CODEWITHSUNDEEP
javascriptalgorithm
bihire boris
bihire boris

Reputation: 1662

COdility Flags solution

I was passing through codility lessons. I tried my best and scored 40% , then tried search for the answer.

Could someone who gets the following code kindly explain to me what's happening from maxFlags line(why maxFlags like that, I thought from what I understand the maximum flags we can have equals the number of peaks before filtering according the distance)

This is the 100% code I found

function solution(A) {
    if (A.length <= 2) return 0;
    var peaks = [];
    var size = 0;
    for (var i = 1; i < A.length-1; ++i) {
        if (A[i] > A[i-1] && A[i] > A[i+1]) {
            peaks[size] = i;
            ++size;
        }
    }
    
    if (size <=2) return size;

   // from here does anyone know what's happening
    
    var maxFlag = parseInt(Math.sqrt(peaks[size-1] - peaks[0]) + 1);
    
    for (var i = maxFlag; i >= 2; --i) {
        var count = 1;
        var curPos = peaks[0];
        for (var j = 1; j < size; ++j) {
            if (curPos + i <= peaks[j]) {
                curPos = peaks[j];
                ++count;
            }
        }
        if (count >= i) return i;
    }
    
    return 2;
}

This what I had tried for getting the flags that scored 40%

...
    if (size<=2) return size
    let newSize = 1
    let left = 0
    for (i = 1; i < size; i++) {
        if(peaks[i] - peaks[left] >= size) {
            newSize++
            left = i
        }
    }

This is the question

Task description

A non-empty array A consisting of N integers is given.

A peak is an array element which is larger than its neighbours. More precisely, it is an index P such that 0 < P < N − 1 and A[P − 1] < A[P] > A[P + 1].

For example, the following array A: A[0] = 1 A[1] = 5 A[2] = 3 A[3] = 4 A[4] = 3 A[5] = 4 A[6] = 1 A[7] = 2 A[8] = 3 A[9] = 4 A[10] = 6 A[11] = 2

has exactly four peaks: elements 1, 3, 5 and 10.

You are going on a trip to a range of mountains whose relative heights are represented by array A, as shown in a figure below. You have to choose how many flags you should take with you. The goal is to set the maximum number of flags on the peaks, according to certain rules.

Flags can only be set on peaks. What's more, if you take K flags, then the distance between any two flags should be greater than or equal to K. The distance between indices P and Q is the absolute value |P − Q|.

For example, given the mountain range represented by array A, above, with N = 12, if you take:

    two flags, you can set them on peaks 1 and 5;
    three flags, you can set them on peaks 1, 5 and 10;
    four flags, you can set only three flags, on peaks 1, 5 and 10.

You can therefore set a maximum of three flags in this case.

Write a function:

function solution(A);

that, given a non-empty array A of N integers, returns the maximum number of flags that can be set on the peaks of the array.

For example, the following array A: A[0] = 1 A[1] = 5 A[2] = 3 A[3] = 4 A[4] = 3 A[5] = 4 A[6] = 1 A[7] = 2 A[8] = 3 A[9] = 4 A[10] = 6 A[11] = 2

the function should return 3, as explained above.

Write an efficient algorithm for the following assumptions:

    N is an integer within the range [1..400,000];
    each element of array A is an integer within the range [0..1,000,000,000].

Upvotes: 1

Views: 588

Answers (2)

Abhinav Mathur
Abhinav Mathur

Reputation: 8101

If you take K flags, they all have to be at distance K. Assuming there exists a peak at every distance of K, there will be a total length of K*K = K^2. So, the maximum value of K can be sqrt(distance between last peak and first peak).
After that it's just iterating through all peaks with K ranging from sqrt(distance between last peak and first peak) to 2. This will have a complexity lesser than O(N*(max(A))).

Upvotes: 1

גלעד ברקן
גלעד ברקן

Reputation: 23955

According to the task, "if you take K flags, then the distance between any two flags should be greater than or equal to K." So for the covering distance, D, the minimal distance between any two flags is K. To maximise the number of flags, we use the minimal distance between them:

 <---------- D ---------->
i1.....i2.....i3.........ik
 <--k--><--k-->

D = (K - 1) * K

K just above represents both the maximum number of flags as well as the minimal distance between them.

In the code, peaks[size-1] - peaks[0] represents D = (K - 1) * K. The square root of D is between the ideal K and (K - 1) (imagine trying to equalise them).

Upvotes: 1

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