#include<iostream>
using namespace std;
int main(void){
int t;
cin>>t;
while(t--){
int flag = 0,n,i,j,k;
cin>>n;
int arr[n];
for(i = 0;i < n;i++)
cin>>arr[i];
for(i = 0;i < n;i++){
for(j = i+1;j < n;j++){
for(k = j+1;j < n;j++){
if(arr[i] + arr[j] == arr[k]){
cout<<i<<","<<j<<","<<k<<endl;
flag = 1;
break;
}
}
}
}
if(flag == 0)
cout<<"No sequence found"<<endl;
}
}
OUTPUT
psProgram 6
Given an array of non-negative integers, design an algorithm and a program to count the number of pairs of integers such that their difference is equal to a given key, K.
Code:
#include<iostream>
#include<cstdlib>
using namespace std;
int main(void){
int t;
cin>>t;
while(t--){
int count = 0,n,key;
cin>>n>>key;
int arr[n];
for(int i = 0;i < n;i++)
cin>>arr[i];
for(int i = 0;i < n;i++){
for(int j = i+1;j < n;j++){
if(abs(arr[i] - arr[j]) == key)
count++;
}
}
cout<<count<<endl;
}
}
OUTPUT
psProgram 7
Given an unsorted array of integers, design an algorithm and a program to sort the array using insertion sort. Your program should be able to find number of comparisons and shifts ( shifts - total number of times the array elements are shifted from their place) required for sorting the array.
Code:
#include<iostream>
using namespace std;
int main(void){
int t;
cin>>t;
while(t--){
int n,shift = 0,comp = 0;
cin>>n;
int arr[n];
for(int i = 0;i < n;i++)
cin>>arr[i];
int v,j;
for(int i = 1;i < n;i++){
v = arr[i];
j = i;
while(arr[j-1] > v && j >= 1){
shift++;
comp++;
arr[j] = arr[j-1];
j--;
}
shift++;
arr[j] = v;
}
for(int i = 0;i < n;i++)
cout<<arr[i]<<" ";
cout<<endl;
cout<<"comparisions = "<<comp<<endl;
cout<<"shifts = "<<shift<<endl;
}
return 0;
}
OUTPUT
psProgram 8
Given an unsorted array of integers, design an algorithm and implement a program to sort this array using selection sort. Your program should also find number of comparisons and number of swaps required.
Code:
#include<iostream>
using namespace std;
int main(void){
int t;
cin>>t;
while(t--){
int n,swap = 0,comp = 0;
cin>>n;
int arr[n];
for(int i = 0;i < n;i++)
cin>>arr[i];
int min,temp;
for(int i = 0;i < n-1;i++){
min = i;
for(int j = i+1;j < n;j++){
comp++;
if(arr[j] < arr[min]){
min = j;
}
}
temp = arr[i];
arr[i] = arr[min];
arr[min] = temp;
swap++;
}
for(int i = 0;i < n;i++)
cout<<arr[i]<<" ";
cout<<endl;
cout<<"Comparisions = "<<comp<<endl;
cout<<"Swaps = "<<swap<<endl;
}
}
OUTPUT
psProgram 9
Given an unsorted array of positive integers, design an algorithm and implement it using a program to find whether there are any duplicate elements in the array or not. (use sorting) (Time Complexity = O(n log n))
Code:
#include<iostream>
using namespace std;
void merge(int arr[],int left,int mid,int right){
int n1 = mid - left + 1, n2 = right - mid;
int leftArr[n1],rightArr[n2];
for(int i = 0;i < n1;i++)
leftArr[i] = arr[left + i];
for(int i = 0;i < n2;i++)
rightArr[i] = arr[mid+i+1];
int i = 0,j = 0,k = left;
while(i < n1 && j < n2){
if(leftArr[i] <= rightArr[j])
arr[k++] = leftArr[i++];
else
arr[k++] = rightArr[j++];
}
while(i < n1)
arr[k++] = leftArr[i++];
while(j < n2)
arr[k++] = rightArr[j++];
}
void mergeSort(int arr[],int left,int right){
if(left >= right)
return;
int mid = left + (right - left)/2;
mergeSort(arr,left,mid);
mergeSort(arr,mid+1,right);
merge(arr,left,mid,right);
}
int main(void){
int t;
cin>>t;
while(t--){
int n,flag = 0;
cin>>n;
int arr[n];
for(int i = 0;i < n;i++)
cin>>arr[i];
mergeSort(arr,0,n-1);
for(int i = 0;i < n-1;i++){
int j = i+1;
if(arr[i] == arr[j]){
flag = 1;
break;
}
}
if(flag == 1)
cout<<"YES"<<endl;
else
cout<<"NO"<<endl;
}
}
OUTPUT
ps
Program 10
Given an unsorted array of integers, design an algorithm and implement it using a program to sort an array of elements by dividing the array into two subarrays and combining these subarrays after sorting each one of them. Your program should also find number of comparisons and inversions during sorting the array.
