Swaps and Sum
Problem Statement :
You are given a sequence a1, a2, a3, . . . an. The task is to perform the following queries on it: Type 1. Given two integers l and r( 1 <= l <= r ; r - l +1 is even ) . Reorder the elements of the sequence in such a way (changed part of the sequence is in brackets): That is swap the first two elements of segment [ l , r ] , the second two elements, and so on. Type 2. Given two integers l and r, print the value of sum . Input Format The first line contains two integers n and q. The second line contains n integers a1, a2, a3 . . . , an, denoting initial sequence. Each of the next q lines contains three integers tpi, li, ri, where tpi denotes the type of the query, and li, ri are parameters of the query. It's guaranteed that for a first-type query ( r - l + 1 ) will be even. Constraints 2 <= n <= 2 x 10^5 1 <= q <= 2 x 10^5 1 <= ai <= 10^6 1 <= tpi <= 2 1 <= li <= ri <= n Output Format For each query of the second type print the required sum
Solution :
Solution in C :
In C++ :
#include <bits/stdc++.h>
using namespace std;
typedef long long ll;
const ll N = 1<<18;
const ll INF = 1000000000;
const ll md =1000*1000*1000;
struct name
{
ll x,y,l,r,val,mi;
};
ll n,m,tt0,x,t0,tt1,t1,type,l,r,l0,r0,l1,r1,t0f,t1f,t0l,t1l,t0m,t1m,t0r,t1r,tr,s,t;
vector <name> treap;
vector <ll> a;
void split(ll t,ll k,ll &t1,ll &t2){
if (t==0)
{
t1=t2=0;
return;
}
if (k>treap[treap[t].l].x){
split(treap[t].r,k-treap[treap[t].l].x-1,treap[t].r,t2);
t1=t;
}
else
{
split(treap[t].l,k,t1,treap[t].l);
t2=t;
}
treap[t].x=treap[treap[t].l].x+treap[treap[t].r].x+1;
treap[t].mi=treap[t].val+treap[treap[t].l].mi+treap[treap[t].r].mi;;
}
void merge (ll & t,ll t1, ll t2){
if (!t1 || !t2) {
if (!t1)
t=t2;
else
t=t1;
return ;
}
if (treap[t1].y>treap[t2].y)
{
merge(treap[t1].r,treap[t1].r,t2);
t=t1;
}
else
{
merge(treap[t2].l,t1,treap[t2].l);
t=t2;
}
treap[t].x=treap[treap[t].l].x+treap[treap[t].r].x+1;
treap[t].mi=treap[t].val+treap[treap[t].l].mi+treap[treap[t].r].mi;
}
ll Pos(ll v)
{
return v/2+v%2;
}
void Getlr()
{
if (l%2==1)
{
l0=Pos(l+1)+n/2+n%2;
l1=Pos(l);
}
else
{
l1=Pos(l+1);
l0=Pos(l)+n/2+n%2;
}
if (r%2==1)
{
r1=Pos(r);
r0=Pos(r-1)+n/2+n%2;
}
else
{
r1=Pos(r-1);
r0=Pos(r)+n/2+n%2;
}
}
int main()
{
s=0;
scanf("%lld%lld",&n,&m);
tr=t=0;
treap.clear();
a.clear();
treap.resize(n+5);
a.resize(n+5);
for (int i=1;i<=n;i++)
scanf("%lld",&a[i]);
for (int i=1;i<=n;i+=2)
{
tr++;
treap[tr].x=1;
treap[tr].y=rand()+1;
treap[tr].val=treap[tr].mi=a[i];
merge(t,t,tr);
}
for (int i=2;i<=n;i+=2)
{
tr++;
treap[tr].x=1;
treap[tr].y=rand()+1;
treap[tr].val=treap[tr].mi=a[i];
merge(t,t,tr);
}
while (m--)
{
scanf("%lld%lld%lld",&type,&l,&r);
if (type==1)
{
Getlr();
split(t,r0,t,t0r);
split(t,l0-1,t,t0m);
split(t,r1,t,t1r);
split(t,l1-1,t,t1m);
merge(t,t,t0m);
merge(t,t,t1r);
merge(t,t,t1m);
merge(t,t,t0r);
}
else
{
Getlr();
split(t,r0,t,t0r);
split(t,l0-1,t,t0m);
split(t,r1,t,t1r);
split(t,l1-1,t,t1m);
printf("%lld\n",treap[t0m].mi+treap[t1m].mi);
merge(t,t,t1m);
merge(t,t,t1r);
merge(t,t,t0m);
