def coin_change_minimum(coins, amount)
    dp = Array.new(amount+1,-1)
    dp[0] = 0
      
    coins.each do |coin|
      (coin..amount).each do |i|
        if dp[i-coin] != -1
          dp[i] = -1 == dp[i] ? dp[i-coin]+1  : [dp[i],dp[i-coin]+1].min
        end
      end
    end
      
    dp[amount]
  end
  
  def coin_change_combinations(coins, amount)
    dp = Array.new(coins.length+1) { Array.new(amount+1,0) }
    dp[0][0] = 1
    (1..coins.length).each do |i|
      (0..amount).each do |j|
          dp[i][j] = dp[i-1][j] + (j < coins[i-1] ? 0 : dp[i][j-coins[i-1]])
      end
    end
    dp[coins.length][amount]
  end
  
  coins = Array[2,4,5]
  amount = 12
  puts "Number of combinations of getting change for " + amount.to_s + " is "+ coin_change_combinations(coins, amount).to_s + "."
  puts "Minimum number of coins required for " + amount.to_s + " is "+ coin_change_minimum(coins, amount).to_s + "."