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HW3

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Problem 1

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      DequeLeft testLeft test
      <2,1,0,2>
      <3,2,1,0,3>Left(2,1,3)TLeft(0,2,3)F
      <3,2,1,0,3>Left(3,2,4)TLeft(0,3,4)T
      <5,3,2,1,0,5>Left(3,2,5)TLeft(0,3,5)F
      <6,3,2,1,0,5,6>Left(5,3,6)FLeft(0,5,6)T
      <6,3,2,1,0,5,6>Left(6,3,7)TLeft(5,6,7)T
      <6,3,2,1,0,5,6>Left(6,3,8)TLeft(5,6,8)T
      <9,2,1,0,5,6,9>Left(6,3,9)FLeft(5,6,9)T
      <10,1,0,5,6,9,10>Left(9,2,10)FLeft(6,9,10)T
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      the first and the last one of each deque are the bottom and the top.

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      1. Impossible, Edge v4v5v_4v_5 would be forced to cross the path v0v1v2v_0v_1v_2.
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      1. Possible, 1_2_2
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      1. Impossible, <2, 1, 0, 2> means 0 is on the left of v2v1v_2v_1. However, <4, 1, 2, 4> contains only right of v2v1v_2v_1, which does not include 0.
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Problem 2

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#include <stdio.h> +#define true 1 +#define false 0 + +typedef int tPointi[2]; + +int Area2(tPointi a, tPointi b, tPointi c) { + return (b[0] - a[0]) * (c[1] - a[1]) - + (c[0] - a[0]) * (b[1] - a[1]); +} + +int Collinear(tPointi a, tPointi b, tPointi c) { + return Area2(a, b, c) == 0; +} + +int Between(tPointi a, tPointi b, tPointi c) { + if (!Collinear(a, b, c)) + return false; + + if (a[0] != b[0]) + return ((a[0] < c[0] && b[0] > c[0]) || + (a[0] > c[0] && b[0] < c[0])); + else + return ((a[1] < c[1] && b[1] > c[1]) || + (a[1] > c[1] && b[1] < c[1])); +} + +int TIntersect(tPointi a, tPointi b, tPointi c, tPointi d) { + if (Between(a, b, c) && !Collinear(a, b, d)) + return true; + + if (Between(a, b, d) && !Collinear(a, b, c)) + return true; + + if (Between(c, d, a) && !Collinear(c, d, b)) + return true; + + if (Between(c, d, b) && !Collinear(c, d, a)) + return true; + + return false; +} + +int main() { + tPointi a = {0, 0}; + tPointi b = {0, 2}; + tPointi c = {0, 1}; + tPointi d = {1, 1}; + printf("TIntersect is %s", TIntersect(a, b, c, d)?"true":"false"); +} + +
+ + + + + \ No newline at end of file diff --git a/HW3/HW3.md b/HW3/HW3.md new file mode 100644 index 0000000..2c8db9a --- /dev/null +++ b/HW3/HW3.md @@ -0,0 +1,74 @@ +# HW3 +## Problem 1 + - 1. + | Deque | Left test | Left test | + | ----------------- | ------------- | ------------- | + | <2,1,0,2> | | | + | <3,2,1,0,3> | Left(2,1,3)T | Left(0,2,3)F | + | <3,2,1,0,3> | Left(3,2,4)T | Left(0,3,4)T | + | <5,3,2,1,0,5> | Left(3,2,5)T | Left(0,3,5)F | + | <6,3,2,1,0,5,6> | Left(5,3,6)F | Left(0,5,6)T | + | <6,3,2,1,0,5,6> | Left(6,3,7)T | Left(5,6,7)T | + | <6,3,2,1,0,5,6> | Left(6,3,8)T | Left(5,6,8)T | + | <9,2,1,0,5,6,9> | Left(6,3,9)F | Left(5,6,9)T | + | <10,1,0,5,6,9,10> | Left(9,2,10)F | Left(6,9,10)T | + + the first and the last one of each deque are the bottom and the top. + - 2. + - 1. Impossible, Edge $v_4v_5$ would be forced to cross the path $v_0v_1v_2$. + - 2. Possible, ![1_2_2](1_2_2.png) + - 3. Impossible, <2, 1, 0, 2> means 0 is on the left of $v_2v_1$. However, <4, 1, 2, 4> contains only right of $v_2v_1$, which does not include 0. +## Problem 2 +``` C +#include +#define true 1 +#define false 0 + +typedef int tPointi[2]; + +int Area2(tPointi a, tPointi b, tPointi c) { + return (b[0] - a[0]) * (c[1] - a[1]) - + (c[0] - a[0]) * (b[1] - a[1]); +} + +int Collinear(tPointi a, tPointi b, tPointi c) { + return Area2(a, b, c) == 0; +} + +int Between(tPointi a, tPointi b, tPointi c) { + if (!Collinear(a, b, c)) + return false; + + if (a[0] != b[0]) + return ((a[0] < c[0] && b[0] > c[0]) || + (a[0] > c[0] && b[0] < c[0])); + else + return ((a[1] < c[1] && b[1] > c[1]) || + (a[1] > c[1] && b[1] < c[1])); +} + +int TIntersect(tPointi a, tPointi b, tPointi c, tPointi d) { + if (Between(a, b, c) && !Collinear(a, b, d)) + return true; + + if (Between(a, b, d) && !Collinear(a, b, c)) + return true; + + if (Between(c, d, a) && !Collinear(c, d, b)) + return true; + + if (Between(c, d, b) && !Collinear(c, d, a)) + return true; + + return false; +} + +int main() { + tPointi a = {0, 0}; + tPointi b = {0, 2}; + tPointi c = {0, 1}; + tPointi d = {1, 1}; + printf("TIntersect is %s", TIntersect(a, b, c, d)?"true":"false"); +} + +``` \ No newline at end of file diff --git a/HW3/HW3.pdf b/HW3/HW3.pdf new file mode 100644 index 0000000000000000000000000000000000000000..98b81cc4f619f8709a5765f8e1c1996ae2d8d8d7 GIT binary patch literal 58825 zcmbrm1yq$=_b!fl1QjV!Qc9$xyFuwr>Fx&U4n+_Jq(MMHV$&hrp|q52x~1K8Y?=*s zZPar=zyBToaqsvs9LKX4?|$F4)|~5^&wS>5rBV`;U}RHF7Z%Gc$28HM=7ubjR7n$;`;^j>kuc zy1c`p#NEbqjUC!+d!{^TM27RCr8>5uq+9_n1s@CYRDG-oDQZ*a+HBrVjxy!nMdPx2 zsJTdSa@<82Z5(|ZMqnUBn^aV`8b;^Gb>zYs=hEC)L3yro;{lbG>d>S5?A1c!{JVtc zC`OBi?%Eb?^He(Tt0ZMoHeV*av$p*KEmQgy!xs0Ve*?oSH)}B^Qig0@EInG~`L~Za zPv}3ES-e)ilQ~V8UY+A9o*q0<{xtavmfINuQ*ctnqw5Z`MY8u+1w{Fm+xMGD6q3M&KC2w=wY8 zI@qLbM`$g}J(W`S^9^IH58tT_Curv=ALo>{ila~PqFYtpAeEk{DAaZNVXG^N=6R;H z9U4+!fRL8yUd;S9X{(b|yn0`rG)HI0GEZx4m?1Z{pY#^-zNQSv%>9RZd~~y%c2k9x zcZ?h+xfC_N7AK`I-qDJuo$mJWeTe3et?EP-L*Rm88gf!b-b`{q}w#Js~zc 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