/home/toolbox/public_html/solutions/109/10991/a.c
1 #include <stdio.h>
2 #include <string.h>
3 #include <sys/types.h>
4 #include <sys/stat.h>
5 #include <fcntl.h>
6 #include <stdlib.h>
7 #include <math.h>
8 #include <stdint.h>
9 #include <ctype.h>
10
11 #define TRUE (1 == 1)
12 #define FALSE (1 != 1)
13
14 #define DEBUG if (FALSE)
15
16 /* fprintf(stderr, "functionName: message", varslist); */
17
18 /*
19 * Author: Isaac Traxler
20 * Date: 20221018
21 * Purpose: fun
22 * Problem: 10991 - Region
23 */
24
25 /*
26 * This template reads data a specified number of times.
27 *
28 *
29 * This problem is to find the ara outsied three circles that intersect each other at two points each
30 * Imagine pushing three circles together so that each circle touches each other circle in exactly 2
31 * points.
32 *
33 * You can calculate the area of the triangle formed with verticies at the center of each circle.
34 * You can then determine how much area of each of the three circles is in each triangle bu calculating
35 * the area of the circle and then multiplying that times the percentage of the circle in the triangle.
36 * Now sum these three ara and subtract from area of triangle to get desireed area (Area G in the
37 * problem description).
38 *
39 * triangle area is 1/2 * b * h
40 *
41 */
42
43 int numberOfTimes;
44 double r1;
45 double r2;
46 double r3;
47 double triangleArea;
48 double t1;
49 double t2;
50 double t3;
51 double PI = (double) 3.141592653589793;
52
53 void init()
54 {
55 /* FUNCTION init */
56 scanf("%d ", &numberOfTimes);
57 } /* FUNCTION init */
58
59 void dump()
60 {
61 /* FUNCTION dump */
62 } /* FUNCTION dump */
63
64 void getInput()
65 {
66 /* FUNCTION getInput */
67 scanf(" %lf %lf %lf ", &r1, &r2, &r3);
68 DEBUG printf("(r1 %lf) (r2 %lf) (r3 %lf)\n", r1, r2, r3);
69 } /* FUNCTION getInput */
70
71 double calcTriangleArea(double r1, double r2, double r3)
72 {
73 /* FUNCTION calcTriangleArea */
74 double ret;
75 double s;
76 double a;
77 double b;
78 double c;
79
80
81 /* heron's formula tells us how to get area of arbitrary triangle
82 * a, b and c are the length of the sides
83 * s = (a + b + c) / 2 (perimiter)
84 * area = sqrt(s * (s-a) * (s-b) * (s-c)
85 */
86
87 a = r1 + r2;
88 b = r2 + r3;
89 c = r3 + r1;
90
91 /* here is the normal calculation
92 s = (a + b + c) / 2;
93 or
94 s = ((r1 + r2) + (r2 + r3) + (r3 + r1)) / 2;
95 which simplies to:
96 s = r1 + r2 + r3;
97 */
98
99 s = r1 + r2 + r3;
100
101 ret = (sqrt(s * (s - a) * (s - b) * (s - c)));
102 DEBUG printf("(a %lf) (b %lf) (c %lf) (s %lf) (area %lf)\n", a, b, c, s, ret);
103 return ret;
104 } /* FUNCTION calcTriangleArea */
105
106 double calcAngle(double a, double b, double c)
107 {
108 /* FUNCTION calcAngle */
109 /* this will use law of cosines to calculate angle
110 * c*c = a*a + b*b - 2*a*b*cos(c)
111 * 2*a*b*cos(c) = a*a + b*b - c*c
112 * cos(c) = (a*a + b*b - c*c) / (2*a*b)
113 * angle = arccos(((a * a) + (b * b) - (c * c) / 2 * a * b))
114 */
115 double top;
116 double bottom;
117 double angle;
118 double angleDegrees;
119
120 top = (a * a) + (b * b) - (c * c);
121 bottom = 2 * a * b;
122 angle = (acos(top / bottom));
123 angleDegrees = angle * 180 / PI;
124 DEBUG printf("calcAngle: (a %lf) (b %lf) (c %lf) (top %lf) (bottom %lf) (div %lf) (angle %lf %lf)\n", a, b, c, top, bottom, (top/bottom), angle, angleDegrees);
125 return angleDegrees;
126 } /* FUNCTION calcAngle */
127
128 void process()
129 {
130 /* FUNCTION process */
131 double s1;
132 double s2;
133 double s3;
134 double angle1;
135 double angle2;
136 double angle3;
137 double area1;
138 double area2;
139 double area3;
140 triangleArea = calcTriangleArea(r1, r2, r3);
141 DEBUG printf("triangle area = %lf\n", triangleArea);
142 s1 = r1 + r2;
143 s2 = r2 + r3;
144 s3 = r1 + r3;
145 /* calculate the 3 angles in radians */
146 angle1 = calcAngle(s3, s1, s2);
147 angle2 = calcAngle(s1, s2, s3);
148 angle3 = calcAngle(s2, s3, s1);
149 DEBUG printf(" sum of angles: %lf + %lf + %lf = %lf\n", angle1, angle2, angle3, angle1 + angle2 + angle3);
150 /* calculate sub area for each slice */
151 /* area1 = (PI * r1 * r1) * (angle1 / (2 * PI)) simplifies to r1 * r1 * angle1 / 2 */
152 area1 = PI * r1 * r1 * angle1 / 360;
153 area2 = PI * r2 * r2 * angle2 / 360;
154 area3 = PI * r3 * r3 * angle3 / 360;
155 DEBUG printf("cirle: %lf area %lf angle: %lf portion: %lf\n", r1, (PI*r1*r1), angle1, area1);
156 DEBUG printf("cirle: %lf area %lf angle: %lf portion: %lf\n", r2, (PI*r2*r2), angle2, area2);
157 DEBUG printf("cirle: %lf area %lf angle: %lf portion: %lf\n", r3, (PI*r3*r3), angle3, area3);
158 DEBUG printf("(sides: %lf,%lf,%lf angle: %lf area: %lf)\n", s1, s2, s3, angle1, area1);
159 DEBUG printf("(sides: %lf,%lf,%lf angle: %lf area: %lf)\n", s2, s3, s1, angle2, area2);
160 DEBUG printf("(sides: %lf,%lf,%lf angle: %lf area: %lf)\n", s3, s1, s2, angle3, area3);
161 printf("%0.6lf\n", triangleArea - area1 - area2 - area3);
162 } /* FUNCTION process */
163
164 int main()
165 {
166 /* main */
167 int i;
168
169 init();
170 for (i=0; i<numberOfTimes; i++)
171 {
172 /* while */
173 getInput();
174 process();
175 } /* while */
176
177 return EXIT_SUCCESS;
178 } /* main */
179
180