Error with matrices and array index out of bounds

Question

So, i need to implement this code that will return me the best solution of parentheses from a multiplication of matrices in java. I made a function for the printing of "(" ")" and in the main i did the construction of the matrices M and S for the resolution (dinamic programming). i keep getting this error after it prints the first "(":

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Exception in thread "main" java.lang.ArrayIndexOutOfBoundsException: 4
    at ProgramacaoDinamica.parenterizacao(ProgramacaoDinamica.java:13)
    at ProgramacaoDinamica.main(ProgramacaoDinamica.java:46)

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code:

public class ProgramacaoDinamica {
    private static int[][] s;

    public static void parenterizacao(int[][] s, int i, int j) {
        if (i == j) {
            System.out.println("M" + i);
        } else {
            System.out.println("(");
            parenterizacao(s, i, s[i][j]);
            parenterizacao(s, s[i][j] + 1, j);
            System.out.println(")");
        }
    }

    public static void main(String[] args) {

        int[] p = {15, 5, 10, 20, 25}; //VETOR P DO ENUNCIADO (alteracoes aqui!!!)

        int n = p.length - 1;


        int[][] m = new int[n][n];
        int[][] s = new int[n - 1][n - 1];

        for (int i = 0; i < n; i++) {
            m[i][i] = 0;
        }

        for (int l = 1; l < n; l++) {
            for (int i = 1; i <= l - n + 1; i++) {
                int j = i + l - 1;
                m[i][j] = 9999;
                for (int k = i; k <= j - 1; k++) {
                    int q = m[i][k] + m[k + 1][j] + p[i - 1] * p[k] * p[j];
                    if (q < m[i][j]) {
                        m[i][j] = q;
                        s[i][j] = k;
                    }
                }
            }
        }
        parenterizacao(s, 1, n);
    }

}

can anyone help me out with this? im starting to get lost with the code? im following this semi codes: java1 java2

Answer 1

The short answer is you're creating a 3x3 array (s), and then attempting to access the 5th element in the second row, which obviously doesn't exist.

As the code stands, you're mapping s[1..n-1,2..n] in the pseudocode to s[0..n-1][0..n-2] in java, e.g. where the pseudocode says s[1,2] your java uses s[0][0] but you're not subtracting the 1 and the 2 in your call to parenterizacao(s,1,n)

You have a mix of indices being mapped to zero-based in some places and not being mapped in others, so you should make it consistent - either use the indices directly as they are in the pseudocode and make the arrays bigger with unused elements (e.g. instead of s[0..2][0..2] have s[0..3][0..4]), or make sure you map the indices every time you access the arrays.

Below I've modified your code and kept the original values for i,j,k,l and n from the pseudocode but subtracted 1 or 2 as appropriate on each array access:

public static void parenterizacao(int[][] s, int i, int j) {
    if (i == j) {
        System.out.println("M" + i);
    } else {
        System.out.println("(");
        parenterizacao(s, i, s[i-1][j-2]);
        parenterizacao(s, s[i-1][j-2] + 1, j);
        System.out.println(")");
    }
}

and

    for (int i = 1; i <= n; i++) {
        m[i-1][i-1] = 0;
    }

    for (int l = 2; l <= n; l++) {
        for (int i = 1; i <= n - l + 1; i++) {
            int j = i + l - 1;
            m[i-1][j-1] = 9999;
            for (int k = i; k <= j - 1; k++) {
                int q = m[i-1][k-1] + m[k][j-1] + p[i - 1] * p[k] * p[j];
                if (q < m[i-1][j-1]) {
                    m[i-1][j-1] = q;
                    s[i-1][j-2] = k;
                }
            }
        }
    }
    parenterizacao(s, 1, n);

(n and l also needed to be switched in the inner loop to match the pseudocode)

Answer 2

The problm is your nested loop.

for (int l = 1; l < n; l++)
    for (int i = 1; i < l - n; i++)

Here, n = 3 and bound for l is already 3. Then you assign i = 3 and try to reach 2 by incrementing i.

One more thing, you should put return; somewhere in your recursive function. Else, you will have an infinite loop.