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# CATSDOGS - Editorial

Author: Praveen Dhinwa
Tester: Istvan Nagy
Editorialist: Misha Chorniy

Cakewalk

None

# Problem Statement

There are $C$ cats and $D$ dogs, and $L$ legs touching the ground. Some of the cats can ride on dogs, but every dog can't have more than 2 cats on his back. Can this be true?

# Explanation

Let's make some obvious observations:

• Every cat has 4 legs.
• Every dog has 4 legs.

If we have $X$ cats and $Y$ dogs staying on the ground then, the number of legs in the barn equal $4 * (X+Y)$. Therefore if $L$ not divisible by 4, the answer is "no".

Constraints are chosen in such way that solutions with complexity $O(D+C)$ per test case can pass.

Iterate over possible numbers of the cats on Chef's dogs back $G$($G$ must be in the range between $0$ and $2*D$ due to the condition of the dog and 2 cats on his back, and not more than the total number of cats). Hence in the barn $4*(C-G+D)$ legs on the ground, if $4*(C-G+D) = L$ for some $G$, then the answer is "yes", and "no" otherwise.

There is possible to solve problem with $O(1)$ solution per test case. Let $G$ number of the cats on the backs of the dogs, $0 ≤ G ≤ min(C,2*D)$

$4*(C-G)+4*D = L$, there are $C-G$ cats on the ground, therefore total number of legs = $4*(C-G)$+$4*D$

$C-G+D = L/4$, divide both parts of the equation by $4$

$C+D-L/4 = G$, add $G-L/4$ to both parts of the equation

if $G$ will be in the range between $0$ and $2*D$ answer is "yes", and "no" otherwise.

The overall time complexity of this approach is $O(1)$ per test case.

# Solution:

Setter's solution can be found here
Tester's solution can be found here

Please feel free to post comments if anything is not clear to you.

This question is marked "community wiki".

6★mgch
3001021
accept rate: 21%

19.0k348495533

# include<stdio.h>

int main() { long unsigned c,d,l,t,max,min,flag,i; scanf("%lu",&t); while(t>0) { flag=0; scanf("%lu %lu %lu",&c,&d,&l); max=4c+4d; min=4*d; for(i=min;i<=max;i+=4) { if (l==i) { flag=1; } } if(flag==1) { printf("yes"); printf("\n"); } else { printf("no"); printf("\n"); } t--; }

return 0;


} 1. List item

want to know what is wrong with this code ...just it is passing only subtask 2. IS it related with time complexity...

1
accept rate: 0%

# include<stdio.h>

int main() { long unsigned c,d,l,t,max,min,flag,i; scanf("%lu",&t); while(t>0) { flag=0; scanf("%lu %lu %lu",&c,&d,&l); max=4c+4d; min=4*d; for(i=min;i<=max;i+=4) { if (l==i) { flag=1; } } if(flag==1) { printf("yes"); printf("\n"); } else { printf("no"); printf("\n"); } t--; }

return 0;


} 1. List item

want to know what is wrong with this code ...just it is passing only subtask 2. IS it related with time complexity...

1
accept rate: 0%

 0 @alpha You are calculating min wrong. Here, have a look at my code and figure out for yourself! my code answered 19 Feb '17, 12:44 13.9k●1●12●40 accept rate: 19%
 0 please can some one of you tell me where is the bug because it works for me but when I subbmit the answer is wrong. the code is in C: typedef struct TEST test; struct TEST{ int c; int d; int l; }; int stats(test te){ int i,k; if(te.c <= te.d){ for(i=0;i<=te.c;i++){ k=4*(te.d) + 4*i; if((te.l)==k){ printf("Yes\n"); return 1; } } printf("No\n"); }else if(te.c >= 2*te.d){ for(i=0;i<=(te.c-(te.c-2 * te.d));i++){ k=4*(te.d) + 4*((te.c) -i); if((te.l)==k){ printf("Yes\n"); return 1; } } printf("No\n"); }else if((te.c > te.d) && (te.c < 2* te.d)){ for(i=0;i<=te.c;i++){ k=4*(te.d) + 4*i; if((te.l)==k){ printf("Yes\n"); return 1; } } printf("No\n"); } return 0;  } main(){ int i; int T; test * t; scanf("%d",&T); t= (test )malloc(Tsizeof(test)); for(i=0;i
 0 @magime The constraints must be stored in long long int. In int, they will overflow and you will fail in final sub task. Check your minimm calculation, I wasn't able to check it thoroughly in that code you posted , so please do a self check and see if its equal to what is given in editorial (PS- min and overflow were 2 main culprits behind this problem having low accuracy rate despite easy nature) answered 21 Feb '17, 18:06 13.9k●1●12●40 accept rate: 19%
 0 import java.util.*; class Catsdogs{  public static void main(String []args){ int tcase,i,j; Scanner sc= new Scanner(System.in); tcase=sc.nextInt(); long cnt[][]=new long[tcase+1][tcase+1]; String res[] = new String[tcase+1]; for(i=0;icnt[i][0]) { res[i]="no"; } else if(cnt[i][0]>2*cnt[i][1]) { res[i]="no"; } else if ((cnt[i][0]+cnt[i][1])*4>cnt[i][2] && cnt[i][2]%4==0) { res[i]="yes"; } else { res[i]="no"; } } for(i=0;i
 0 @mihir1440 Your code throws out of index error whenever T=1 Exception in thread "main" java.lang.ArrayIndexOutOfBoundsException: 2 at Catsdogs.main(Main.java:14)  I strongly suspect that it is due to wrong allocation of memory to cnt[][]. Please have a look at it. answered 21 Mar '17, 17:51 13.9k●1●12●40 accept rate: 19%
 0 What I'm doing is this: Calculate maximum value of legs possible which is max = 4*(c+d) when all cats and dogs are on the floor. Calculate minimum value of legs possible which is min = 4*(c-d) when max cats are on top of dogs. Number of legs should be positive multiples of 4. Number of legs should be between max and min. To my surprise, it doesn't work. It gives a straight WA. Where did I go wrong? long long int t; scanf("%lld", &t); while(t--) { long long int c, d, l; scanf("%lld %lld %lld", &c, &d, &l); long long int max = (c+d)*4; long long int min = (c-d)*4; if(l >= min && l <= max && l%4 == 0 && l >= 4) printf("yes\n"); else printf("no\n"); } return 0;  } Any help? PS: It works fine with the given test case! answered 08 Apr '17, 17:43 1★mr_nair 2●1 accept rate: 0%
 0 @mr_nair Your calculation of min is only partially correct. Its correct if number of cats are way more than number of dogs, but what if number of cats are less than number of dogs? In a scenario when all cats can be on top of dogs, the min is not 4x(c-d), but its simply 4xd. Visualise it, when all cats on top of dogs, minimum legs is equal to number legs of dogs. Your case fails at this test case- Input 1 1 3 4 Output yes Expected output no  Your min here is 4x(1-3) = -8. While practically we can see that min should be 4*3=12. answered 08 Apr '17, 18:34 13.9k●1●12●40 accept rate: 19%
 0 https://ideone.com/VWl7gD Can someone tell why i am failing my testcases answered 08 Nov '17, 13:24 1●1 accept rate: 0%
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question asked: 18 Jan '17, 04:02

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last updated: 29 May, 12:46