2015
04-13

# Find the Circle

Given three circles (center of them are not co-linear), your job is to find a circle that is tangent with all these three circles. However, the circle might be not unique, as they can be either externally or internally tangent to each other. To make it clearer, you have to give the answer in some specific model. For example, you might be asked to give a circle which should be internally tangent with circle 1 and circle 2, while externally tangent with circle 3.

The first line of input contains an integer n, which is the number of test cases. Each case have three lines, each have four integers x, y, r, m. (0 <= x, y <= 10000 and 0 <= r <= 500), where x, y is position of one circle, and r is the radius. m represents the model of circle you should give. m = 0 means your circle should internally tangent with this circle, and m = 1 for externally case.

The first line of input contains an integer n, which is the number of test cases. Each case have three lines, each have four integers x, y, r, m. (0 <= x, y <= 10000 and 0 <= r <= 500), where x, y is position of one circle, and r is the radius. m represents the model of circle you should give. m = 0 means your circle should internally tangent with this circle, and m = 1 for externally case.

2
1 3 2 0
0 1 5 0
1 0 1 0
3 5 20 1
2 1 1 1
4 4 1 1

-0.4904 2.2264 3.6792
NO SOLUTION!

Problem Description
When people drink some tea in the teahouse, they also play some casual games. Now, inverting cups is a popular game. The meaning of the question is, now there are some cups which are upturned, we can regard the total number of the cups as a positive integer
number A , and we can invert some cups, the number is B and B is also a positive integer number. We define one retroflexion that if the original cup is upturned, one retroflexion makes it downward, and if the original cup is downward, one retroflexion makes
it upturned. So the question is if the whole original cups are upturned , can we invert these cups to make all the cups downward? And if it is possible, how many is the least of times?

Input
The input contains multiple test cases(cases<=100000). Each case one line given two numbers , the first integer A (1<=A<=2^63) and the second integer B (1<=B<=A). The input is terminated by the end of file.

Output
For each test case, you should output how many the least of times if it is possible for us to invert all the cups, and if it is impossible please output “No Solution!”

Sample Input
5 3
14 4
8 5
11 4

Sample Output
3
4
4
No Solution!


//

#include<iostream>
#include<cstdio>
using namespace std;
int main() {
__int64 a, b, t, ans;
while (scanf("%I64d%I64d",&a,&b)==2) {
ans = 0;
if (a % 2 && b % 2 == 0) {
printf("No Solution!\n");
continue;
}
while (1) {
if (a / b >= 3) {
t = (a-2*b)/b;
ans += t;
a -= t*b;
}
if (a % b == 0)ans += a / b;
else if (a % 2 == b % 2)ans += 3;
else if (a / b >= 2)ans += 4;
else {
b = a – b;
continue;
}
break;
}
printf("%I64d\n", ans);
}
return 0;
}

1. 我还有个问题想请教一下，就是感觉对于新手来说，递归理解起来有些困难，不知有没有什么好的方法或者什么好的建议？

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