Euler 31

gistfile1.txt

#!/usr/local/bin/node

// our basic method here is to start with the largest coin and count down to the smallest
// each time you use up a coin (ie. that loop gets to zero) you're still checking the next
// smallest coin, down to the smallest one.  there is probably a way to write this recursively
// instead of copying out the loop 8 times, but i don't know recursive functions yet.  
// remove the comments if you want an actual enumeration of each set.  

goal = 200;
count = 0; 

for (a=1;a>=0;a--)
	{
	atotal = goal - a*200; 
	if (atotal == 0)
		{
//		console.log(a+" 200s is equal to 200");
		count +=1;
		}
	if (atotal > 0)
		{
		for (b=2;b>=0;b--)
			{
			btotal = atotal - b*100;
			if (btotal == 0)
				{
//				console.log(a+" 200s plus "+b+ " 100s is equal to 200");
				count +=1;
				}
			if (btotal > 0)
				{
				for (c=4;c>=0;c--)
					{
					ctotal = btotal - c*50;
					if (ctotal == 0)
						{
//						console.log(a+" 200s plus "+b+ " 100s plus "+c+" 50s is equal to 200");
						count +=1;
						}
					if (ctotal > 0)
						{
						for (d=10;d>=0;d--)
							{
							dtotal = ctotal - d*20;
							if (dtotal == 0)
								{
//								console.log(a+" 200s plus "+b+ " 100s plus "+c+" 50s plus " + d+" 20s is equal to 200");
								count +=1;
								}
							if (dtotal > 0)
								{
								for (e=20;e>=0;e--)
									{
									etotal = dtotal - e*10;
									if (etotal == 0)
										{
//										console.log(a+" 200s plus "+b+ " 100s plus "+c+" 50s plus " + d+" 20s plus "+ e + " 10s is equal to 200");
										count +=1;
										}
									if (etotal > 0)
										{
										for (f=40;f>=0;f--)
											{
											ftotal = etotal - f*5;
											if (ftotal == 0)
												{
//												console.log(a+" 200s plus "+b+ " 100s plus "+c+" 50s plus " + d+" 20s plus "+ e + " 10s plus " + f + " 5s is equal to 200");
												count +=1;
												}
											if (ftotal > 0)
												{
												for (g=100;g>=0;g--)
													{
													gtotal = ftotal - g*2;
													if (gtotal == 0)
														{
//														console.log(a+" 200s plus "+b+ " 100s plus "+c+" 50s plus " + d+" 20s plus "+ e + " 10s plus " + f + " 5s plus "+g+" 2s is equal to 200");
														count +=1;
														}
													if (gtotal > 0)
														{
														for (h=200;h>=0;h--)
															{
															htotal = gtotal - h*1;
															if (htotal == 0)
																{
//																console.log(a+" 200s plus "+b+ " 100s plus "+c+" 50s plus " + d+" 20s plus "+ e + " 10s plus " + f + " 5s plus "+g+" 2s plus " + h+ " 1s is equal to 200");
																count +=1;
																}
															if (htotal > 0)
																{
																//
																}	
															}
														}	
													}		
												}	
											}		
										}	
									}		
								}
							}
						}
					}
				}
			}
		}	
	}
	
console.log(count);
		

I couldn't get the recursion to work- the closest I got was this- which gives a total of 11, instead of the 73K we need. But I don't understand recursion enough to figure out why that is!

#!/usr/local/bin/node

goal = 200;
count = 0; 
total = new Array();
lettervalue = [200,100,50,20,10,5,2,1];

function calculation(index)
    {
    for (var i=(200/lettervalue[index]);i>=0;i--)
        {
        total[index] = goal - i*lettervalue[index]; 
        if (total[index] == 0)
            {
            count +=1;
            }
        if (total[index] > 0)
            {
            goal = total[index];
            index = index+1;
            calculation(index);
            }
        }   
    }   


calculation(0);

console.log(count);