Code:
#include<iostream>
using namespace std;
int compare = 0;
void merge(int arr[],int left,int mid,int right){
int n1 = mid - left + 1, n2 = right - mid;
int leftArr[n1],rightArr[n2];
for(int i = 0;i < n1;i++)
leftArr[i] = arr[left + i];
for(int i = 0;i < n2;i++)
rightArr[i] = arr[mid+i+1];
int i = 0,j = 0,k = left;
while(i < n1 && j < n2){
if(leftArr[i] <= rightArr[j]){
arr[k++] = leftArr[i++];
compare++;
}
else{
arr[k++] = rightArr[j++];
compare++;
}
}
while(i < n1)
arr[k++] = leftArr[i++];
while(j < n2)
arr[k++] = rightArr[j++];
}
void mergeSort(int arr[],int left,int right){
if(left >= right)
return;
int mid = left + (right - left)/2;
mergeSort(arr,left,mid);
mergeSort(arr,mid+1,right);
merge(arr,left,mid,right);
}
int main(void){
int t;
cin>>t;
while(t--){
int n;
cin>>n;
int arr[n];
for(int i = 0;i < n;i++)
cin>>arr[i];
mergeSort(arr,0,n-1);
for(int i = 0;i < n;i++)
cout<<arr[i]<<" ";
cout<<endl;
cout<<"Comparisions: "<<compare<<endl;
compare = 0;
}
}
OUTPUT
psProgram 11
Given an unsorted array of integers, design an algorithm and implement it using a program to sort an array of elements by partitioning the array into two subarrays based on a pivot element such that one of the sub array holds values smaller than the pivot element while another sub array holds values greater than the pivot element. Pivot element should be selected randomly from the array. Your program should also find number of comparisons and swaps required for sorting the array.
Code:
#include<iostream>
using namespace std;
int compare = 0;
int swaps = 0;
int partition(int arr[],int low, int high){
int pivot = arr[high];
int i = low - 1, temp;
for(int j = low;j <= high-1;j++){
compare++;
if(arr[j] <= pivot){
i++;
temp = arr[i];
arr[i] = arr[j];
arr[j] = temp;
swaps++;
}
}
temp = arr[i+1];
arr[i+1] = arr[high];
arr[high] = temp;
swaps++;
return i+1;
}
void quickSort(int arr[],int low, int high){
if(low >= high)
return;
int pivot = partition(arr,low,high);
quickSort(arr,low,pivot-1);
quickSort(arr,pivot+1,high);
}
int main(void){
int t;
cin>>t;
while(t--){
int n;
cin>>n;
int arr[n];
for(int i = 0;i < n;i++)
cin>>arr[i];
quickSort(arr,0,n-1);
for(int i = 0;i < n;i++)
cout<<arr[i]<<" ";
cout<<endl;
cout<<"Comparisions: "<<compare<<endl;
cout<<"Swaps: "<<swaps;
compare = 0;
swaps = 0;
}
}
OUTPUT
psProgram 12
Given an unsorted array of integers, design algorithm and implement it using a program to an find Kth smallest or largest element in the array.(Worst case Time Complexity = O(n))
Code:
#include <bits/stdc++.h>
using namespace std;
int main()
{
int t;
cin>>t;
while(t--){
int n;
cin>>n;
int arr[n];
for(int i = 0;i < n;i++)
cin>>arr[i];
int k;
cin>>k;
set<int> s(arr, arr + n);
set<int>::iterator itr
= s.begin(); // s.begin() returns a pointer to first
// element in the set
advance(itr, k - 1); // itr points to kth element in set
cout << *itr << "\n";
}
return 0;
}
OUTPUT
psProgram 13
Given an unsorted array of alphabets containing duplicate elements. Design an algorithm and implement it using a program to find which alphabet has maximum number of occurrences and print it.