merge(t,t,t0r);
}
}
}
In Java :
import java.io.*;
import java.util.*;
public class Solution {
private static Reader in;
private static PrintWriter out;
public static void main(String[] args) throws IOException {
in = new Reader();
out = new PrintWriter(System.out, true);
int N = in.nextInt(), Q = in.nextInt();
arr = new int[N+1];
for (int i = 1; i <= N; i++) arr[i] = in.nextInt();
rootEven = initRec(1, N/2, true);
rootOdd = initRec(1, (N+1)/2, false);
for (int i = 0; i < Q; i++) {
int cmd = in.nextInt();
if (cmd == 1) {
flip(in.nextInt(), in.nextInt());
} else {
out.println(getSum(in.nextInt(), in.nextInt()));
}
// for (int j = 1; j <= N; j++) out.print(" "+getSum(j, j));
// out.println();
}
out.close();
System.exit(0);
}
public static int[] arr;
static class Node {
int size;
Node left;
Node right;
Node parent;
int val;
long sum;
public Node(int val) {
this.val = val;
this.sum = val;
this.size = 1;
left = null;
right = null;
parent = null;
}
public String toString() {
return val + " " + size;
}
}
// Whether x is a root of a splay tree
static boolean isRoot(Node x) {
return x.parent == null;
}
static void connect(Node ch, Node p, boolean leftChild) {
if (leftChild)
p.left = ch;
else
p.right = ch;
join(p);
if (ch != null) {
ch.parent = p;
}
}
// rotate edge (x, x.parent)
static void rotate(Node x) {
Node p = x.parent;
Node g = p.parent;
boolean isRootP = isRoot(p);
boolean leftChildX = (x == p.left);
Node next = leftChildX ? x.right : x.left;
connect(next, p, leftChildX);
connect(p, x, !leftChildX);
if (!isRootP)
connect(x, g, p == g.left);
else
x.parent = g;
}
static Node splay(Node x) {
while (!isRoot(x)) {
Node p = x.parent;
Node g = p.parent;
if (!isRoot(p))
rotate((x == p.left) == (p == g.left) ? p : x);
rotate(x);
}
return x;
}
static Node cutLeft(Node x) {
Node ret = x.left;
if (ret != null) {
x.left.parent = null;
x.left = null;
join(x);
}
return ret;
}
static Node cutRight(Node x) {
Node ret = x.right;
if (ret != null) {
x.right.parent = null;
x.right = null;
join(x);
}
return ret;
}
static void join(Node x) {
x.size = (x.left == null ? 0 : x.left.size) + (x.right == null ? 0 : x.right.size) + 1;
x.sum = (x.left == null ? 0 : x.left.sum) + (x.right == null ? 0 : x.right.sum) + x.val;
}
private static Node getElementAtPosition(boolean even, int a) {
Node cur = even ? rootEven : rootOdd;
while (a > 0) {
int sz = (cur.left == null ? 0 : cur.left.size);
if (a <= sz) {
cur = cur.left;
continue;
}
a -= sz + 1;
if (a == 0)
break;
cur = cur.right;
}
Node ret = splay(cur);
if (even) rootEven = ret; else rootOdd = ret;
return cur;
}
private static long getSum(int a, int b) {
if (a == b) {
return getElementAtPosition(a % 2 == 0, (a+1)/2).val;
}
Node righte = getElementAtPosition(true, b/2);
Node rae = cutRight(righte);
Node lefte = getElementAtPosition(true, (a+1)/2);
Node lae = cutLeft(lefte);
Node righto = getElementAtPosition(false, (b+1)/2);
Node rao = cutRight(righto);
Node lefto = getElementAtPosition(false, a/2+1);
Node lao = cutLeft(lefto);
long res = lefte.sum + lefto.sum;
