Here you will find solutions of many problems on spoj. If you want solution of some problem which is not listed in blog or have doubt regarding any spoj problem (which i have solved) or any programming concept (data structure) you can mail me @ raj.nishant360@gmail.com
And my humble request to you all that don't copy the code only try to understand the logic and algorithm behind the code. I have started this because if you tried as hard as you can and still can't find any solution to the problem then you can refer to this.
You can read my answer how to start competitive programming CLICK HERE

Friday, October 16, 2015

SEGSQRSS-Sum of Squares with Segment Tree

Sum of Squares with Segment Tree

Given below c++ code is for segsqrss spoj or sum of squares with segment tree spoj.

Main logic of code is within Merge and Split function in class 'node'




/*
===================================================
Name :- Nishant Raj
Email :- raj.nishant360@gmail.com
College :- Indian School of Mines
Branch :- Computer Science and Engineering
Time :- 16 October 2015 (Friday) 02:09
===================================================*/
#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 fill_ans(){
        initalize(1,left_most,right_most);
        for(int i = left_most ;i< left_most+size ; i++){
            for(int j=1;j<=26;j++)
                if(tree[i].arr[j]){
                    cout<<char(j+96);
                    break;
                }
        }
    }
    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:
    ll sum , sq_sum , lazy1 , lazy2;
    int child_count;
    void merge(node &a , node &b){
        sum = a.sum + b.sum;
        sq_sum = a.sq_sum + b.sq_sum;
        child_count = a.child_count + b.child_count;
        lazy1 = lazy2 = 0;
    }
    void split(node &a , node &b){
        if(lazy1){
            a.sq_sum += lazy1 * lazy1 * (ll)a.child_count + 2LL * lazy1 * a.sum;
            b.sq_sum += lazy1 * lazy1 * (ll)b.child_count + 2LL * lazy1 * b.sum;
            a.sum += lazy1 * a.child_count;
            b.sum += lazy1 * b.child_count;
            a.lazy1 += lazy1;
            b.lazy1 += lazy1;
            lazy1 = 0;
        }
        if(lazy2){
            a.sq_sum = a.child_count * lazy2 * lazy2;
            a.sum = a.child_count * lazy2;
            a.lazy2 += lazy2;
            b.sq_sum = b.child_count * lazy2 * lazy2;
            b.sum = b.child_count * lazy2;
            b.lazy2 += lazy2;
        }
    }
    void update(node &a){
        if(a.lazy1){
            sq_sum = sq_sum + a.lazy1 * a.lazy1 * child_count + 2LL * a.lazy1 * sum;
            sum += a.lazy1 * child_count;
            lazy1 += a.lazy1;
        }
        if(a.lazy2){
            sq_sum = child_count * a.lazy2 * a.lazy2;
            sum = child_count * a.lazy2;
            lazy2 += a.lazy2;
        }
    }
    node(){
        sum = sq_sum = lazy1 = lazy2 = 0;
        child_count = 0;
    }
    node(ll a , ll l1 , ll l2){ 
        sum = a;
        sq_sum = a*a;
        child_count = 1;
        lazy1 = l1;
        lazy2 = l2;
    }
};
node arr[100009];
int main(){
    int t;
    scanf("%d",&t);
    for(int test = 1 ; test <= t ; test++){
        int n , temp ,q;
        scanf("%d%d",&n,&q);
        segmentTree<node> s(n);

        for(int i =0;i<n;i++){
            scanf("%d",&temp);
            arr[i]=node(temp , 0 , 0);
        }
        s.init(arr);
        printf("Case %d:\n",test);
        while(q--){
            int l,r,k,val;
            scanf("%d%d%d",&k,&l,&r);
            l-- , r--;
            if(k == 2){
                printf("%lld\n",s.Query(l,r).sq_sum);
            }
            else if(k==1){
                scanf("%d",&val);
                s.Update(l , r , node(0 , val , 0));
            } else{
                scanf("%d",&val);
                s.Update(l , r , node(0 , 0 , val));
            }
        }
    }
    return 0;
}