Matrix Chain Multiplication -DP

DP/MatrixChainMultiplication.java

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+
+import java.util.*;
+
+public class MatrixChainMultiplication {
+
+    static Scanner input = new Scanner(System.in);
+    static int[][] mem = new int[100][100];
+
+    public static void print2dArray(int[][] array) {
+        for (int i = 1; i < array.length; i++) {
+            for (int j = 1; j < array[i].length; j++) {
+                System.out.print(array[i][j] + " ");
+            }
+            System.out.println();
+        }
+    }
+
+    public static void inputArray(int[] array) {
+        for (int i = 0; i < array.length; i++) {
+            array[i] = input.nextInt();
+        }
+    }
+
+    public static int bruteForceRec(int[] matrices, int[][] subProblems, int i, int j) {
+
+        if (i == j) {
+            return 0;
+        }
+        subProblems[i][j]++;
+        int minCount = Integer.MAX_VALUE;
+
+        for (int iter = i; iter < j; iter++) {
+
+            int count = bruteForceRec(matrices, subProblems, i, iter)
+                    + bruteForceRec(matrices, subProblems, iter + 1, j)
+                    + matrices[i - 1] * matrices[iter] * matrices[j];
+
+            if (count < minCount) {
+                minCount = count;
+            }
+
+        }
+
+        return minCount;
+    }
+
+    public static int storedRec(int[] matrices, int[][] subProblems, int i, int j) {
+        if (i == j) {
+            return 0;
+        }
+
+        if (mem[i][j] != -1) {
+            return mem[i][j];
+        }
+        subProblems[i][j]++;
+        int minCost = Integer.MAX_VALUE;
+
+        for (int iter = i; iter < j; iter++) {
+            int cost1, cost2;
+
+            if (mem[i][iter] != -1) {
+                cost1 = mem[i][iter];
+            } else {
+                cost1 = storedRec(matrices, subProblems, i, iter);
+            }
+
+            if (mem[iter + 1][j] != -1) {
+                cost2 = mem[iter + 1][j];
+            } else {
+                cost2 = storedRec(matrices, subProblems, iter + 1, j);
+            }
+
+            int cost = cost1 + cost2 + matrices[i - 1] * matrices[iter] * matrices[j];
+
+            if (cost < minCost) {
+                minCost = cost;
+            }
+        }
+
+        mem[i][j] = minCost;
+        return minCost;
+    }
+
+    static int storedIter(int matrices[], int[][] subProblems) {
+        int n = matrices.length;
+        int memIter[][] = new int[n][n];
+
+        int i, j, k, chainLength, q;
+
+        for (i = 1; i < n; i++)
+            memIter[i][i] = 0;
+
+        for (chainLength = 2; chainLength < n; chainLength++) {
+            for (i = 1; i < n - chainLength + 1; i++) {
+                j = i + chainLength - 1;
+                if (j == n)
+                    continue;
+                subProblems[i][j]++;
+                memIter[i][j] = Integer.MAX_VALUE;
+                for (k = i; k <= j - 1; k++) {
+                    q = memIter[i][k] + memIter[k + 1][j]
+                            + matrices[i - 1] * matrices[k] * matrices[j];
+                    if (q < memIter[i][j])
+                        memIter[i][j] = q;
+                }
+            }
+        }
+
+        return memIter[1][n - 1];
+    }
+
+    public static void main(String[] a) {
+        for (int i = 0; i < 100; i++) {
+            for (int j = 0; j < 100; j++) {
+                mem[i][j] = -1;
+            }
+        }
+
+        System.out.println("Enter size of Array");
+
+        int size = input.nextInt();
+
+        int[] matrices = new int[size];
+        inputArray(matrices);
+        int[][] subProblems = new int[size][size];
+        int[][] subProblems2 = new int[size][size];
+        int[][] subProblems3 = new int[size][size];
+        System.out.println("Brute Force : ");
+        System.out.println("Answer = " + bruteForceRec(matrices, subProblems, 1, size - 1));
+        print2dArray(subProblems);
+
+        System.out.println("Dynamic : ");
+        System.out.println("Answer = " + storedRec(matrices, subProblems2, 1, size - 1));
+        print2dArray(subProblems2);
+
+        System.out.println("Iterative : ");
+        System.out.println("Answer = " + storedIter(matrices, subProblems3));
+        print2dArray(subProblems3);
+
+    }
+}