Code:
#include <bits/stdc++.h>
using namespace std;
int main()
{
int t;
cin>>t;
while(t--)
{
int flag = 0;
int n;
cin>>n;
char arr[n];
for(int i = 0;i < n;i++)
cin>>arr[i];
int freq[26];
for(int i = 0;i < 26;i++)
freq[i] = 0;
for(int i = 0;i < n;i++)
{
freq[arr[i] - 97]++;
}
int max = 1;
int j = 0;
for(int i = 0;i < 26;i++)
{
if(freq[i] > max)
{
flag = 1;
max = freq[i];
j = i;
}
}
if(flag == 0)
cout<<"No duplicates present"<<endl;
else{
cout<<char(j + 97)<<"-"<<max<<endl;
}
}
return 0;
}
OUTPUT
psProgram 14
Given an unsorted array of integers, design an algorithm and implement it using a program to find whether two elements exist such that their sum is equal to the given key element. (Time Complexity = O(n log n)).
Code:
#include<iostream>
#include<cstdlib>
using namespace std;
int main(void){
int t;
cin>>t;
while(t--){
int flag = 0,n,key;
cin>>n;
int arr[n];
for(int i = 0;i < n;i++)
cin>>arr[i];
cin>>key;
for(int i = 0;i < n;i++){
for(int j = i+1;j < n;j++){
if(arr[i] + arr[j] == key){
flag = 1;
cout<<arr[i]<<" "<<arr[j]<<endl;
}
}
}
if(flag == 0)
cout<<"No such elements exist"<<endl;
}
}
OUTPUT
psProgram 15
You have been given two sorted integer arrays of size m and n. Design an algorithm and implement it using a program to find list of elements which are common to both. (Time Complexity = O(m+n))
Code:
#include<iostream>
using namespace std;
int partition(int arr[],int low, int high){
int pivot = arr[high];
int i = low - 1, temp;
for(int j = low;j <= high-1;j++){
if(arr[j] <= pivot){
i++;
temp = arr[i];
arr[i] = arr[j];
arr[j] = temp;
} }
temp = arr[i+1];
arr[i+1] = arr[high];
arr[high] = temp;
return i+1;
}
void quickSort(int arr[],int low, int high){
if(low >= high)
return;
int pivot = partition(arr,low,high);
quickSort(arr,low,pivot-1);
quickSort(arr,pivot+1,high);
}
int main(void){
int m,n;
cin>>m;
int arr1[m];
for(int i = 0;i < m;i++)
cin>>arr1[i];
quickSort(arr1,0,m-1);
cin>>n;
int arr2[n];
for(int i = 0;i < n;i++)
cin>>arr2[i];
quickSort(arr2,0,n-1);
int i = 0,j = 0;
while(i < m && j < n){
if(arr1[i] > arr2[j])
j++;
else if(arr1[i] < arr2[j])
i++;
else{
cout<<arr1[i]<<" ";
i++;
j++;
} } }
OUTPUT
psProgram 16
Given a (directed/undirected) graph, design an algorithm and implement it using a program to find if a path exists between two given vertices or not. (Hint: use DFS)
Code:
#include<bits/stdc++.h>
using namespace std;
bool findpath(int src, int dest, vector<vector<int>>& graph){
if( src == dest)
return true;
int n = graph.size();
vector<bool> visited(n, false);
visited[src] = true;
// DFS method
stack<int> s;
s.push(src);
while(!s.empty()){
int a = s.top();
s.pop();
for(int x: graph[a]){
if(x==dest)
return true;
if(!visited[x]){
visited[x] = true;
s.push(x);
} } }
return false;
}
int main(){
#ifndef ONLINE_JUDGE
freopen("input.txt","r",stdin);
freopen("output.txt","w",stdout);
#endif
int n,m;
cin>>n>>m;
vector<vector<int>> graph(n);
for(int i=0;i<m;i++){
int u,v;
cin>>u>>v;
graph[u].push_back(v);
graph[v].push_back(u);
}
int source,dest;
cin>>source>>dest;
if(findpath(source,dest, graph)){
cout<<"Yes Path Exists";
}
else{
cout<<"No Such Path Exists";
}
return 0;
}
OUTPUT
psProgram 17
Given a graph, design an algorithm and implement it using a program to find if a graph is bipartite or not.
