Dynamic Programming : Making coin change
1) I have  used "-1" to represent infinity. Hence I have an extra check to avoid the condition when "1 +(-1) = 0", because I want to treat "-1" as infinity and not number -1.

 public class MakeChange{  
      int[][] c;  
      public int[] a;  
      int sum;  
      int numCoins;  
      public MakeChange(int targetSum, int[] coins){  
           sum = targetSum;  
           numCoins = coins.length;  
           a = coins;  
           c = new int[numCoins][sum + 1];  
      }  
      public int getMinCoins(){  

           c[0][0] = 0;
           for(int i = 1; i <= sum; i++){  
                c[0][i] = -1; //This indicates infinite value, bcoz one cannot make sum of n using coin of value "0"  
           }  
           for(int i = 1; i < numCoins; i++){  
                for(int j = 1; j <= sum; j++){  
                     System.out.println("Trying to make change for "+j+" using coin "+a[i]);  
                     if(j < a[i]){ //sum to be made is less than coin value  
                          System.out.println("Assign value of coin "+c[i-1][j]+" which is "+c[i-1][j]);  
                          c[i][j] = c[i-1][j];  
                     }else{ //Make sum j using coin i or without using coin i and select the one with min coins  
                          int n = c[i][j-a[i]];  
                          if(n < 0){ //This check is required as I am using -1 for infinity  
                               c[i][j] = c[i-1][j];  
                          }else{  
                               System.out.println("Min of "+c[i-1][j]+" and "+(1+n));  
                               int min = findMin(c[i-1][j],1+n);  
                               c[i][j] = min;  
                          }  
                     }  
                }  
           }  
           System.out.println("The DP table is: ");  
           for (int i=0; i<c.length; i++) {  
                for (int j=0; j<c[i].length; j++) {  
                     System.out.print(" " + c[i][j]);  
                }  
                System.out.println("");  
           }  
           return c[numCoins - 1][sum];  
      }  
      private int findMin(int i, int j){  
           if(i < 0 && j < 0) {  
                return -1; //return infinity  
           }else if(i < 0 && j >=0){  
                return j;  
           }else if(j < 0 && i >=0){  
                return i;  
           }else if(i < j){  
                return i;  
           }else{  
                return j;  
           }  
      }  
      public static void main(String args[]){  
           int[] a = {1,2,4,8};  
           MakeChange m = new MakeChange(8,a);  
           System.out.println("The min # of coins are "+m.getMinCoins());  
      }  
 }