Create Matrix Chain_Multiplication.java

Java/Matrix Chain_Multiplication.java

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+// Memoization
+public class Solution {
+    public static int matrixMultiplication(int[] arr , int N) {
+        if(N < 3) return 0;
+
+        int[][] dp = new int[N][N]; 
+        for(int i = 0; i < N; i++)
+            for(int j = 0; j < N; j++)
+                dp[i][j] = -1;
+
+        return partition(1, N-1, arr, dp);
+    }
+
+    private static int partition(int i, int j, int[] arr, int[][] dp) {
+        if(i == j) return 0;
+
+        if(dp[i][j] != -1) return dp[i][j];
+
+        int min = Integer.MAX_VALUE;
+
+        for(int k = i; k < j; k++) {
+            int curr = (arr[i-1] * arr[k] * arr[j]) + 
+                    partition(i, k, arr, dp) + partition(k+1, j, arr, dp);
+            min = Math.min(min, curr);
+        }
+
+        return dp[i][j] = min;
+    }
+}
+
+// Tabulation
+public class Solution {
+    public static int matrixMultiplication(int[] arr , int N) {
+        if(N < 3) return 0;
+
+        int[][] dp = new int[N][N]; 
+
+        for(int i = N-1; i > 0; i--) {
+            for(int j = i+1; j < N; j++) {
+                if(i == j) continue;
+
+                int min = (int) 1e9;
+                for(int k = i; k < j; k++) {
+                    min = Math.min(min, (arr[i-1] * arr[k] * arr[j]) + 
+                                  dp[i][k] + dp[k+1][j]);
+                }
+
+                dp[i][j] = min;
+            }
+        }
+
+        return dp[1][N-1];
+    }
+}