rootEven = splay(righte);
connect(rae, righte, false);
rootEven = splay(lefte);
connect(lae, lefte, true);
rootOdd = splay(righto);
connect(rao, righto, false);
rootOdd = splay(lefto);
connect(lao, lefto, true);
return res;
}
private static void flip(int a, int b) {
if (a == b)
return;
int off = (b-a+1) / 2;
int se = (a+1)/2;
Node righte = getElementAtPosition(true, se+off-1);
Node rae = cutRight(righte);
Node lefte = getElementAtPosition(true, se);
Node lae = cutLeft(lefte);
int so = a/2+1;
Node righto = getElementAtPosition(false, so+off-1);
Node rao = cutRight(righto);
Node lefto = getElementAtPosition(false, so);
Node lao = cutLeft(lefto);
rootOdd = splay(righte);
connect(rao, righte, false);
rootOdd = splay(lefte);
connect(lao, lefte, true);
rootEven = splay(righto);
connect(rae, righto, false);
rootEven = splay(lefto);
connect(lae, lefto, true);
}
private static Node initRec(int start, int end, boolean even) {
if (start == end) {
int idx = (start-1) * 2;
if (!even) idx++; else idx += 2;
return new Node(arr[idx]);
}
int mid = (start + end) >> 1;
int idx = (mid-1) * 2;
if (!even) idx++; else idx += 2;
Node x = new Node(arr[idx]);
if (start <= mid - 1)
connect(initRec(start, mid - 1, even), x, true);
if (mid + 1 <= end)
connect(initRec(mid + 1, end, even), x, false);
return x;
}
private static Node rootEven, rootOdd;
static class Reader {
final private int BUFFER_SIZE = 1 << 16;
private DataInputStream din;
private byte[] buffer;
private int bufferPointer, bytesRead;
public Reader() {
din = new DataInputStream(System.in);
buffer = new byte[BUFFER_SIZE];
bufferPointer = bytesRead = 0;
}
public Reader(String file_name) throws IOException {
din = new DataInputStream(new FileInputStream(file_name));
buffer = new byte[BUFFER_SIZE];
bufferPointer = bytesRead = 0;
}
public String readLine() throws IOException {
byte[] buf = new byte[1 << 20];
int cnt = 0;
byte c = read();
while (c <= ' ')
c = read();
do {
buf[cnt++] = c;
} while ((c = read()) != '\n');
return new String(buf, 0, cnt);
}
public String next() throws IOException {
byte[] buf = new byte[1 << 20];
int cnt = 0;
byte c = read();
while (c <= ' ')
c = read();
do {
buf[cnt++] = c;
} while ((c = read()) > ' ');
return new String(buf, 0, cnt);
}
public int nextInt() throws IOException {
int ret = 0;
byte c = read();
while (c <= ' ')
c = read();
boolean neg = (c == '-');
if (neg)
c = read();
do {
ret = ret * 10 + c - '0';
} while ((c = read()) >= '0' && c <= '9');
if (neg)
return -ret;
return ret;
}
public long nextLong() throws IOException {
long ret = 0;
byte c = read();
while (c <= ' ')
c = read();
boolean neg = (c == '-');
if (neg)
c = read();
do {
ret = ret * 10 + c - '0';
} while ((c = read()) >= '0' && c <= '9');
if (neg)
return -ret;
return ret;
}
public double nextDouble() throws IOException {
double ret = 0, div = 1;
byte c = read();
while (c <= ' ')
c = read();
boolean neg = (c == '-');
if (neg)
c = read();
do {
ret = ret * 10 + c - '0';
} while ((c = read()) >= '0' && c <= '9');
if (c == '.')
