51nod 1285 Peaks and Segments

1285 Peaks and Segments 

Topic source:  Codility

Base Time Limit: 1 second Space Limit: 131072 KB Score: 20Difficulty  : Level 3 Algorithm Questions

 collect

 focus on

Use an integer array A of length N that describes the heights of peaks and valleys. A mountain needs to satisfy the following conditions, 0 < P < N - 1 and A[P - 1] < A[P] > A[P + 1].

 

 

Take the above picture as an example, the height is: 1 5 3 4 3 4 1 2 3 4 6 2.

Now to divide the whole mountain into K sections, it is required that the number of points in each section is the same, and there is at least one mountain in each section, and how many sections can be divided into at most.

Input

Line 1: A number N representing the length of the array (1 <= N <= 50000).
Lines 2 - N + 1: 1 number Ai per line (1 <= Ai <= 10^9).

Output

Output how many segments the mountain can be divided into at most.

Input example

12
1
5
3
4
3
4
1
2
3
4
6
2

Output example

3. 

First find the factor of n. Since there are not many, you can calculate it all, and output whichever is larger.

 1 #include <bits/stdc++.h>
 2 using namespace std;
 3 const int N = 5e4+10;
 4 int a[N], n, b[N];
 5 vector<int> vs;
 6 bool ok(int x) {
 7     if(b[n] < x) return false;
 8     int len = n/x;
 9     for(int i = 0; i < x; i ++) {
10         if(b[(i+1)*len]-b[i*len+1] == 0) return false;
11     }
12     return true;
13 }
14 int main() {
15     cin >> n;
16     for(int i = 1; i <= n; i ++) cin >> a[i];
17     for(int i = 2; i < n; i ++) {
18         b[i+1] = (a[i]>a[i-1]&&a[i]>a[i+1]) + b[i];
19     }
20     if(!b[n])return 0*printf("0\n");
21     // for(int i = 1; i<= n; i ++) printf("%d ",b[i] );printf("\n" );
22     for(int i = 2; i <= sqrt(n); i ++) {
23         if(n%i==0) {
24             vs.push_back(i);
25             vs.push_back(n/i);
26         }
27     }
28     sort(vs.begin(),vs.end());
29     for(int i = vs.size()-1; i >= 0; i --) {
30         if(ok(vs[i])) return 0*printf("%d\n",vs[i]);
31     }
32     printf("1\n");
33     return 0;
34 }