Code:
#include<bits/stdc++.h>
using namespace std;
vector<vector<int>> adj;
vector<bool> vis;
vector<int> col;
bool bipart;
//assign color to nodes either 0 or 1
void color(int u, int curr){
if(col[u] != -1 and col[u]!= curr){
bipart = false;
return;
}
col[u]= curr;
if(vis[u])
return;
vis[u] = true;
for(auto i: adj[u]){
color(i,curr xor 1);
}
}
int main(){
#ifndef ONLINE_JUDGE
freopen("input.txt","r",stdin);
freopen("output.txt","w",stdout);
#endif
int n,m;
cin>>n>>m;
adj = vector<vector<int>>(n);
vis = vector<bool>(n,false);
col = vector<int>(n,-1);
bipart = true;
for(int i=0;i<m;i++){
int u,v;
cin>>u>>v;
adj[u].push_back(v); adj[v].push_back(u);
}
for(int i=0;i<n;i++){
if(!vis[i]){
color(i,0);
} }
if(bipart)
cout<<"Yes Bipartite";
else
cout<<"Not Bipartite";
return 0;
}
OUTPUT
psProgram 18
Given a directed graph, design an algorithm and implement it using a program to find whether a cycle exists in the graph or not.
Code:
#include<bits/stdc++.h>
using namespace std;
bool iscycle(int src, vector<vector<int>>& adj, vector<bool>& vis, int
parent){
vis[src] = true;
for(auto i: adj[src]){
if(i != parent){
if(vis[i])
return true;
if(!vis[i] and iscycle(i,adj,vis,src)){
return true;
}
}
}
return false;
}
int main()
{
#ifndef ONLINE_JUDGE
freopen("input.txt","r",stdin);
freopen("output.txt","w",stdout);
#endif
int n,m;
cin>>n>>m;
vector<vector<int>> adj(n);
vector<bool> vis(n,false);
bool cycle = false;
for(int i=0;i<m;i++){
int u,v;
cin>>u>>v;
adj[u].push_back(v);
adj[v].push_back(u);
}
// set node 0 as visited
vis[0] = true;
for(int i=0;i<n;i++){
if(!vis[i] and iscycle(i, adj, vis, -1)){
cycle = true;
break;
}
}
if(cycle)
cout<<"Yes Cycle Exists";
else
cout<<"Cycle Not Present";
return 0;
}
OUTPUT
psProgram 19
After end term examination, Akshay wants to party with his friends. All his friends are living as paying guest and it has been decided to first gather at Akshay’s house and then move towards party location. The problem is that no one knows the exact address of his house in the city. Akshay as a computer science wizard knows how to apply his theory subjects in his real life and came up with an amazing idea to help his friends. He draws a graph by looking in to location of his house and his friends’ location (as a node in the graph) on a map. He wishes to find out shortest distance and path covering that distance from each of his friend’s location to his house and then whatsapp them this path so that they can reach his house in minimum time. Akshay has developed the program that implements Dijkstra’s algorithm but not sure about correctness of results. Can you also implement the same algorithm and verify the correctness of Akshay’s results? (Hint: Print shortest path and distance from friends’ location to Akshay’s house).
Code:
#include<bits/stdc++.h>
using namespace std;
void path(vector<int>& parent, int j){
if (parent[j] == - 1){
cout<<j;
return;
}
printf("%d ", j);
path(parent, parent[j]);
}
int main()
{
#ifndef ONLINE_JUDGE
freopen("input.txt","r",stdin);
freopen("output.txt","w",stdout);
#endif
int n,e;
cin>>n>>e;
vector<vector<pair<int,int>>> graph(n+1);
for(int i=0;i<e;i++)
{
int s,d,w;
cin>>s>>d>>w;
graph[s].push_back({d,w});
graph[d].push_back({s,w});
}
vector<int> dist(n+1,INT_MAX);
set<pair<int,int>> s;
int source;
cin>>source;
dist[source]=0;
s.insert({0,source});
vector<int> parent(n+1, -1);
while(!s.empty()){
auto x = *(s.begin()); // get the lowest weighted verte from set
s.erase(x); //remove from set
// now iterate through all other verteces to relax them if req
for(auto it: graph[x.second]){
if(dist[it.first] > dist[x.second]+it.second){ //relax
s.erase({dist[it.first],it.first});
dist[it.first] = dist[x.second]+it.second;
s.insert({dist[it.first],it.first});
parent[it.first]= x.second;
} }
}
for(int i=1;i< n+1;i++){
path(parent, i);
cout<<" : "<<dist[i]<<endl;
}
return 0;
}
OUTPUT
psProgram 20
Design an algorithm and implement it using a program to solve previous question's problem using Bellman- Ford's shortest path algorithm.
