Algorithm
Problem link- https://www.spoj.com/problems/CRDS/
CRDS - Cards
Maricruz have a lot of cards, she always uses her cards to build pyramids as shown in the following image:
A pyramid card of 3 levels. She always wonder how many cards does she need to make a pyramid card of N levels. Your task is to answer that question.
Input
The first line of the input contains an integer 1 <= T <= 1,000. Each of the following T lines will have an integer 1 <= N <= 1,000,000.
Output
For each case, output a single line consisting of the number of cards needed to build a pyramid card of level N modulo 1,000,007.
Example
Input Example 2 3 7 Output Example 15 77
Code Examples
#1 Code Example with Python Programming
Code -
Python Programming
T = int(input())
for _ in range(T):
N = int(input())
print(N * (3 * N + 1) / 2 % 1000007)Input
3
7
Output
77
#2 Code Example with Java Programming
Code -
Java Programming
import java.io.BufferedReader;
import java.io.InputStreamReader;
import java.io.PrintWriter;
/**
* SPOJ Problem: Cards(CRDS)
* This one was all about deriving the formula. Also it is equally important that all calculations are done on 'long' vars.
* @author madhurbhargava
*/
public class CRDS {
public static void main(String[] arguments) throws Exception
{
BufferedReader reader = new BufferedReader(new InputStreamReader(System.in));
PrintWriter out = new PrintWriter(System.out);
int numTestCases = Integer.parseInt(reader.readLine());
//it is imp that this is long
long modNum = 1000007;
for(int i = 0; i < numTestCases; i++)
{
//it is imp that all calculations are done on long
long numLevels = Long.parseLong(reader.readLine());
long cards = 3*((numLevels*(numLevels+1))/2) - numLevels;
cards = cards % modNum;
out.println(cards);
out.flush();
}
}
}Input
3
7
Output
77
#3 Code Example with C++ Programming
Code -
C++ Programming
#include <iostream>
using namespace std;
int main() {
int t,l,sum=0,i;
cin>>t;
while(t--){
cin>>l;
sum=l*2;
for(i=l-1;i>0;i--){
sum+=i*2+i;
}
cout<<sum<<endl;
}
return 0;
}Input
3
7
Output
77
Demonstration
SPOJ Solution-Cards-Solution in C, C++, Java, Python