MO's Algorithm (Query Square Root Decomposition) | Set 1 (Introduction)

// Java Program to compute sum of ranges for different range
// queries.
import java.util.*;
 
// Class to represent a query range 
class Query{ 
    int L; 
    int R; 
    Query(int L, int R){
        this.L = L;
        this.R = R;
    }
} 

class GFG
{
    // Prints sum of all query ranges. m is number of queries
    // n is the size of the array.
    static void printQuerySums(int a[], int n, ArrayList<Query> q, int m)
    {
        // One by one compute sum of all queries
        for (int i=0; i<m; i++)
        {
            // Left and right boundaries of current range
            int L = q.get(i).L, R = q.get(i).R;
    
            // Compute sum of current query range
            int sum = 0;
            for (int j=L; j<=R; j++)
                sum += a[j];
    
            // Print sum of current query range
            System.out.println("Sum of [" + L +
                           ", " + R + "] is "  + sum);
        }
    }
    
    // Driver program
    public static void main(String argv[])
    {
        int a[] = {1, 1, 2, 1, 3, 4, 5, 2, 8};
        int n = a.length;
        
        ArrayList<Query> q = new ArrayList<Query>();
        q.add(new Query(0,4));
        q.add(new Query(1,3));
        q.add(new Query(2,4));
        
        int m = q.size();
        printQuerySums(a, n, q, m);
    }
}

// This code is contributed by shivanisinghss2110

// Java Program to compute sum of ranges for
// different range queries 

import java.util.*;

// Class to represent a query range 
class Query{ 
    int L; 
    int R; 
    Query(int L, int R){
        this.L = L;
        this.R = R;
    }
} 

class MO{

    // Prints sum of all query ranges. m is number of queries 
    // n is size of array a[]. 
    static void queryResults(int a[], int n, ArrayList<Query> q, int m){
        
        // Find block size 
        int block = (int) Math.sqrt(n); 
    
        // Sort all queries so that queries of same blocks 
        // are arranged together.
        Collections.sort(q, new Comparator<Query>(){
            
            // Function used to sort all queries so that all queries  
            // of the same block are arranged together and within a block, 
            // queries are sorted in increasing order of R values. 
            public int compare(Query x, Query y){

                // Different blocks, sort by block. 
                if (x.L/block != y.L/block) 
                    return (x.L < y.L ? -1 : 1); 

                // Same block, sort by R value 
                return (x.R < y.R ? -1 : 1);
            }
        });

        // Initialize current L, current R and current sum 
        int currL = 0, currR = 0; 
        int currSum = 0; 
    
        // Traverse through all queries 
        for (int i=0; i<m; i++) 
        { 
            // L and R values of current range
            int L = q.get(i).L, R = q.get(i).R; 

            // Remove extra elements of previous range. For 
            // example if previous range is [0, 3] and current 
            // range is [2, 5], then a[0] and a[1] are subtracted 
            while (currL < L) 
            { 
                currSum -= a[currL]; 
                currL++; 
            } 

            // Add Elements of current Range 
            while (currL > L) 
            { 
                currSum += a[currL-1]; 
                currL--; 
            } 
            while (currR <= R) 
            { 
                currSum += a[currR]; 
                currR++; 
            } 

            // Remove elements of previous range.  For example 
            // when previous range is [0, 10] and current range 
            // is [3, 8], then a[9] and a[10] are subtracted 
            while (currR > R+1) 
            { 
                currSum -= a[currR-1]; 
                currR--; 
            } 

            // Print sum of current range 
            System.out.println("Sum of [" + L +
                           ", " + R + "] is "  + currSum); 
        } 
    }

    // Driver program 
    public static void main(String argv[]){
        ArrayList<Query> q = new ArrayList<Query>();
        q.add(new Query(0,4));
        q.add(new Query(1,3));
        q.add(new Query(2,4));

        int a[] = {1, 1, 2, 1, 3, 4, 5, 2, 8}; 
        queryResults(a, a.length, q, q.size()); 
    }
}
// This code is contributed by Ajay