Code:
#include<bits/stdc++.h>
using namespace std;
void path(vector<int>& parent, int j){
if (parent[j] == - 1){
cout<<j;
return;
}
printf("%d ", j);
path(parent, parent[j]);
}
int main()
{
#ifndef ONLINE_JUDGE
freopen("input.txt","r",stdin);
freopen("output.txt","w",stdout);
#endif
int n,e;
cin>>n>>e;
vector<vector<int>> edges;
for(int i=0;i<e;i++){
int u,v,w;
cin>>u>>v>>w;
edges.push_back({u,v,w});
edges.push_back({v,u,w});
}
vector<int> parent(n+1,-1);
//initialize distance array
vector<int> dist(n+1, 1e9);
int src;
cin>>src; //input source
dist[src] = 0; // initialize source distance to 0
//iterate n-1 times to relax each edge
bool negative_cycle;
for(int i=1;i<n;i++)
{
negative_cycle = false; //to detect -ve cycle
for(auto it: edges){
int u,v,w;
u = it[0];
v = it[1];
w = it[2];
if(dist[v] > dist[u]+w){
dist[v] = dist[u]+w;
parent[v] = u;
negative_cycle = true;
}
}
}
if(negative_cycle)
cout<<"negative cycle present";
else{
for(int i=1;i< n+1;i++){
path(parent, i);
cout<<" : "<<dist[i]<<endl;
}
}
return 0;
}
OUTPUT
psProgram 21
Given a directed graph with two vertices ( source and destination). Design an algorithm and implement it using a program to find the weight of the shortest path from source to destination with exactly k edges on the path.
Code:
#include<bits/stdc++.h>
using namespace std;
#define V 100
#define INF INT_MAX
int arr[100][100];
int shortestpath(int arr[][V],int u,int v,int k, int n)
{
if(k==0 && u==v) return 0;
if(k==1 && arr[u][v] != INF) return arr[u][v];
if(k<=0)
return INF;
int res = INF;
for(int i=0;i<n;i++)
{
if(arr[u][i] != INF && u!=i && v!=i)
{
int rec_res = shortestpath(arr, i,v,k-1, n);
if(rec_res != INF)
res = min(res, arr[u][i]+rec_res);
}
}
return res;
}
int main()
{
#ifndef ONLINE_JUDGE
freopen("input.txt","r",stdin);
freopen("output.txt","w",stdout);
#endif
int n;
cout<<"for values INF enter -1"<<endl;
cin>>n;
int a;
for(int i=0;i<n;i++){
for(int j=0;j<n;j++){
cin>>a;
if(a<0){
arr[i][j] = INF;
}
else
arr[i][j] = a;
}
}
int u,v,k;
cin>>u>>v>>k;
cout<<"weight of the shortest path is "<<shortestpath(arr,u-1,v-1,k,n)<<endl;// 0 indexing is followed
return 0;
}
OUTPUT
psProgram 22
Assume that a project of road construction to connect some cities is given to your friend. Map of these cities and roads which will connect them (after construction) is provided to him in the form of a graph. Certain amount of rupees is associated with construction of each road. Your friend has to calculate the minimum budget required for this project. The budget should be designed in such a way that the cost of connecting the cities should be minimum and number of roads required to connect all the cities should be minimum (if there are N cities then only N-1 roads need to be constructed). He asks you for help. Now, you have to help your friend by designing an algorithm which will find minimum cost required to connect these cities. (use Prim's algorithm)
Code:
#include<bits/stdc++.h>
