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This P(x) can be written as ((...((cn-1)x +cn-2)x + cn-3)x + ... c2)x + c1
Assuming V is the vector/array holding the coefficients.

int y=0;
for(i=n-1; i>=0; i)
    y = V[i] + x.y;

The above way of evaluating polynomial is also known as Horner's rule.

i m not sure we need to calculate the value..i think we need to gen the expression which can be done using linked list....

The vector is already a compact form of the polynomial, so simply iterate over it and sum the results.

Optimization: Horner's rule is known to sum polynomials in O(n) running, more efficient than plain summing.

for i in range(1, n):
    C += C[i] * x^(n-1)

The following is my code:
any bug/error exist?

public class construct_polynomial {

public static void polynomial(Vector<Double> v, double x){
double sum = 0.0;

for(int i = 0 ; i<=v.size()-1 ; i++){
sum += v.elementAt(i) * Math.pow(x,i);
}
System.out.println(sum);
}
}