Beautiful Quadruples


Problem Statement :


We call an quadruple of positive integers, , beautiful if the following condition is true:

Note:  is the bitwise XOR operator.

Given , , , and , count the number of beautiful quadruples of the form  where the following constraints hold:

When you count the number of beautiful quadruples, you should consider two quadruples as same if the following are true:

They contain same integers.
Number of times each integers occur in the quadruple is same.
For example  and  should be considered as same.

nput Format

A single line with four space-separated integers describing the respective values of A, B, C, and D.


Solution :



title-img 


                            Solution in C :

In  C  :





#include <math.h>
#include <stdio.h>
#include <string.h>
#include <stdlib.h>
#include <assert.h>
#include <limits.h>
#include <stdbool.h>
int A; 
    int B; 
    int C; 
    int D; 
long long int d[4097][3002][5];
long long int dp(int x,int i,int k){
    if(k==0){
        if(x!=0){
            return 1;
        } 
        return 0;
    }
    int p=0;
    if(i<=A) p++;
    if(i<=B) p++;
    if(i<=C) p++;
    if(i<=D) p++;
    if(p==0) return 0;
    int j=0;
    if(p<k) return 0;
    long long int l=0;
    for(j=0;j<=k;j++){
        if(d[x][i+1][k-j]==-1){
            d[x][i+1][k-j] = dp(x, i+1, k-j);
        }
        l+=d[x][i+1][k-j];
        x=x^i;
    }
    return l;
}

int main(){
    memset(d, -1, sizeof(d));
    scanf("%d %d %d %d",&A,&B,&C,&D);
    
    printf("%lld\n",dp(0, 1, 4));
    return 0;
}
                        


                        Solution in C++ :

In  C++  :







#include <iostream>
#include <sstream>
#include <fstream>
#include <string>
#include <vector>
#include <deque>
#include <queue>
#include <stack>
#include <set>
#include <map>
#include <algorithm>
#include <functional>
#include <utility>
#include <bitset>
#include <cmath>
#include <cstdlib>
#include <ctime>
#include <cstdio>

using namespace std;

#define REP(i,n) for((i)=0;(i)<(int)(n);(i)++)
#define snuke(c,itr) for(__typeof((c).begin()) itr=(c).begin();itr!=(c).end();itr++)

int a[4];
int A,B,C,D;

typedef long long ll;

ll total;
ll cnt[10000];

int main(void){
	int i,j;
	
	REP(i,4) cin >> a[i];
	sort(a, a+4);
	
	A = a[0];
	B = a[1];
	C = a[2];
	D = a[3];
	
	for(i=1;i<=C;i++) for(j=i;j<=D;j++){
		total++;
		cnt[i^j]++;
	}
	
	ll ans = 0;
	
	for(j=1;j<=B;j++){
		for(i=1;i<=A&&i<=j;i++) ans += total - cnt[i^j];
		for(i=j;i<=D;i++){
			total--;
			cnt[i^j]--;
		}
	}
	
	cout << ans << endl;
	
	return 0;
}
                    


                        Solution in Java :

In  Java :






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

public class Solution {

    public static void main(String[] args) {
        Scanner in = new Scanner(System.in);
        int A = in.nextInt();
        int B = in.nextInt();
        int C = in.nextInt();
        int D = in.nextInt();
        
        int[] m = new int[] {A, B, C, D};
        Arrays.sort(m);
        
        long[][] count = new long[3001][4096];
        
        for (int i=1; i<=m[0]; i++) {
            for (int j=i; j<=m[1]; j++) {
                count[j][i ^ j] ++;
            }
        }
        for (int i=0; i<4096; i++) {
            for (int j=1; j<=3000; j++) {
                count[j][i] += count[j-1][i];
            }
        }
        
        
        long[] sum = new long[3001];
        for (int j=1; j<=3000; j++) {
            for (int i=0; i<4096; i++) {
                sum[j] += count[j][i];
            }
        }
        
        long res=0;
        for (int i=1; i<=m[2]; i++) {
            for (int j=i; j<=m[3]; j++) {
                int x = i ^ j;
                res += sum[i] - count[i][i^j];
            }
        }
        System.out.println(res);
    }
}
                    


                        Solution in Python : 
                            
In  Python3 :







#!/bin/python3

import sys


A,B,C,D = input().strip().split(' ')
temp = [int(A),int(B),int(C),int(D)]
temp.sort()
A,B,C,D=temp

tot=[0]*4100

tree=[([0]*3100).copy() for i in range(4100)]
cnt=[([0]*3100).copy() for i in range(4100)]
def updateBIT(treeNo,ind):
    while(ind<3100):
        tree[treeNo][ind]+=1
        ind+=ind&-ind

def getBITVal(treeNo,ind):
    ret=0
    while(ind>0):
        ret+=tree[treeNo][ind]
        ind-=ind&-ind
    return ret

zero=0
tot=[0]*3100
for i in range(1,A+1):
    for j in range(i,B+1):
        #updateBIT(i^j,j)
        cnt[i^j][j]+=1
        tot[j]+=1

for i in range(len(cnt)):
    for j in range(1,len(cnt[i])):
        cnt[i][j]+=cnt[i][j-1]
        
for i in range(1,len(tot)):
    tot[i]+=tot[i-1]
    
ans=0        
for i in range(1,C+1):
    ans+=tot[i]*(D+1-i)
    for j in range(i,D+1):
        zero+=cnt[i^j][i]
        #ans+=getBITVal2(i)
        #print(i,j)
#print(ans)
ans-=zero
#print(zero)
print(ans)


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