From b070883ceb430a2f39603a778ee9aeda9bc3af5a Mon Sep 17 00:00:00 2001 From: pezy_mbp Date: Wed, 13 May 2015 00:55:34 +0800 Subject: [PATCH] Added 2.2-1, 2.2-2 1. added 2.2-1 2. part of 2.2-2(pseudocode and code) --- Foundations/overview/README.md | 13 +++++++++++- Foundations/overview/insertion_sort.py | 10 +++++++++ .../overview/insertion_sort_unittest.py | 6 ++++++ Foundations/overview/selection-sort.pdf | Bin 0 -> 73794 bytes Foundations/overview/selection-sort.tex | 20 ++++++++++++++++++ 5 files changed, 48 insertions(+), 1 deletion(-) create mode 100644 Foundations/overview/selection-sort.pdf create mode 100644 Foundations/overview/selection-sort.tex diff --git a/Foundations/overview/README.md b/Foundations/overview/README.md index d26341e..4f86c83 100644 --- a/Foundations/overview/README.md +++ b/Foundations/overview/README.md @@ -115,10 +115,21 @@ appear in A. [unittest](insertion_sort_unittest.py) ### 2.1-4 -Consider the problem of adding two n-bit binary integers, stored in two n-element arrays A and B. The sum of the two integers should be stored in binary form in an (n+1)-element array `C`. State the problem formally and write pseudocode for adding the two integers. +> Consider the problem of adding two n-bit binary integers, stored in two n-element arrays A and B. The sum of the two integers should be stored in binary form in an (n+1)-element array `C`. State the problem formally and write pseudocode for adding the two integers. **Input**: Two n-bit binary integers, `A=` and `B=`. **Output**: An (n+1)-element array, `C=` which is the sum of the two input integers. [pseudocode](add-binary.pdf) | [code](insertion_sort.py) | [unittest](insertion_sort_unittest.py) + +### 2.2-1 +> Express the function `n^3/1000 - 100n^2 + 100n + 3` in terms of O-notation. + +![image](https://cloud.githubusercontent.com/assets/1147451/7592456/dd19381e-f905-11e4-8089-8ec444fca706.png) + +### 2.2-2 +> Consider sorting `n` numbers stored in array `A` by first finding the smallest element of `A` and exchanging it with the element in `A[1]`. Then find the second smallest element of `A`, and exchange it with `A[2]`􏰃. Continue in this manner for the first `n-1` elements of `A`. Write pseudocode for this algorithm, which is known as **selection sort**. What loop invariant does this algorithm maintain? Why does it need to run for only the first `n-1` elements, rather than for all `n` elements? Give the best-case and worst-case running times of selection sort in O-notation. + +[pseudocode](selection-sort.pdf) | [code](insertion_sort.py) | +[unittest](insertion_sort_unittest.py) diff --git a/Foundations/overview/insertion_sort.py b/Foundations/overview/insertion_sort.py index 8aff7d5..3f594b6 100644 --- a/Foundations/overview/insertion_sort.py +++ b/Foundations/overview/insertion_sort.py @@ -38,3 +38,13 @@ def add_binary(a_lst, b_lst): carry = (a_lst[j] + b_lst[j] + carry) // 2 c_lst[0] = carry return c_lst + + +def selection_sort(lst): + for j in range(0, len(lst)-1): + smallest = j + for i in range(j+1, len(lst)): + if lst[i] < lst[smallest]: + smallest = i + lst[j], lst[smallest] = lst[smallest], lst[j] + return lst diff --git a/Foundations/overview/insertion_sort_unittest.py b/Foundations/overview/insertion_sort_unittest.py index 8f8251d..1d9897e 100644 --- a/Foundations/overview/insertion_sort_unittest.py +++ b/Foundations/overview/insertion_sort_unittest.py @@ -24,5 +24,11 @@ class InsertionSortTest(unittest.TestCase): self.assertEqual(add_binary([0, 0, 1], [1, 1, 1]), [1, 0, 0, 0]) self.assertEqual(add_binary([1, 1, 1], [1, 1, 1]), [1, 1, 1, 0]) + def test_selection_sort(self): + self.assertEqual(selection_sort([5, 2, 4, 6, 1, 3]), [1, 2, 3, 4, 5, 6]) + self.assertEqual(selection_sort([5]), [5]) + self.assertEqual(selection_sort([]), []) + self.assertEqual(selection_sort([1, 5, 2, 1, 6]), [1, 1, 2, 5, 6]) + if __name__ == '__main__': unittest.main() diff --git a/Foundations/overview/selection-sort.pdf b/Foundations/overview/selection-sort.pdf new file mode 100644 index 0000000000000000000000000000000000000000..f106e8fd2b1b079ffdaa5f6bfaba8cb2bfa98fc9 GIT binary patch literal 73794 zcma&sLy#?i5}4t!ZQFClwr$%s@7T6&+_7!jwr!lTCoh$}s#GP5^s0ORZ@TIuR}>Ye zW1?q+A)j9!S%+aEVkB}fwua&5g<+62v$t@yBw}OZAo^be!ys;D>uTmq#2{{KFJc0pP#$-xY5)`1r9-kW-y%&J^~i!TS(O(8TDRvSV>lp zReAN!BVrQ>B^83x9FFCyq!N-*KeDUF7U~SR>K)iZ4*X|G3rgCS@XC=YbX%1rC39SM z6NV@K2~k2Kq`Y_)MdV{4$Z;wgnUNzI%yKPGge^T3nBf$}jqd=$YeH4tk zRuVvpBm(Cb-!TpbOlXM)y47q9=4N`#8v?POV?3rWzIMa=&i}L6PM~bLyw*JC!*`4{ z;F3Q^t3o^cWddEK)&zRX-qD6N{G1SdriX?vf@JA&>(=no{kbUiK$@|lyCjKyh7ifY zvn#@VGM|IAqW-0lyK2xeNcAR^>QMD;VH=vE>1?4|KCPqo559c zrcmhM$lAMx3I=v|@PkC|fg!L=A;JcNL>$|Igg`>}!Q6woWCHf(>w%zAf=&`iU-Mjk z{cB!VtDoiWD)m;>cDk}6<#pm!RxzyMm4k%$bGmhTje$JnxJ>j3fDjP{FcA?6AyAX~ zv2Ni$w&Dg%p@KSs3y~W98IO&Kh`ts|fkFgO*b0#Xvcg#c(h2)%$wq1aj1GbB9~~fn zXG4WX0;2`w8R`U3U<$&+0C$)$PKfCF8X9^-z8&%VGXVc#uLjarQZkAY7zA#lC&F5X zfC9DzIY1yvAH%l`m<8f1hsOeYeb<1&fQIDUR*T8rnwpA+JwKcU58aSya0cq`cZ3X} zAIArK1ls`dYlE8y=?wU>j)e_|F1Q17`&}x8Yzg)THX`aT9>BH*4Qdw%^ANNZV(dS< z1>#eK?|0EaI#y^L%?Cs1HwXvaKRNtX= zwQ?NjIlu!V8h+tGKEForje+z68JHEkk{Bc`0R@(BU( zKK{u)1!SNTw>~IhVj_Xv#sRwc!5QI9A3bjQxBc~MQNb?30pGYAfyAwDeOvX1pIAl@PvBNVT+V(RQ^YXCFOJV*Y|~dtzixl5 zbzH;AM=Ak*pt-v}fA!ONn5IzS9N!bnav`-It|MctkbO_BK93=JrJ{Kz?!c~;fMT@Q9=Ze9=_$DIQ2KS#irl6hF{#_y+JI3wN1BH$+D~>ll z%UMGxN!&|>pYLWMPESvdpRrd?J$Cu{x$w_oieJY-g7C9F9U5WVg4VvWm^(mNAS2d1 zAhE+=CvHLik91|)5kMKwsWz=9y6yx2AUiy(fId!`CK*UgW22f)!r{` zKwd!`iDxC_VVhUfu^ASsuID4A=jvlBZEWz&{qIX<$THL2q&epiobgOhv;fnI&e?S0 zLUBJ=#lkw&Y`2qup8gC4$!fN4r7*i_MR*8=x7Jb8XAqeD8w?)CK47+%<+3&jC(qA9r`H9o?96^dv z+*h-~&{OFo$0|}v!Sh>67+;G|Ks;GJ>;qnJsZV}@43Ip#1 zZz?#UeLaVYC#0!E@7j5!%>U9FW?3YT59Q4QOj%1@Ol*8)CD?WtVp+WNmjErYURq}% z`FN*A?KRx4ZiwMeVoYTNmCX?O@%heUVKgDyLO|oQY_sdzw9a}fy zaB@NXMr^=~Rwn$LRD28MV~h_+t+5%c$z{SDbIK9}AO& zlgpWdjkZ4Xne*fqhVISj#c2A{PjV^1_x}KNYjCR1E}OSWIF6qzESEe=Xc}b(@gEnJ zpH4dNoFxy&>cV@5H%i?}bHSN-m{L>fPh#BcJ%*kv&j~&fVcyqq;;5DQV|A29qav^= zTOs`2*{R9|?fgo#9f|EO)#5}O*vx}xZ68J|GkiLq?8da&(z_G zrd8{EYtAXT_Qj3h^d;AmtiG@qBLOYGbPij&`1F+UtpGOmn>j`c8&@Q>y${J?oCYe^b%&YXTxv1!jvc-@n{aipv zU4f`OGjUVXKfP`zn8r$S6;1#BT6|$?7h_^9`8Wl~$$pob!9X27ExhsPUC{))nU#zR zFi5;!qULTIe7RbGBJnQrW~0kNctheMok7J%UB|J3=Q%92zuB*w*_-z}v#2nXZ;S{0 zi9vPmG^pQMTH#G=Y{yegRHx^%a;Mq{USAkrYmUj!TV>{qmx2NVtTTt^LLZ$-t#LHl z@|Q;?B9WKtk*uL_>)dhdu`WCkFU$Xq664}?iz7579Kv1Bdpy1TI2n1V4PF^jwI24i z4gTdLj$pN_$tjzPoB?sV-DciBdprLf>d~2xkXcYj&PD4o;KWo#f8P>!bP8H#>|2J{ zpQJ1;guswmOsjNAW~DOZ5w29d@QsKerD{+|!}+ew+)iVLWO`hz()bR$`d(H)B4e6pQC6dTg*!;& z@VHrx^m(YX1)BfN)_6F?sNIHRad@>$gE*%_+{55ujFLe9OO8)E8gND3Y8>OUMe(a+ z`s)dabo|!qv{a3;wog8Tg6okxr+oy<=^~ z$842@NLz{=-E74Phsb>N!sXIAYV)amC3!6#qSZ|(|?I! 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