Detecting local minima and maxima, java

Question

- any sequence of integers, such as 23 7 13 4 8 6. I want to define local minimums and maximums with the following rules:

• the first number in the sequence is a local minimum when the next number is greater
• the last number in the sequence is a local minimum when the previous number is greater
• the number in the sequence is a local minimum when it is less than the previous and next number

I can use the hasNextInt and getNextInt methods .

I am currently thinking of an algorithm. But I'm not sure if I understand the logic. First, I build a tuple and compare its numbers. For instance. I compare 23 and 7. 7 is a local minimum. What would I do then? Create a triple ? But which numbers have three, 23 7 13 or 13 4 8? I'm not sure.

Any ideas?

Update:

Let's say we save the left neighbor and the number in the middle of three numbers:

left    middle    current

0        0         23

23       0         7

23       7         13 <- you have a triple, compare => minimum 7

What will happen then? Set vars to 0 and start with the next number 4? Or save 7 on the left, 13 in the middle to have 4 as current?

Update (this code works):

    int left   = 0;
    int center = 0;
    while(hasNextInt()){
        int current = getNextInt();

        if((left != 0) && (center != 0)){
            if(current > center && center < left){
                System.out.println("Min: "+center);
                left = center; center = current;
            }else{
                left = center; center = current;
            }
        }else if((left != 0) && (center == 0)){
            if(left < current){
                System.out.println("Min: "+left);
                center = current;
            }else{
                center = current;
            }
        }else if((left == 0) && (center == 0)){
            left = current;
        }
    }

    if(left > center){
        System.out.println("Min: "+center);
    }

Thank you for your help!

Answer 1

What you have there seems like a good start.

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? 0 4? 7 , 13 4 ?

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Answer 2

:

private void findMin() {

    int count = 0; // To handle special case of singleton list

    int left  = Integer.MAX_VALUE;
    int mid   = Integer.MAX_VALUE;
    int right = Integer.MAX_VALUE;

    while (hasNextInt()) {
        count++;
        left = mid;
        mid = right;
        right = getNextInt();

        if (right > mid && mid < left)
            System.out.println("local min: " + mid);
    }

    if (count > 1 && right < mid)
        System.out.println("local min: " + right);
}

( .)

Answer 3

, . , 4 :

local_minimum = previously_decreased && just_increased;
local_maximum = previously_increased && just_decreased;

→ .

previous_ booleans true. , just_ booleans, true.

, / , false.

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Answer 4

, , - :

... A, B, C,  ...

, B iff ( ): A-B > 0 && B-C <0

B iff: A-B < 0 && B-C >0

, , O (n).