Dorsey Thief


Problem Statement :


Mr. Dorsey Dawson recently stole X grams of gold from ACME Jewellers. He is now on a train back home. To avoid getting caught by the police, he has to convert all the gold he has into paper money. He turns into a salesman and starts selling the gold in the train.

There are N passengers who have shown interest in buying the gold. The ith passenger agrees to buy ai grams of gold by paying vi dollars. Dawson wants to escape from the police and also maximize the profit. Can you help him maximize the profit?

Note: The ith passenger would buy exactly ai grams if the transaction is successful.

Input Format

The first line contains two space separated integers, N and X, where N is the number of passengers who agreed to buy and X is the stolen amount of gold (in grams).
N lines follow. Each line contains two space separated integers -vi  and ai, where vi is the the value which the ith passenger has agreed to pay in exchange for ai grams of gold.

Constraints

1 <= X <= 5000
1 <= N <= 10^6
all vi's and ai's are less than or equal to 10^6 and greater than 0.
Output Format

If it's possible for Dorsey to escape, print the maximum profit he can enjoy, otherwise print Got caught!.



Solution :



title-img


                            Solution in C :

In C++ :





#include <algorithm>
#include <iostream>
#include <cstring>
#include <cassert>
#include <iomanip>
#include <climits>
#include <cstdio>
#include <vector>
#include <string>
#include <stack>
#include <cmath>
#include <ctime>
#include <queue>
#include <list>
#include <map>
#include <set>

#define REP(i,n) for(int i = 0; i <(int)n; i++)
#define foreach(it,x) for(__typeof(x.begin()) it = x.begin() ;
   it!=x.end() ; it++ )

#ifdef KAZAR
    #define eprintf(...) fprintf(stderr, __VA_ARGS__)
#else
    #define eprintf(...)
#endif

using namespace std;

const int inf = (int)1e9 + 5757;

template<class T> inline void umax(T &a,T b){if(a<b) a = b;}
template<class T> inline void umin(T &a,T b){if(a>b) a = b;}
template<class T> inline T abs(T a){return a>0 ? a : -a;}
template<class T> inline T lcm(T a,T b){return a/gcd(a,b)*b;}

inline int read(){int x;scanf(" %d",&x);return x;}

const int N = 5050;

long long dp[N];
vector<int> g[N];
vector<int> a,b;

int main(){

#ifdef KAZAR
    freopen("f.i","r",stdin);
    freopen("f.cik","w",stdout);
    freopen("error","w",stderr);
#endif

    int n = read();
    int x = read();

    for(int i = 1; i <= n; i++){
        int a = read(), v = read();
        if(v <= x){
            g[v].push_back(a);
        }
    }

    for(int i = 1; i <= x; i++){
        sort(g[i].begin(), g[i].end());
        reverse(g[i].begin(), g[i].end());
        int cnt = min(5000 / i + 1,(int)g[i].size());
        for(int j = 0; j < cnt; j++){
            a.push_back(i);
            b.push_back(g[i][j]);
        }
    }

    memset(dp, -1, sizeof dp);

    dp[0] = 0;

    eprintf("%d\n",a.size());

    for(int i = 0; i < (int)a.size(); i++){
        for(int j = x; j >= 0; j--)
            if(dp[j] != -1 && j + a[i] <= x)
                umax(dp[j + a[i]],dp[j] + b[i]);
    }

    if(dp[x] == -1){
        puts("Got caught!");
    }else{
        cout << dp[x] << endl;
    }

    return 0;
}








In Java :





import java.io.*;
import java.util.*;

public class Solution {

	BufferedReader br;
	PrintWriter out;
	StringTokenizer st;
	boolean eof;

	void solve() throws IOException {
		int n = nextInt();
		int x = nextInt();

		long[] max = new long[x + 1];
		Arrays.fill(max, -1);
		max[0] = 0;

		long freeBonus = 0;

		List<Integer>[] byNeed = new List[x + 1];
		for (int i = 1; i <= x; i++) {
			byNeed[i] = new ArrayList<>(0);
		}

		for (int i = 0; i < n; i++) {
			int gain = nextInt();
			int need = nextInt();
			if (need == 0) {
				freeBonus += gain;
				continue;
			}
			if (need <= x) {
				byNeed[need].add(gain);
			}

		}

		for (int need = 1; need <= x; need++) {
			List<Integer> cur = byNeed[need];
			Collections.sort(cur);
			Collections.reverse(cur);
			for (int i = 0; (i + 1) * need <= x && i < cur.size(); i++) {
				int gain = cur.get(i);
				for (int j = x; j >= need; j--) {
					if (max[j - need] != -1) {
						max[j] = Math.max(max[j], max[j - need] + gain);
					}
				}
			}
		}

		if (max[x] == -1) {
			out.println("Got caught!");
		} else {
			out.println(max[x] + freeBonus);
		}
	}

	Solution() throws IOException {
		br = new BufferedReader(new InputStreamReader(System.in));
		out = new PrintWriter(System.out);
		solve();
		out.close();
	}

	public static void main(String[] args) throws IOException {
		new Solution();
	}

	String nextToken() {
		while (st == null || !st.hasMoreTokens()) {
			try {
				st = new StringTokenizer(br.readLine());
			} catch (Exception e) {
				eof = true;
				return null;
			}
		}
		return st.nextToken();
	}

	String nextString() {
		try {
			return br.readLine();
		} catch (IOException e) {
			eof = true;
			return null;
		}
	}

	int nextInt() throws IOException {
		return Integer.parseInt(nextToken());
	}

	long nextLong() throws IOException {
		return Long.parseLong(nextToken());
	}

	double nextDouble() throws IOException {
		return Double.parseDouble(nextToken());
	}
}








In C :





#include <stdio.h>
#include <stdlib.h>

int main()
{ 
    int n,x;
    scanf("%d %d",&n,&x);
    int v[n],a[n];
    int temp=0;
    while(temp<n){
                  scanf("%d %d",&v[temp],&a[temp]);
                  temp++;
    }
    
    long long int dp[x+1];
    dp[0]=0;
    for(int i=1;i<=x;i++){
            dp[i]=-100000000000000000;
    }
    
    temp=0;
    while(temp<n){
                  for(int j=x;j>=a[temp];j--){
                          dp[j]=(dp[j]>dp[j-a[temp]]+v[temp])?dp[j]:(dp[j-a[temp]]+v[temp]);
                  }
                  temp++;
    }
    if(dp[x]>0){
                printf("%lld",dp[x]);
    }else{
          printf("Got caught!");
    }

return 0;   
}
                        








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