CoinExchange

// wrong
public int ways(int x) {
  int[] ans = new int[x + 1];
  for (int i = 1; i < ans.length; i++) {
    if (i == 1 || i == 5 || i == 10) {
      ans[i] += 1;
    }
    if (i - 1 > 0) {
      ans[i] += ans[i - 1];
    }
    if (i - 5 > 0) {
      ans[i] += ans[i - 5];
    }
    if (i - 10 > 0) {
      ans[i] += ans[i - 10];
    }
  }
  return ans[x];
}

// correct
public int ways(int[] coins, int x) {
  return ways(coins, coins.length, x);
}

public int ways(int[] coins, int m, int n) {
  int[][] ans = new int[n + 1][m];
  for (int i = 0; i < m; ++i) {
    ans[0][i] = 1;
  }

  for (int i = 1; i <= n; ++i) {
    for (int j = 0; j < m; j++) {
      final int withCoinJ = (i - coins[j] >= 0)? ans[i - coins[j]][j]: 0;
      final int withoutCoinJ =  (j >= 1) ? ans[i][j - 1]: 0;
      ans[i][j] = withCoinJ + withoutCoinJ;
    }
  }
  return ans[n][m - 1];
}