Snow White and the N dwarfs
Given below code is for patuljci spoj or snow white and the N dwarfs spoj .
Hint:- source( http://hsin.hr/ )
For now, forget about the problem we are solving.
Suppose we had a sequence of integers and an algorithm like this:
while there are different numbers in the sequence
select any two different numbers from the sequence
and erase them
For example if the sequence were:
1 2 3 1 2 3 2 3
the algorithm could have done this:
1 2 3 1 2 3 2 3 --> 3 1 2 3 2 3 -> 1 3 2 3 -> 3 3
Note that we could also end up with other sequences if we selected pairs in a different way.
Let candidate be the number that is left in a sequence (3 in the example above).
Let count be the number of numbers left in a sequence (2 in the example above).
The cool thing about the algorithm is that if there is a number that appears more than N/2 times in the sequence it must end up as a candidate no matter the way we select pairs. Intuitively, we don't have enough other numbers to kill all of the candidate numbers. So we can choose our own way to select pairs. Let's do it recursively like this.
1) Split the sequence S in two halves L and R.
2) Run the recursive algorithm on sequence L to get L.candidate and L.count
3) Run the recursive algorithm on sequence R to get R.candidate and R.count
4) Kill the remaining pairs among L.count + R.count numbers that are left.
The step #4 can be done very efficiently like this:
if L.candidate == R.candidate
S.candidate = L.candidate
S.count = L.count + R.count
else
if L.count > R.count
S.candidate = L.candidate
S.count = L.count - R.count
else
S.candidate = R.candidate
S.count = R.count - L.count
end
end
So, we can use this idea to build the interval tree, every node containing info (candidate and count) about the sub-sequence it represents. We can also query the interval tree to get candidate number for any interval [A, B]. Then we can use binary search to count the number of appearances of the candidate number in the interval and determine if the picture is pretty or not.
/*
===================================================
Name :- Nishant Raj
Email :- raj.nishant360@gmail.com
College :- Indian School of Mines
Branch :- Computer Science and Engineering
Time :- 18 October 2015 (Sunday) 17:10
===================================================*/
#include <bits/stdc++.h>
using namespace std;
#define ll long long
#define pii pair < int , int >
#define pb push_back
#define mp make_pair
#define mod 1000000009
template<class T>
class segmentTree{
public:
segmentTree(){
height = 1;
left_most = 1<<height;
right_most = (left_most<<1) - 1;
tree = new T[right_most];
}
segmentTree(int s){
size=s;
height = ceil(log2(s));
left_most = 1<<height;
right_most = (left_most<<1) - 1;
tree = new T[right_most+9];
}
void init(T * arr){
build(arr);
}
void Update(int pos , T val){
point_update(1 , left_most , right_most , left_most+pos , val);
}
void Update(int l , int r , T val){
range_update(1 , left_most , right_most , left_most+l , left_most+r , val);
}
T Query(int pos){
return point_query(1 , left_most , right_most , left_most+pos);
}
T Query(int l ,int r){
return range_query(1 , left_most , right_most , left_most+l , left_most+r);
}
private:
T *tree;
int size , left_most , right_most , height;
void build(T * arr){
for(int i = 0 ; i < size ; i++)
tree[left_most+i] = arr[i];
initalize(1 , left_most , right_most);
}
void initalize(int root , int left_most , int right_most){
if(left_most == right_most) return;
int mid = (left_most + right_most)>>1 , l_child = (root<<1) , r_child = (root<<1)+1;
tree[root].split(tree[l_child] , tree[r_child]);
initalize(l_child , left_most , mid);
initalize(r_child , mid+1 , right_most);
tree[root].merge(tree[l_child] , tree[r_child]);
}
void point_update(int root , int left_most , int right_most , int pos , T val){
if(left_most == right_most && root == pos) { tree[root].update(val); return ;}
int mid = (left_most + right_most)>>1 , l_child = root<<1 , r_child = (root<<1)+1;
tree[root].split(tree[l_child] , tree[r_child]);
if(pos <= mid) point_update(l_child , left_most , mid , pos , val);
else point_update(r_child , mid+1 , right_most , pos , val);
tree[root].merge(tree[l_child] , tree[r_child]);
}
void range_update(int root , int left_most , int right_most , int l , int r , T val){
if(l <= left_most && r >= right_most){ tree[root].update(val);return;}
int mid = (left_most + right_most)>>1 , l_child = root<<1 , r_child = (root<<1)+1;
tree[root].split(tree[l_child] , tree[r_child]);
if(l <= mid) range_update(l_child , left_most , mid, l , r , val);
if(r > mid) range_update(r_child , mid+1 , right_most , l , r , val);
tree[root].merge(tree[l_child] , tree[r_child]);
}
T range_query(int root , int left_most ,int right_most ,int l , int r){
if( l <= left_most && r >= right_most )
return tree[root];
int mid = (left_most + right_most)>>1 , l_child = root<<1 , r_child = (root<<1)+1;
tree[root].split(tree[l_child] , tree[r_child]);
T l_node , r_node , temp;
if(l <= mid) l_node = range_query(l_child , left_most , mid , l , r );
if(r > mid) r_node = range_query(r_child , mid+1 , right_most , l , r );
tree[root].merge(tree[l_child] , tree[r_child]);
temp.merge(l_node , r_node);
return temp;
}
T point_query(int root , int left_most , int right_most , int pos){
if(left_most == right_most && root == pos) return tree[root];
int mid = (left_most + right_most)>>1 , l_child = root<<1 , r_child = (root<<1)+1;
T temp;
tree[root].split(tree[l_child] , tree[r_child]);
if(pos <= mid) temp = point_query(l_child , left_most , mid , pos);
else temp = point_query(r_child , mid+1 , right_most , pos);
tree[root].merge(tree[l_child] , tree[r_child]);
return temp;
}
};
class node{
public:
int count , number;
void merge(node &l , node &r){
if(l.number == r.number){
count = l.count + r.count;
number = l.number;
} else {
if( l.count > r.count ){
count = l.count - r.count;
number = l.number;
} else{
count = r.count - l.count;
number = r.number;
}
}
}
void split(node &a , node &b){
}
void update(node &a){
}
node(){
count = 0 , number = 0;
}
node(int num){
count = 1;
number = num;
}
};
node arr[300009];
vector<int> Index[100009];
int main(){
int n , c;
scanf("%d%d",&n , &c);
int temp;
for(int i = 0; i < n ; i++){
scanf("%d",&temp);
Index[temp].pb(i);
arr[i] = node(temp);
}
segmentTree<node> s(n);
s.init(arr);
int q , l , r;
scanf("%d",&q);
while(q--){
scanf("%d%d",&l,&r);
l-- , r--;
int num = s.Query(l , r).number;
int count = upper_bound(Index[num].begin() , Index[num].end() , r) - lower_bound(Index[num].begin() , Index[num].end() , l);
int req = r - l +1;
if(count*2 > req){
printf("yes %d\n", num);
} else
printf("no\n");
}
return 0;
}
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