using namespace std;
int main()
{
#ifndef ONLINE_JUDGE
freopen("input.txt","r",stdin);
freopen("output.txt","w",stdout);
#endif
int nodes, edges;
cin>>nodes;
cin>>edges;
vector<pair<int,int>> graph[nodes];
int source, destination, weight;
for(int i=0;i<edges;i++)
{
cin>>source>>destination>>weight;
graph[source].push_back(make_pair(destination,weight));
graph[destination].push_back(make_pair(source, weight));
}
int key[nodes];//to select the min weight
int parent[nodes];// to store the parent node
bool mst[nodes]; // to construct the path
for(int i=0;i< nodes;i++)// initialization
{
key[i]= INT_MAX;
mst[i] = false;
parent[i] = -1;
}
// priority queue APPROACH
priority_queue<pair<int, int>, vector<pair<int,int>>,
greater<pair<int,int>>> pq;
key[0] = 0;//select a node to start from
parent[0] = 0;
pq.push({0, 0}); //{weight, index of starting node}
for(int i=0;i< nodes-1;i++)
{
int u = pq.top().second;//get the index of top node
pq.pop();//remove the node from queue
mst[u] = true;//set mst as true for the node u
for(auto it: graph[i])
{
int dest = it.first;
int wt = it.second;
if(mst[dest]== false && wt<key[dest])//check if the parent
array needs to be changed
{
parent[dest] = u;
pq.push({key[dest], dest});
key[dest] = wt;
}
}
}
int mstwt = 0;
// to print the list with minimun weight
for(int i=0;i<nodes;i++)
mstwt += key[i];
cout<<"Min Spanning Weight is: "<<mstwt;
return 0;
}
OUTPUT
psProgram 23
Implement the previous problem using Kruskal's algorithm.
Code:
#include<bits/stdc++.h>
using namespace std;
vector<int> parent(100);
vector<int> sz(100);
void make_set(int v)
{
parent[v]=v;
sz[v] = 1;
}
int find_set(int v)
{
if(v==parent[v])
return v;
return parent[v] = find_set(parent[v]);
}
void union_set(int a, int b)
{
a = find_set(a);
b = find_set(b);
if(a != b){//dont belong to same set
if(sz[a] < sz[b])
swap(a,b);
parent[b] = a;
sz[a] += sz[b];
}
}
int main()
{
#ifndef ONLINE_JUDGE
freopen("input.txt","r",stdin);
freopen("output.txt","w",stdout);
#endif
int n,e;
cin>>n>>e;
for(int i=0;i<n;i++)
make_set(i);
vector<vector<int>> graph;
for(int i=0;i<e;i++)
{
int u,v,w;
cin>>u>>v>>w;
graph.push_back({w,u,v});
graph.push_back({w,v,u});
}
sort(graph.begin(), graph.end());//sort according to weight
int total_weight = 0;
for(auto i: graph){
int w = i[0];
int u = i[1];
int v = i[2];
int x = find_set(u);
int y = find_set(v);
if(x == y){
continue;
}
else{
total_weight += w;
union_set(u,v);//add to set
}
}
cout<<"Minimum Spanning Weight is: "<<total_weight;
return 0;
}
OUTPUT
psProgram 24
Assume that the same road construction project is given to another person. The amount he will earn from this project is directly proportional to the budget of the project. This person is greedy, so he decided to maximize the budget by constructing those roads which have the highest construction cost. Design an algorithm and implement it using a program to find the maximum budget required for the project.
