Question

A function f(i,j) satisfies the following recurrence relation and boundary conditions.

f(i,j) = { 0 if i=0 or j=n+1

{ 1 + max{f(i, j+1), f(i-1,j)} otherwise

Write a non-recursive algorithm to compute the value of f(i,j) for all 1<=i<=n, 1<=j<=n

Answer 1

int max(int a, int b) {
        if(a > b) {
                return a;
        }
        return b;
}

int f(int r, int c) {
        
        int values[n+1][n+1];
        
        for(int i=0; i<=n; i++) {
                values[0][i] = 0;
                values[i][n] = 0;
        }
        
        for(int i=1; i<=n; i++) {
                for(int j=n-1; j>=0; j--) {
                        values[i][j] = 1 + max(values[i][j+1], values[i-1][j]);
                }
        }
        
        return f[r-1][c-1];
}

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