# CARRANGE - Editorial

Setter: Nandeesh Gupta
Tester: Tejas Pandey and Utkarsh Gupta
Editorialist: Taranpreet Singh

Cakewalk

None

# PROBLEM

The fuel economy of a car is the distance which it can travel on one litre of fuel.

The base fuel economy (i.e, its fuel economy when there is only one person - the driver - in the car) of a certain car is M kilometres per litre. It was also observed that every extra passenger in the car decreases the fuel economy by 1 kilometre per litre.

P people want to take this car for a journey. They know that the car currently has V litres of fuel in its tank.

What is the maximum distance this car can travel under the given conditions, assuming that all P people always stay in the car and no refuelling can be done?

Note that among the P people is also a driver, i.e, there are exactly P people in the car.

# QUICK EXPLANATION

The fuel economy with P people is M-(P-1), since P-1 more passengers enter the car. For V liters, the car can cover distance V*(M-(P-1))

# EXPLANATION

Since the base economy is M when there’s one person (driver) in car, the fuel economy with P people would be equivalent to P-1 people joining the car, reducing the fuel economy of car from M to M - (P-1).

Hence, the fuel economy with P passengers is (M-(P-1)) kilometers per liter. There is V liters of fuel available, so the maximum distance the car can cover is V * (M-(P-1)).

# TIME COMPLEXITY

The time complexity is O(1) per test case.

# SOLUTIONS

Tester's Solution 1
``````#include <bits/stdc++.h>
using namespace std;

/*
------------------------Input Checker----------------------------------
*/

long long readInt(long long l,long long r,char endd){
long long x=0;
int cnt=0;
int fi=-1;
bool is_neg=false;
while(true){
char g=getchar();
if(g=='-'){
assert(fi==-1);
is_neg=true;
continue;
}
if('0'<=g && g<='9'){
x*=10;
x+=g-'0';
if(cnt==0){
fi=g-'0';
}
cnt++;
assert(fi!=0 || cnt==1);
assert(fi!=0 || is_neg==false);

assert(!(cnt>19 || ( cnt==19 && fi>1) ));
} else if(g==endd){
if(is_neg){
x= -x;
}

if(!(l <= x && x <= r))
{
cerr << l << ' ' << r << ' ' << x << '\n';
assert(1 == 0);
}

return x;
} else {
assert(false);
}
}
}
string ret="";
int cnt=0;
while(true){
char g=getchar();
assert(g!=-1);
if(g==endd){
break;
}
cnt++;
ret+=g;
}
assert(l<=cnt && cnt<=r);
return ret;
}
long long readIntSp(long long l,long long r){
}
long long readIntLn(long long l,long long r){
}
}
}

/*
------------------------Main code starts here----------------------------------
*/

const int MAX_T = 30000;
const int MAX_P = 5;
const int MAX_M = 56;
const int MAX_V = 100;

#define fast ios_base::sync_with_stdio(0); cin.tie(0); cout.tie(0)

int sum_len=0;

void solve()
{
int p, m, v;
m = readIntSp(MAX_P + 1, MAX_M);
cout << v*(m - p + 1) << "\n";
}

signed main()
{
fast;
#ifndef ONLINE_JUDGE
freopen("input.txt", "r", stdin);
freopen("output.txt", "w", stdout);
#endif

for(int i=1;i<=t;i++)
{
solve();
}

assert(getchar() == -1);
}
``````
Tester's Solution 2
``````#include <bits/stdc++.h>
using namespace std;

/*
------------------------Input Checker----------------------------------
*/

long long readInt(long long l,long long r,char endd){
long long x=0;
int cnt=0;
int fi=-1;
bool is_neg=false;
while(true){
char g=getchar();
if(g=='-'){
assert(fi==-1);
is_neg=true;
continue;
}
if('0'<=g && g<='9'){
x*=10;
x+=g-'0';
if(cnt==0){
fi=g-'0';
}
cnt++;
assert(fi!=0 || cnt==1);
assert(fi!=0 || is_neg==false);

assert(!(cnt>19 || ( cnt==19 && fi>1) ));
} else if(g==endd){
if(is_neg){
x= -x;
}

if(!(l <= x && x <= r))
{
cerr << l << ' ' << r << ' ' << x << '\n';
assert(1 == 0);
}

return x;
} else {
assert(false);
}
}
}
string ret="";
int cnt=0;
while(true){
char g=getchar();
assert(g!=-1);
if(g==endd){
break;
}
cnt++;
ret+=g;
}
assert(l<=cnt && cnt<=r);
return ret;
}
long long readIntSp(long long l,long long r){
}
long long readIntLn(long long l,long long r){
}
}
}

/*
------------------------Main code starts here----------------------------------
*/

const int MAX_T = 30000;
const int MAX_P = 5;
const int MAX_M = 56;
const int MIN_M = 6;
const int MAX_V = 100;

#define fast ios_base::sync_with_stdio(0); cin.tie(0); cout.tie(0)

void solve()
{
int mileage=(m+1-p);
int ans=mileage*v;
cout<<ans<<'\n';
}

signed main()
{
// fast;
#ifndef ONLINE_JUDGE
freopen("input.txt", "r", stdin);
freopen("output.txt", "w", stdout);
#endif

for(int i=1;i<=t;i++)
{
solve();
}

assert(getchar() == -1);
}
``````
Editorialist's Solution
``````import java.util.*;
import java.io.*;
class CARRANGE{
//SOLUTION BEGIN
void pre() throws Exception{}
void solve(int TC) throws Exception{
int P = ni(), M = ni(), V = ni();
pn(V*(M-P+1));
}
//SOLUTION END
void hold(boolean b)throws Exception{if(!b)throw new Exception("Hold right there, Sparky!");}
static boolean multipleTC = true;
void run() throws Exception{
out = new PrintWriter(System.out);
//Solution Credits: Taranpreet Singh
int T = (multipleTC)?ni():1;
pre();for(int t = 1; t<= T; t++)solve(t);
out.flush();
out.close();
}
public static void main(String[] args) throws Exception{
new CARRANGE().run();
}
int bit(long n){return (n==0)?0:(1+bit(n&(n-1)));}
void p(Object o){out.print(o);}
void pn(Object o){out.println(o);}
void pni(Object o){out.println(o);out.flush();}
String n()throws Exception{return in.next();}
String nln()throws Exception{return in.nextLine();}
int ni()throws Exception{return Integer.parseInt(in.next());}
long nl()throws Exception{return Long.parseLong(in.next());}
double nd()throws Exception{return Double.parseDouble(in.next());}

StringTokenizer st;
}

}

String next() throws Exception{
while (st == null || !st.hasMoreElements()){
try{
}catch (IOException  e){
throw new Exception(e.toString());
}
}
return st.nextToken();
}

String nextLine() throws Exception{
String str = "";
try{