二分
Time Limit:2000MS Memory Limit:32768KB 64bit IO Format:%lld & %llu
Description
You are given N sticks having distinct lengths; you have to form some triangles using the sticks. A triangle is valid if its area is positive. Your task is to find the number of ways you can form a valid triangle using the sticks.
Input
Input starts with an integer T (≤ 10), denoting the number of test cases.
Each case starts with a line containing an integer N (3 ≤ N ≤ 2000). The next line contains N integers denoting the lengths of the sticks. You can assume that the lengths are distinct and each length lies in the range [1, 109].
Output
For each case, print the case number and the total number of ways a valid triangle can be formed.
Sample Input
3
5
3 12 5 4 9
6
1 2 3 4 5 6
4
100 211 212 121
Sample Output
Case 1: 3
Case 2: 7
Case 3: 4
1 #include <iostream>
2 #include <stdio.h>
3 #include <algorithm>
4 #include <math.h>
5
6 using namespace std;
7 typedef long long LL;
8 LL a[2000+5];
9 int n;
10
11 int Binary_search(int x)
12 {
13 int l = 0,r = n-1;
14 while(l<=r)
15 {
16 int mid = (l+r)/2;
17 if(a[mid] == x)
18 return mid;
19 else if(a[mid] > x)
20 r= mid-1;
21 else
22 l = mid +1;
23 }
24 return l;
25
26 }
27
28 int main()
29 {
30 int T;
31 cin>>T;
32 int flag = 0;
33 while(T--)
34 {
35
36 cin>>n;
37 for(int i = 0; i < n; i++)
38 scanf("%lld",&a[i]);
39 sort(a,a+n);
40 int ans = 0;
41 for(int i = 0; i < n-1; i++)
42 for(int j = i+1; j < n; j++)
43 {
44 LL sum = a[i] + a[j];
45 LL cha = abs(a[j] - a[i]);
46
47 int up = Binary_search(sum)-1;
48 if(up <= j)
49 continue;
50 int low = Binary_search(cha);
51 if(low < j)
52 low = j;
53 ans += (up-low);
54
55
56 }
57
58 cout<<"Case "<<++flag<<": "<<ans<<endl;
59
60 }
61 return 0;
62 }
1 #include <iostream>
2 #include <stdio.h>
3 #include <algorithm>
4 #include <math.h>
5
6 using namespace std;
7 typedef long long LL;
8 LL a[2000+5];
9 int n;
10
11 int Binary_search(int x)
12 {
13 int l = 1,r = n;
14 while(l<r)
15 {
16 int mid = (l+r)/2;
17 if(a[mid] == x)
18 return mid;
19 else if(a[mid] > x)
20 r= mid;
21 else
22 l = mid +1;
23 }
24 return l;
25
26 }
27
28 int main()
29 {
30 int T;
31 cin>>T;
32 int flag = 0;
33 while(T--)
34 {
35
36 cin>>n;
37 for(int i = 0; i < n; i++)
38 scanf("%lld",&a[i]);
39 sort(a,a+n);
40 int ans = 0;
41 for(int i = 0; i < n-1; i++)
42 for(int j = i+1; j < n; j++)
43 {
44 LL sum = a[i] + a[j];
45 LL cha = abs(a[j] - a[i]);
46
47 int up = Binary_search(sum)-1;
48 if(up <= j)
49 continue;
50 int low = Binary_search(cha);
51 if(low < j)
52 low = j;
53 ans += (up-low);
54
55
56 }
57
58 cout<<"Case "<<++flag<<": "<<ans<<endl;
59
60 }
61 return 0;
62 }
1 #include <iostream>
2 #include <stdio.h>
3 #include <algorithm>
4 #include <math.h>
5
6 using namespace std;
7 typedef long long LL;
8 LL a[2000+5];
9 int n;
10
11 int main()
12 {
13 int T;
14 cin>>T;
15 int flag = 0;
16 while(T--)
17 {
18
19 cin>>n;
20 for(int i = 0; i < n; i++)
21 scanf("%lld",&a[i]);
22 sort(a,a+n);
23 int ans = 0;
24 for(int i = 0; i < n-1; i++)
25 for(int j = i+1; j < n; j++)
26 {
27 LL sum = a[i] + a[j];
28 LL cha = abs(a[j] - a[i]);
29
30 int up = upper_bound(a+j+1,a+n,sum)-a;
31
32
33 int low = lower_bound(a+j+1,a+n,cha)-a;
34
35 ans += (up-low);
36
37
38 }
39
40 cout<<"Case "<<++flag<<": "<<ans<<endl;
41
42 }
43 return 0;
44 }