JavaAlgorithms/DynamicProgramming/MemoizationTechniqueKnapsack.java

package DynamicProgramming;
// Here is the top-down approach of
// dynamic programming
public class MemoizationTechniqueKnapsack {

  // A utility function that returns
  // maximum of two integers
  static int max(int a, int b) {
    return (a > b) ? a : b;
  }

  // Returns the value of maximum profit
  static int knapSackRec(int W, int wt[], int val[], int n, int[][] dp) {

    // Base condition
    if (n == 0 || W == 0) return 0;

    if (dp[n][W] != -1) return dp[n][W];

    if (wt[n - 1] > W)

      // Store the value of function call
      // stack in table before return
      return dp[n][W] = knapSackRec(W, wt, val, n - 1, dp);
    else

      // Return value of table after storing
      return dp[n][W] =
          max(
              (val[n - 1] + knapSackRec(W - wt[n - 1], wt, val, n - 1, dp)),
              knapSackRec(W, wt, val, n - 1, dp));
  }

  static int knapSack(int W, int wt[], int val[], int N) {

    // Declare the table dynamically
    int dp[][] = new int[N + 1][W + 1];

    // Loop to initially filled the
    // table with -1
    for (int i = 0; i < N + 1; i++) for (int j = 0; j < W + 1; j++) dp[i][j] = -1;

    return knapSackRec(W, wt, val, N, dp);
  }

  // Driver Code
  public static void main(String[] args) {
    int val[] = {60, 100, 120};
    int wt[] = {10, 20, 30};

    int W = 50;
    int N = val.length;

    System.out.println(knapSack(W, wt, val, N));
  }
}