Algorithms/DP/MatrixChainMultiplication.java at 438313d5fe6fbc7553d4cb387e4976aa02ff5c66 · LakshaySK106/Algorithms · GitHub

1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141

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);

    }
}