Function Curve
Time Limit: 2000/1000 MS (Java/Others) Memory Limit: 65535/65535 K (Java/Others)Total Submission(s): 151 Accepted Submission(s): 13
Problem Description
Given sequences of k1, k2, … kn, a1, a2, …, an and b1, b2, …, bn. Consider following function:
Then we draw F(x) on a xy-plane, the value of x is in the range of [0,100]. Of course, we can get a curve from that plane.
Can you calculate the length of this curve？
Then we draw F(x) on a xy-plane, the value of x is in the range of [0,100]. Of course, we can get a curve from that plane.
Can you calculate the length of this curve？
Input
The first line of the input contains one integer T (1<=T<=15), representing the number of test cases.
Then T blocks follow, which describe different test cases.
The first line of a block contains an integer n ( 1 <= n <= 50 ).
Then followed by n lines, each line contains three integers ki, ai, bi ( 0<=ai, bi<100, 0<ki<100 ) .
Then T blocks follow, which describe different test cases.
The first line of a block contains an integer n ( 1 <= n <= 50 ).
Then followed by n lines, each line contains three integers ki, ai, bi ( 0<=ai, bi<100, 0<ki<100 ) .
Output
For each test case, output a real number L which is rounded to 2 digits after the decimal point, means the length of the curve.
Sample Input
2 3 1 2 3 4 5 6 7 8 9 1 4 5 6
Sample Output
215.56 278.91
Hint
All test cases are generated randomly.