coinchange.java

import java.util.Scanner;

public class coinchange{
 public static int [][]dp= new int[1001][1001]; // since constraint is given of 1000, we take dp[1001][1001]
 public static int numberOfWays(int []coins, int n, int sum){
 for(int i = 0; i<n+1; i++){
 for(int j = 0; j<sum+1; j++){
 if(i == 0){ // if coin's value is 0, we can't form the sum
 dp[i][j] = 0;
 }
 if(j == 0){ // if sum is 0, there will always be one way to form sum 0
 dp[i][j] = 1;
 }
 }
 }
 for(int i = 1; i<n+1; i++){
 for(int j = 1; j<sum+1; j++){
 if(coins[i-1]<=j){// if the coin's value is less than the given sum
 // there will be two possibilities whether to take it or leave it
 // Total // we pick it so sum got reduced and we will stay on the same index 
 dp[i][j] = dp[i][j-coins[i-1]] + dp[i-1][j];
 // we didn't pick it
 }
 else{
 dp[i][j] = dp[i-1][j]; // if we didn't pick it then the sum remains same and we will move to the next index
 }
 }
 }
 return dp[n][sum]; // return ans

 }
 public static void main(String args[]){
 int n, sum;
 Scanner sc = new Scanner(System.in);
 n = sc.nextInt();
 sum = sc.nextInt();
 int []coins = new int[n];
 for(int i = 0; i<n; i++){
 coins[i] = sc.nextInt();
 }
 // coinchange ref = new coinchange();
 System.out.println(numberOfWays(coins,n,sum));
 }
}