# Array and simple queries

### Problem Statement :

Given two numbers N  and M. N  indicates the number of elements in the array  A[](1-indexed) and  M indicates number of queries. You need to perform two types of queries on the array A[] .

You are given  queries. Queries can be of two types, type 1 and type 2.

Type 1 queries are represented as 1 i j : Modify the given array by removing elements from i to j and adding them to the front.

Type 2 queries are represented as 2 i j : Modify the given array by removing elements from i to j and adding them to the back.

Your task is to simply print | A[1] -  A[N] | of the resulting array after the execution of  queries followed by the resulting array.

Note While adding at back or front the order of elements is preserved.

Input Format

First line consists of two space-separated integers, N and M .
Second line contains N integers,  which represent the elements of the array.
M queries follow. Each line contains a query of either type 1 or type 2 in the form type i j

Output Format

Print the absolute value i.e. abs(A[1] - A[N] )  in the first line.
Print elements of the resulting array in the second line. Each element should be seperated by a single space.

### Solution :

Solution in C :

In C ++ :

#include <iostream>
#include <cstdlib>
#include <vector>
#include <ctime>

struct ctree {
long value, size;
int prio;
ctree *left, *right;
};

static const long MAX_N = 100000l;
static ctree nodes[MAX_N];
static long values[MAX_N];

static long csize(ctree *t)
{ return t ? t->size : 0; }

static ctree *cmerge(ctree *l, ctree *r)
{
if (!l) return r;
if (!r) return l;

if (l->prio > r->prio) {
l->right = cmerge(l->right, r);
l->size = csize(l->left) + csize(l->right) + 1;
return l;
}
r->left = cmerge(l, r->left);
r->size = csize(r->left) + csize(r->right) + 1;
return r;
}

static void csplit(ctree *t, long idx, ctree *&l, ctree *&r)
{
if (!t) {
l = r = 0;
return;
}

const long cur = csize(t->left) + 1;
if (cur <= idx) {
csplit(t->right, idx - cur, t->right, r);
l = t;
} else {
csplit(t->left, idx, l, t->left);
r = t;
}
t->size = csize(t->left) + csize(t->right) + 1;
}

static ctree *cextract(ctree *&t, long from, long to)
{
ctree *l, *m, *r;

csplit(t, from, l, m);
csplit(m, to - from, m, r);
t = cmerge(l, r);
return m;
}

static long traverse(ctree *tree, long i)
{
if (!tree)
return i;

i = traverse(tree->left, i);
values[i++] = tree->value;
return traverse(tree->right, i);
}

int main()
{
srand(time(NULL));
for (long i = 0; i != MAX_N; ++i) {
nodes[i].prio = rand();
nodes[i].size = 1;
}

long n, m;
std::cin >> n >> m;

ctree *tree = 0;
for (long i = 0; i != n; ++i) {
std::cin >> nodes[i].value;
tree = cmerge(tree, nodes + i);
}

for (long i = 0; i != m; ++i) {
long l, r;
int type;

std::cin >> type >> l >> r;

ctree *sub = cextract(tree, l - 1, r);
if (type == 1)
tree = cmerge(sub, tree);
else
tree = cmerge(tree, sub);
}

traverse(tree, 0);
std::cout << std::abs(values[0] - values[n - 1]) << "\n";
for (long i = 0; i != n; ++i)
std::cout << values[i] << " ";
std::cout << "\n";

return 0;
}

In C :

#include <stdio.h>
#include <stdlib.h>
typedef struct _ct_node{
int size;
int priority;
int value;
struct _ct_node *left,*right;
} ct_node;
void tar(ct_node *root);
int get_size(ct_node *root);
ct_node* merge(ct_node *L,ct_node *R);
int sizeOf(ct_node *root);
void recalc(ct_node *root);
void split(int x,ct_node **L,ct_node **R,ct_node *root);
void computeTree();
int P[100000],T[100000],st[100000],N;
ct_node pool[100000];

