从MathRandom生成的数字中打印最大数字

Question

My task is to print 1,000,000 random numbers between 0 and 1 with the use of loops.

I've chosen to use the function Math.random to do this and a for loop to create 1,000,000.

Now I need to print the max value of the numbers...but how? Is it possible to do it within putting them into an array?

Here's my code so far:

public class GenerateRandomNumbers    
{    
public static void main(String[]args)
    {
        for(int i=0; i < 1000000; i++){
        System.out.println(Math.random());
        }       
    }   
}

Answer 1

You simply need to keep track of the current maximum, and update it accordingly:

public static void main(String[]args) {
    double max = 0.0d;
    for(int i=0; i < 1000000; i++){
        double x = Math.random();
        max = Math.max(max,x);
        System.out.println(x);
    }
    System.out.println("The maximum is "+max);
}

The code works as follows: from the specifications of Math.random , we known that the lowest value is 0.0 , so we first set max to 0.0d .

Next we iterate over the 1000000 samples. Before printing the value, we first store it in a double x . Next we update the maximum: max stored the maximum thus far, by calculating the maximum of max and x , we include x as well.

Finally after the for loop, we know for sure that max contains the maximum value encountered, and we can print it (or do other things with it).

Answer 2

Ask yourself the question "can I compute the maximum on the fly ?", ie using some induction rule without storing the numbers.

More precisely, assume that you computed the maximum of the N first numbers. If you compute the next number, can you get the maximum of the N+1 first ?

The answer is an obvious yes, as "the maximum of the N+1 first numbers is the largest of the N+1th number and the maximum of the N first numbers". In other words, if the new number is larger than the maximum so far, it supersedes it.

Also note that the "maximum" of the first number is that number.

Hence, in pseudo-code,

Maximum= Random()
for i in range(1, 1000000):
    R= Random()
    if R > Maximum:
        Maximum= R

You can use a slightly simpler variant based on the rule "the maximum of no number is conventionally the smallest possible value", here 0.

Maximum= 0
for i in range(0, 1000000):
    R= Random()
    if R > Maximum:
        Maximum= R

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This way of thinking introduces an important concept in programming: the loop invariant. Throughout execution of the loop, the following condition is maintained: "the variable Maximum holds the largest value among those that have been computed so far". Thinking in terms of invariants helps you in the design of algorithms.