Code:
#include<bits/stdc++.h>
using namespace std;
bool compare(const pair<int,int>& a, const pair<int, int>& b){
return b.first > a.first;
}
vector<int> parent(100);
vector<int> sz(100);
void make_set(int v)
{
parent[v]=v;
sz[v] = 1;
}
int find_set(int v)
{
if(v==parent[v])
return v;
return parent[v] = find_set(parent[v]);
}
void union_set(int a, int b)
{
a = find_set(a);
b = find_set(b);
if(a != b){//dont belong to same set
if(sz[a] < sz[b])
swap(a,b);
parent[b] = a;
sz[a] += sz[b];
}
}
int main()
{
#ifndef ONLINE_JUDGE
freopen("input.txt","r",stdin);
freopen("output.txt","w",stdout);
#endif
int n,e;
cin>>n>>e;
for(int i=0;i<n;i++)
make_set(i);
vector<vector<int>> graph;
for(int i=0;i<e;i++)
{
int u,v,w;
cin>>u>>v>>w;
graph.push_back({w,u,v});
graph.push_back({w,v,u});
}
sort(graph.rbegin(), graph.rend());//sort according to weight
int total_weight = 0;
for(auto i: graph){
int w = i[0];
int u = i[1];
int v = i[2];
int x = find_set(u);
int y = find_set(v);
if(x == y){
continue;
}
else{
//cout<<u<<" "<<v<<endl;
total_weight += w;
union_set(u,v);//add to set
}
}
cout<<"Maximum Spanning Weight is: "<<total_weight;
return 0;
}
OUTPUT
psProgram 25
Given a graph, Design an algorithm and implement it using a program to implement FloydWarshall all pair shortest path algorithm
Code:
#include<bits/stdc++.h>
using namespace std;
#define INF 1e9
int main()
{
#ifndef ONLINE_JUDGE
freopen("input.txt","r",stdin);
freopen("output.txt","w",stdout);
#endif
int n;
cout<<"for values INF enter -1"<<endl;
cin>>n;
int a;
int arr[n][n], dist[n][n];
for(int i=0;i<n;i++){
for(int j=0;j<n;j++){
cin>>a;
if(a<0){
arr[i][j] = INF;
}
else
arr[i][j] = a;
dist[i][j] = arr[i][j];
}
}
for(int k=0;k<n;k++){
for(int i=0;i<n;i++){
for(int j=0;j<n;j++){
if(dist[i][k]+dist[k][j] < dist[i][j]){
dist[i][j] = dist[i][k]+dist[k][j];
}
}
}
}
cout<<"Shortest Distance Matrix: "<<endl;
for(int i=0;i<n;i++){
for(int j=0;j<n;j++){
if(dist[i][j]==INF){
cout<<"INF ";
}
else
cout<<dist[i][j]<<" ";
}
cout<<endl;
}
return 0;
}
OUTPUT
psProgram 26
Given a knapsack of maximum capacity w. N items are provided, each having its own value and weight. You have to Design an algorithm and implement it using a program to find the list of the selected items such that the final selected content has weight w and has maximum value. You can take fractions of items,i.e. the items can be broken into smaller pieces so that you have to carry only a fraction xi of item i, where 0 ≤xi≤ 1.
Code:
#include<bits/stdc++.h>
using namespace std;
int main()
{
#ifndef ONLINE_JUDGE
freopen("input.txt","r",stdin);
freopen("output.txt","w",stdout);
#endif
int n;
cin>>n;
vector<double> items(n);
vector<double> val(n);
vector<vector<double>> job;//to store pair of
for(int i=0;i<n;i++){
cin>>items[i];
}
for(int i=0;i<n;i++){
cin>>val[i];
job.push_back({val[i]/items[i],items[i],i+1});
}
double k;
cin>>k;
sort(job.rbegin(), job.rend());//sort acc to val per wt
vector<pair<double,double>> ls;
float profit =0;
for(int i=0;i<n;i++)
{
if(job[i][1] >= k)
{
profit += k*job[i][0];
ls.push_back(make_pair(k, job[i][2]));
break;
}
else
{
profit += job[i][1]*job[i][0];
}
ls.push_back(make_pair(job[i][1], job[i][2]));
k = k - job[i][1];
}
cout<<"Maximum Value is: "<<profit<<endl;
cout<<"Item - Weight"<<endl;
for(auto it: ls)
cout<<it.first<<" - "<<it.second<<endl;
return 0;
}
OUTPUT
psProgram 27
Given an array of elements. Assume arr[i] represents the size of file i. Write an algorithm and a program to merge all these files into single file with minimum computation. For given two files A and B with sizes m and n, computation cost of merging them is O(m+n). (Hint: use greedy approach)
Code:
#include<bits/stdc++.h>
using namespace std;
int main()
{
#ifndef ONLINE_JUDGE
freopen("input.txt","r",stdin);
freopen("output.txt","w",stdout);
#endif
int n;
cin>>n;
vector<int> a(n);
for(int i=0;i<n;i++){
cin>>a[i];
}
priority_queue<int, vector<int>, greater<int>> minheap;
for(int i=0;i<n;i++){
minheap.push(a[i]);
}
int ans = 0;
while(minheap.size()>1){
int e1 = minheap.top();
minheap.pop();
int e2 = minheap.top();
minheap.pop();
ans += e1+e2;
minheap.push(e1 + e2);
}
cout<<ans;
return 0;
}
OUTPUT
psProgram 28
Given a list of activities with their starting time and finishing time. Your goal is to select maximum number of activities that can be performed by a single person such that selected activities must be non-conflicting. Any activity is said to be non-conflicting if starting time of an activity is greater than or equal to the finishing time of the other activity. Assume that a person can only work on a single activity at a time.