int main(){
int M,x,y,z,i;
ct_node *root,*l,*m,*r,*t;
scanf("%d%d",&N,&M);
for(i=0;i<N;i++){
scanf("%d",&pool[i].value);
P[i]=pool[i].priority=rand();
pool[i].left=pool[i].right=NULL;
}
computeTree();
for(i=0;i<N;i++)
if(T[i]==-1)
root=&pool[i];
else
if(i<T[i])
pool[T[i]].left=&pool[i];
else
pool[T[i]].right=&pool[i];
get_size(root);
for(i=0;i<M;i++){
scanf("%d%d%d",&x,&y,&z);
switch(x){
case 1:
split(y-2,&l,&t,root);
split(z-y,&m,&r,t);
root=merge(merge(m,l),r);
break;
default:
split(y-2,&l,&t,root);
split(z-y,&m,&r,t);
root=merge(merge(l,r),m);
}
}
N=0;
tar(root);
printf("%d\n",(T[0]>T[N-1])?T[0]-T[N-1]:T[N-1]-T[0]);
for(i=0;i<N;i++)
printf("%d ",T[i]);
return 0;
}
void tar(ct_node *root){
if(!root)
return;
tar(root->left);
T[N++]=root->value;
tar(root->right);
return;
}
int get_size(ct_node *root){
if(!root)
return 0;
root->size=get_size(root->left)+get_size(root->right)+1;
return root->size;
}
ct_node* merge(ct_node *L,ct_node *R){
if(!L)
return R;
if(!R)
return L;
if(L->priority>R->priority){
L->right=merge(L->right,R);
recalc(L);
return L;
}
R->left=merge(L,R->left);
recalc(R);
return R;
}
int sizeOf(ct_node *root){
return (root)?root->size:0;
}
void recalc(ct_node *root){
root->size=sizeOf(root->left)+sizeOf(root->right)+1;
return;
}
void split(int x,ct_node **L,ct_node **R,ct_node *root){
if(!root){
*L=*R=NULL;
return;
}
int curIndex=sizeOf(root->left);
ct_node *t;
if(curIndex<=x){
split(x-curIndex-1,&t,R,root->right);
root->right=t;
recalc(root);
*L=root;
}
else{
split(x,L,&t,root->left);
root->left=t;
recalc(root);
*R=root;
}
return;
}
void computeTree(){
int i,k,top=-1;
for(i=0;i<N;i++){
k=top;
while(k>=0 && P[st[k]]<P[i])
k--;
if(k!=-1)
T[i]=st[k];
if(k<top)
T[st[k+1]]=i;
st[++k]=i;
top=k;
}
T[st[0]]=-1;
return;
}

In Java :

import java.io.*;
import java.util.*;
import java.text.*;
import java.math.*;
import java.util.regex.*;

public class Solution {

Node root;

public Solution() {
root = null;
}

public int size(Node root) {
if (root == null)
return 0;
return root.size;
}

private void update(Node root) {
if (root != null)
root.size = 1 + size(root.left) + size(root.right);
}

public DNode split(Node root, int key) {
DNode pair = new DNode();
if (root == null) {
return pair;
}
if (size(root.left) >= key) {
pair = split(root.left, key);
root.left = pair.right;
update(root);
pair.right = root;
} else {
pair = split(root.right, key - size(root.left) - 1);
root.right = pair.left;
update(root);
pair.left = root;
}
return pair;
}

public Node merge(Node left, Node right) {
if (left == null) return right;
if (right == null) return left;

if (left.pri > right.pri) {
left.right = merge(left.right, right);
update(left);
return left;
} else {
right.left = merge(left, right.left);
update(right);
return right;
}
}

public Node getFirst() {
if (root == null)
return null;
return getFirst(root);
}

private Node getFirst(Node root) {
if (root.left != null)
return getFirst(root.left);
return root;
}

public Node getLast() {
if (root == null)
return null;
return getLast(root);
}

private Node getLast(Node root) {
if (root.right != null)
return getLast(root.right);
return root;
}

public void query1(int left, int right) {
DNode pair1 = split(root, right);
DNode pair2 = split(pair1.left, left-1);

root = merge(pair2.left, pair1.right);
root = merge(pair2.right, root);
}

public void query2(int left, int right) {
DNode pair1 = split(root, right);
DNode pair2 = split(pair1.left, left-1);

root = merge(pair2.left, pair1.right);
root = merge(root, pair2.right);
}

public void add(int val, int pri) {
Node n = new Node(val, pri);
root = merge(root, n);
}

public void inorder() {
inorder(root);
System.out.println();
}

private void inorder(Node n) {
if (n == null)
return;
inorder(n.left);
System.out.print(n + " ");
inorder(n.right);
}

private static class DNode {
Node left;
Node right;

DNode() {
left = null;
right = null;
}

public String toString() {
return "L:" + left + " R:" + right;
}
}

private static class Node {
int val;
int pri;
int size;

Node left;
Node right;

Node(int val, int pri) {
this.val = val;
this.pri = pri;
size = 1;
left = null;
right = null;
}

public String toString() {
return String.valueOf(val);
}
}

public static void main(String[] args) {
Solution t = new Solution();
Scanner sc = new Scanner(System.in);
Random rd = new Random();
int n = sc.nextInt();
int m = sc.nextInt();
for (int i = 0;  i < n; i++) {
int v = sc.nextInt();
}
for (int i = 0; i < m; i++) {
int op = sc.nextInt();
int low = sc.nextInt();
int high = sc.nextInt();
if (op == 1)
t.query1(low, high);
else
t.query2(low, high);
}
System.out.println(Math.abs(t.getFirst().val - t.getLast().val));
t.inorder();
sc.close();
}
}

In python3 :

from array import array

n, n_queries = map(int, input().split())
data = array('L', map(int, input().split()))
assert len(data) == n
for m in range(n_queries):
t, i, j = map(int, input().split())
if t == 1:
aux1 = i-1
aux2 = j - aux1
data[:aux2], data[aux2:j] = data[aux1:j], data[:aux1]
else:
aux1 = i-1
aux2 = aux1 + n - j
data[aux1:aux2], data[aux2:] = data[j:], data[aux1:j]
print(abs(data[0] - data[-1]))
print(*data)

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