Boolean Game - CodeChef Solution in Java| AskTheCode

Updated: Apr 12

CodeChef April Long Challenge Solution | Boolean Game (BOOLGAME) solution | AskTheCode

Problem:

Consider N binary variables x1,x2,…,xN. For each valid i, the i-th of these variables can be xi=0 or xi=1; therefore, there are 2N possible assignments of values to the variables. For each valid i, setting xi=1 gives you score gi.


In addition, there are M special intervals (numbered 1 through M). For each valid i, the i-th interval is [ui,vi] and if xui=xui+1=…=xvi=1, then your score increases by di.


Note that both gi and di can be negative (setting more variables to 1 can decrease your score), and your score can also be negative. Formally, the score of an assignment of values to the binary variables is


Find the K highest scores among all assignments on these variables. Formally, if we computed the scores of all 2N assignments and sorted them in non-increasing order, you should find the first K of these values.

Input:

  • The first line of the input contains a single integer T denoting the number of test cases. The description of T test cases follows.

  • The first line of each test case contains three space-separated integers N, M and K.

  • The second line contains N space-separated integers g1,g2,…,gN.

  • M lines follow. For each valid i, the i-th of these lines contains three space-separated integers ui, vi and di.

Output:

For each test case, print a single line containing K space-separated integers ― the K highest scores of assignments on the binary variables, in decreasing order.

Example Input:

1 4 2 3 -4 -2 5 2 1 3 0 1 4 -3

Example Output:

7 5 5

Explanation:

Example case 1: The best assignment is x=(0,0,1,1), with score 7. The second and third best assignments are (0,0,1,0) and (0,1,1,1), each with score 5.

Code:

In Java

/* package codechef; // don't place package name! */
import java.util.*;
import java.lang.*;
import java.io.*;
import java.math.*;

/* Name of the class has to be "Main" only if the class is public. */
class Solution
{
    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[64];
            int cnt = 0, c;
            while ((c = read()) != -1)
            {
                if (c == '\n')
                    break;
                buf[cnt++] = (byte) c;
            }
            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();
        }
    }
    
    static long power(long x, long y, long p){ 
        long res = 1;      
        x = x % p;  
        while (y > 0) { 
            if((y & 1)==1) 
                res = (res * x) % p; 
            y = y >> 1;  
            x = (x * x) % p;  
        } 
        return res; 
    }
    
    static class Orientation implements Comparable<Orientation>{
        public long score;
        public long orient;
        
        public Orientation(long score, long orient){
            this.score = score;
            this.orient = orient;
        }
        
        public static Orientation of (long score, long orient){
            return new Orientation(score, orient);
        }
        
        @Override
        public int compareTo(Orientation b){
            return b.score > this.score ? 1 : -1;
        }
    }
    
    public static PriorityQueue<Orientation> withPq(Orientation o){
        PriorityQueue<Orientation> pq = new PriorityQueue<>();
        pq.add(o);
        
        return pq;
    }
    
	public static void main (String[] args) throws java.lang.Exception{
		Reader r = new Reader();
		int t = r.nextInt();
		StringBuffer ans = new StringBuffer("");
		long M = 1000000007;
		while(t-- > 0){
		    int n = r.nextInt(), m = r.nextInt(), k = r.nextInt();
		    long []g = new long[n + 1];
		    long []intScore = new long[m];
		    Map<Integer, List<Integer>> intervals = new HashMap<>();
		    
		    for (int i=1;i<=n;i++) {
		        g[i] = r.nextLong();
		        intervals.put(i, new ArrayList<>());
		    }
		        
		    for (int i=0;i<m;i++) {
		        int u = r.nextInt(), v = r.nextInt(), d = r.nextInt();
		        intScore[i] = d;
		        intervals.get(u).add(i);
		        intervals.get(v).add(i);
		    }   
		    
		    Map<Integer, PriorityQueue<Orientation>> dp = new HashMap<>();
		    dp.put(0, withPq(Orientation.of(0,0)));
		    
		    for (int i=1;i<=n;i++) {
		        PriorityQueue<Orientation> temp = new PriorityQueue<>(dp.get(i - 1));
		        long cur = 0, mask = 0;
		        Set<Integer> activeIntervals = new HashSet<>();
		        for (int j=i;j>=1;j--) {
		            cur += g[j];
		            mask = mask ^ (1<<j);
		            
		            for (int interval : intervals.get(j)) {
		                if (activeIntervals.contains(interval))
		                    cur += intScore[interval];
		                else
		                    activeIntervals.add(interval);
		            }
		            
		            if (j>1) 
		                for (Orientation o : dp.get(j-2))
		                    temp.add(Orientation.of(o.score + cur, o.orient ^ mask));
		            else 
		                temp.add(Orientation.of(cur, mask));
		        }
		        
		        PriorityQueue<Orientation>pq = new PriorityQueue<>();
		        Set<Long>selection = new HashSet<>();
		        while(!temp.isEmpty()) {
		            if (selection.size() >= k) break;
		            selection.add(temp.peek().score);
		            pq.add(temp.poll());
		        }
		        
		        dp.put(i, pq);
		    }
		    
		    for (int i=0;i<k;i++)
		        ans.append(dp.get(n).poll().score + " ");
		        
		    ans.append("\n");
		}
		
		OutputStream out = new BufferedOutputStream(System.out);
		out.write(String.valueOf(ans).getBytes());
		out.flush();
	}
}

In C++

#include <bits/stdc++.h>
using namespace std;
#define ll long long int

int main(){
	ll testcase;
	cin >> testcase;
	while(testcase--){
		ll n, m, k_Val;
		cin >> n >> m >> k_Val;
		vector<ll> g(n+1);
		for (ll i = 0; i < n; i++)
			cin >> g[i+1];
		vector<vector<pair<ll, ll>>> m_Arr(n+1), dynamic(n+1);
		for (ll i = 0; i < m; i++){
			ll uVal, vVal, dVal;
			cin >> uVal >> vVal >> dVal;
			m_Arr[uVal].push_back(make_pair(i,dVal));
			m_Arr[vVal].push_back(make_pair(i, dVal));
		}
		dynamic[0].push_back(make_pair(0,0));
		for (ll i = 1; i <= n; i++){
			vector<pair<ll, ll>> tmp;
			tmp.insert(tmp.end(), dynamic[i-1].begin(), dynamic[i-1].end());
			ll cur_idx = 0, tmp_idx = 0;
			set<ll> set1;
			for (ll j = i; j >= 1; j--){
				cur_idx += g[j];
				tmp_idx ^= 1LL << j;
				for (auto alpha:m_Arr[j]){
					if (set1.count(alpha.first)){
						cur_idx += alpha.second;
					}
					else{
						set1.insert(alpha.first);
					}
				}
				if(j > 1){
					for (auto alpha:dynamic[j-2])
						tmp.push_back(make_pair(alpha.first+cur_idx, tmp_idx^alpha.second));
				}
				else{
					tmp.push_back(make_pair(cur_idx, tmp_idx));
				}
			}
			sort(tmp.begin(), tmp.end());
			reverse(tmp.begin(), tmp.end());
			set<ll> set2;
			ll filled = 0;
			for (ll j = 0; j < tmp.size() && filled < k_Val; j++){
				if (set2.count(tmp[j].second)){
					continue;
				}
				dynamic[i].push_back(tmp[j]);
				filled++;
				set2.insert(tmp[j].second);
			}
		}
		for (ll i = 0; i < k_Val; i++)
			cout << dynamic[n][i].first << " ";
		cout << endl;
	}
	return 0;
}
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