Code:
#include<bits/stdc++.h>
using namespace std;
int main()
{
#ifndef ONLINE_JUDGE
freopen("input.txt","r",stdin);
freopen("output.txt","w",stdout);
#endif
int n;
cin>>n;
vector<int> st(n), dline(n);
vector<vector<int>> activity;
for(int i=0;i<n;i++){
cin>>st[i];
}
for(int i=0;i<n;i++){
cin>>dline[i];
activity.push_back({dline[i],st[i], i+1});
}
sort(activity.begin(), activity.end());
vector<int> selected;
int count=0;
int currentEnd = -1;
for(int i=0;i<n;i++){
if(activity[i][1]>currentEnd){
count++;
currentEnd = activity[i][0];
selected.push_back(activity[i][2]);
}
}
cout<<"No. of non-conflictin activities: "<<count<<endl;
cout<<"List of selected activites: ";
for(auto i: selected){
cout<<i<<" ";
}
return 0;
}
OUTPUT
psProgram 29
Given a long list of tasks. Each task take specific time to accomplish it and each task has a deadline associated with it. You have to design an algorithm and implement it using a program to find maximum number of tasks that can be completed without crossing their deadlines and also find list of selected tasks.
Code:
#include<bits/stdc++.h>
using namespace std;
bool compare(pair<int,int>a,pair<int,int>b){
return a.first > b.first;
}
int main()
{
#ifndef ONLINE_JUDGE
freopen("input.txt","r",stdin);
freopen("output.txt","w",stdout);
#endif
int n;
cin>>n;
int p[n];
int d[n];
for(int i=0;i<n;i++)
cin>>p[i];
for(int i=0;i<n;i++)
cin>>d[i];
vector<pair<int,int> > jobs;
int profit,deadline;
for(int i=0;i<n;i++){
jobs.push_back(make_pair(p[i],d[i]));
}
sort(jobs.begin(),jobs.end(),compare);
int maxEndTime = 0;
for(int i=0;i<n;i++){
if(jobs[i].second > maxEndTime)
maxEndTime = jobs[i].second;
}
vector<int> ans;
int fill[maxEndTime];
int count = 0, maxProfit = 0;
for(int i=0;i<n;i++) fill[i] = -1;
for(int i=0;i<n;i++){
int j = jobs[i].second - 1;
while(j>=0 && fill[i]!=-1) j--;
if(j>=0 && fill[j]==-1){
fill[j] = i;
ans.push_back(i);
count++;
maxProfit = maxProfit + jobs[i].first;
}
}
cout<<"Maximum no of tasks : "<<count<<endl;
cout<<"Selected task numbers : ";
for(int i=0;i<ans.size();i++)
cout<<ans[i]<<" ";
return 0;
}
OUTPUT
psProgram 30
Given an unsorted array of elements, design an algorithm and implement it using a program to find whether majority element exists or not. Also find median of the array. A majority element is an element that appears more than n/2 times, where n is the size of array.
Code:
#include <bits/stdc++.h>
using namespace std;
string majorityElement(int *arr, int n)
{
int count = 1, max_ele = -1, temp = arr[0], ele, f=0;
for(int i=1;i<n;i++)
{
if(temp==arr[i])
{
count++;
}
else
{
count = 1;
temp = arr[i];
}
if(max_ele<count)
{
max_ele = count;
ele = arr[i];
if(max_ele>(n/2))
{
f = 1;
break;
}
}
}
return (f==1 ? "yes" : "no");
}
int main()
{
#ifndef ONLINE_JUDGE
freopen("input.txt","r",stdin);
freopen("output.txt","w",stdout);
#endif
int n;
cin>>n;
int arr[n];
for(int i=0;i<n;i++){
cin>>arr[i];
}
sort(arr, arr+n);
cout<<majorityElement(arr, n)<<endl;
if(n%2 == 0){
cout<<(arr[n/2 -1]+arr[n/2])/2;
}
else{
cout<<arr[n/2];
}
return 0;
}
OUTPUT
Raw Text
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Happy birthday! I'll let you fuck me, but don't cum inside! - AdaKham
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My sexy stepsister invite me for great fuck
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i n c e s t
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y0ung parad1se
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Mixed 720GB CeePee
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