View source for Printing A ← Printing A

Imagine you have a special keyboard with the following keys:

A

Ctrl+A

Ctrl+C

Ctrl+V

where CTRL+A, CTRL+C, CTRL+V each acts as one function key for “Select All”, “Copy”, and “Paste”
operations respectively.

If you can only press the keyboard for N times (with the above four keys), please write a program to produce
maximum numbers of A. If possible, please also print out the sequence of keys.
That is to say, the input parameter is N (No. of keys that you can press), the output is M (No. of As that you
can produce).

==={{Template:Author|Arjun Suresh|{{arjunweb}} }}===
A key to the solution is that we can continue pressing CTRL-V multiple times and the characters in the buffer will get printed continuously. The recurrence relation for the solution is 

sol[n] = max(2*sol[n-3], 3*sol[n-4], 4*sol[n-5]) | n > 6 and 1 for 1<= n <= 6

<syntaxhighlight lang="c" name="printa">
#include <stdio.h>
 
int max(int a, int b, int c)
{
	return a > b ? a > c? a:c : b > c? b:c;
}

int maxp(int a, int b, int c)
{
	return a > b ? a > c? 1:3 : b > c? 2:3;
}

void print(int *, int);

int main()
{
	unsigned int n, i;
	unsigned long long sol[1000];
	unsigned int prin[1000];
	printf("Enter N: ");
	scanf("%u", &n);
 
	for(i = 1 ;n>5? i<=5: i<= n; i++)
	{
		sol[i] = i;
		prin[i] = 0;
	}
	if(n >= 6)
	{
		sol[6] = 6;
		prin[6] = 1;
	}
	for(i = 7; i <= n; i++)
	{
		sol[i] = max(2 * sol[i-3], 3 * sol[i-4], 4 * sol[i-5]);
		prin[i] = maxp(2 * sol[i-3], 3 * sol[i-4], 4 * sol[i-5]);
	}
	printf("M = %llu\n", sol[n]);
	printf("Enter any char to start printing the key sequence: \n");
	scanf("%d", &n);
	printf("Printing the sequence: \n\n");
	print(prin, n);
}

void print(int * prin, int n)
{
	if(n < 1 )
		return;
	switch(prin[n])
	{
		case 0: 
			print(prin, n-1);
			printf("A\n");
			break;
		case 1: 
			print(prin, n-3);
			printf("CTRL-A\nCTRL-C\nCTRL-V\n");
			break;
		case 2: 
			print(prin, n-4);
			printf("CTRL-A\nCTRL-C\nCTRL-V\nCTRL-V\n");
			break;
		case 3: 
			print(prin, n-5);
			printf("CTRL-A\nCTRL-C\nCTRL-V\nCTRL-V\n");
	}
}

</syntaxhighlight>


{{Template:FBD}}