while ((c = read()) >= '0' && c <= '9')
ret += (c - '0') / (div *= 10);
if (neg)
return -ret;
return ret;
}
private void fillBuffer() throws IOException {
bytesRead = din.read(buffer, bufferPointer = 0, BUFFER_SIZE);
if (bytesRead == -1)
buffer[0] = -1;
}
private byte read() throws IOException {
if (bufferPointer == bytesRead)
fillBuffer();
return buffer[bufferPointer++];
}
public void close() throws IOException {
if (din == null)
return;
din.close();
}
}
}
In C :
#include <stdio.h>
#include <stdlib.h>
typedef struct _ct_node{
int size;
int priority;
int value;
long long sum;
struct _ct_node *left,*right;
} ct_node;
long long get_sum(int x,int y,ct_node *root);
void get_size(ct_node *root);
ct_node* merge(ct_node *L,ct_node *R);
int sizeOf(ct_node *root);
long long sumOf(ct_node *root);
void recalc(ct_node *root);
void split(int x,ct_node **L,ct_node **R,ct_node *root);
void reverse(int x,int y);
void computeTree(int x);
int N,P[200000],T[200000],st[200000];
ct_node poll[200000],*odd,*even;
int main(){
int Q,x,y,i;
scanf("%d%d",&N,&Q);
for(i=0;i<N;i++){
scanf("%d",&poll[i].value);
poll[i].priority=P[i]=rand();
poll[i].size=-1;
poll[i].left=poll[i].right=NULL;
}
computeTree(0);
computeTree(1);
for(i=0;i<N;i++)
if(T[i]==-1)
if(i%2)
odd=&poll[i];
else
even=&poll[i];
else
if(i<T[i])
poll[T[i]].left=&poll[i];
else
poll[T[i]].right=&poll[i];
get_size(odd);
get_size(even);
while(Q--){
scanf("%d",&x);
switch(x){
case 1:
scanf("%d%d",&x,&y);
reverse(x,y);
break;
default:
scanf("%d%d",&x,&y);
if(x==y)
if(x%2)
printf("%lld\n",get_sum((x-1)/2,(x-1)/2,even));
else
printf("%lld\n",get_sum((x-1)/2,(x-1)/2,odd));
else
printf("%lld\n",get_sum((x-1)/2,(y-2)/2,odd)+get_sum(x/2,(y-1)/2,even));
}
}
return 0;
}
long long get_sum(int x,int y,ct_node *root){
if(!root || x>y || x>root->size-1 || y<0)
return 0;
if(x<=0 && y>=root->size-1)
return root->sum;
int curidx=sizeOf(root->left),t;
long long ls,rs,ans=0;
if(curidx>=x && curidx<=y)
ans=root->value;
if(y<curidx)
ls=get_sum(x,y,root->left);
else
ls=get_sum(x,curidx-1,root->left);
if(x>curidx)
rs=get_sum(x-curidx-1,y-curidx-1,root->right);
else
rs=get_sum(0,y-curidx-1,root->right);
return ans+ls+rs;
}
void get_size(ct_node *root){
if(!root)
return;
int ls=0,rs=0;
long long lsu=0,rsu=0;
if(root->left){
if(root->left->size==-1)
get_size(root->left);
ls=root->left->size;
lsu=root->left->sum;
}
if(root->right){
if(root->right->size==-1)
get_size(root->right);
rs=root->right->size;
rsu=root->right->sum;
}
root->size=ls+rs+1;
root->sum=lsu+rsu+root->value;
return;
}
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;
}
long long sumOf(ct_node *root){
return (root)?root->sum:0;
}
void recalc(ct_node *root){
root->size=sizeOf(root->left)+sizeOf(root->right)+1;
root->sum=sumOf(root->left)+sumOf(root->right)+root->value;
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 reverse(int x,int y){
ct_node *ol,*om,*or,*el,*em,*er;
int A,B;
A=(x-1)/2;
B=(y-2)/2;
split(A-1,&ol,&or,odd);
split(B-A,&om,&or,or);
A=x/2;
B=(y-1)/2;
split(A-1,&el,&er,even);
split(B-A,&em,&er,er);
odd=merge(merge(ol,em),or);
even=merge(merge(el,om),er);
return;
}
void computeTree(int x){
int i,k,top=-1;
for(i=x;i<N;i+=2){
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 Python3 :
def read_numbers():
return [int(i) for i in input().split(" ")]
def swap_numbers(l,r, numbers):
sub = numbers[l:r]
for i in range(0, r-l, 2):
l1 = sub[i]
r1 = sub[i+1]
sub[i+1] = l1
sub[i] = r1
return sub
n,q = read_numbers()
numbers = read_numbers()
results = []
for x in range(q):
t,l,r = read_numbers()
l -= 1
if t == 1:
numbers[l:r] = swap_numbers(l,r,numbers)
else:
results.append(str(sum(numbers[l:r])))
print("\n".join(results))
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