Merge pull request #87 from Rastrian/dynamicprogramming-coinchange

[Dynamic Programming] Coin Change

dynamic_programming/coin_change.rb

@@ -0,0 +1,30 @@
+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 + "."