Dendrochronology

Statement

Goal

Determine the age of a tree by counting the number of rings in a horizontal cross-section of its trunk.

You are presented with a 10×N grid representing a cross-section of a tree.

Every year, the tree alternates between a phase of rapid and slow growth depending on the season.

To compute the age of the tree, count the number of transitions between a cycle of rapid grow (line of 0), and slow growth (a line of 1).

A few considerations:

- There is an arbitrary number of lines per cycle.

- The tree trunk is not perfect and you must expect to see errors (i.e a 0 instead of 1 or vice-versa) or unwanted particles (represented by any other printable character).

- However, on any given line there will always be 10 characters, and less errors than valid characters.

Here is an example:

The age of this tree is 2 years since there are 2 transitions.

Input

Line 1: An integer N representing the height of the grid
Next N lines: Lines of 10 characters representing a section of the tree trunk

Output

An integer representing the age of the tree

Constraints

0 < N ≤ 1000

Example

Input

2
0000000000
1111111111

Output

Game modes

Fastest, Shortest

Test cases

Simple case Test

Input

2 0000000000 1111111111

Output

Validator 1 Validator

Input

2 1111111111 0000000000

Output

Variable length Test

Input

5 0000000000 0000000000 0000000000 1111111111 1111111111

Output

Validator 2 Validator

Input

5 0000000000 0000000000 1111111111 1111111111 1111111111

Output

Errors Test

Input

8 1000000000 1000000000 1111111110 0111111111 1111000000 0000001111 1111111111 1000000000

Output

Validator 3 Validator

Input

8 1111000000 0000001111 1111111110 0111111111 0000000001 1000000000 1111111111 1111000000

Output

More Errors Test

Input

6 #000000000 000000000# 1101110111 00000!0000 0000000000 111111111#

Output

Validator 4 Validator

Input

8 L000000000 110000000L 1111111111 00000!0000 %000000000 1L1111111# ####000000 0000000!!!

Output

Very dirty trunk Test

Input

9 ####000000 !0!0!0!000 1111111111 AZER111111 QWER111111 000000LKLZ Y1Y1Y1Y111 1111000000 1111111111

Output

Validator 5 Validator

Input

9 1111111111 ;;;;000000 WXYZ111111 ABCD111111 000000LYLY N1N1N1N111 1111000000 1111111111 K0K0K0K000

Output

Very old tree Test

Input

603 *111111111 111*111111 21V11+1111 111116111Y 1111111111 100U0I0*01 1000&00001 1111SN1111 1111111111 11S1\11O1Q 000))#000D 00000,0P00 000000%000 1111211111 000000000E 0000000000 00000V0000 000000#002 111(#11),1 161111111# 1111,1111Z 11111111*1 1111111111 00H0500000 0I00804000 000UV000X0 0C0$0,0I00 1111111111 11191'1111 0000000&00 000000000& O0000M00O0 Z1B11211-1 1111111111 1111000000 11!111W11R 1111-1N111 1111111111 1111111111 0000000000 0000000000 &00000A00/ Y000000000 1111!"1G11 1111>11111 1111111M11 0000000000 0000000000 00000C!000 11R1111111 111EL91111 91T1(11U11 1?11+11&11 00$000000# 000W000NV0 11?112&111 1111111111 Z11P11C'11 1;11111111 111.=11B11 0000[A1000 00*:0\X000 000\00"000 1[11111111 1N1111<191 0000000000 1111I-S1U1 111111)111 1111111111 1#11"111@1 000000000> Q0;000Q00R :Q11111%11 N111211H:1 W11M11:111 1-11X%111X 0Z0,,00$00 00OW000A0@ "000B0000V 0000000000 1L1111'111 B11;11:.11 111"11U1U' ("000000V, 0000000000 00000000/0 0000000000 L000000000 11111R11)[ 11[01111=1 11110111ZQ 11&1111111 0000000000 1V1K111121 F11111=&41 111111X121 0220O00J00 1000000000 000T000000 00000000!0 000Y0100$0 114,11E1%1 000000A000 00C0000000 <00,W0000L 00000000K0 1(11511+1C 000!0000W0 0NK000000I 0000000000 0.00000)S0 1111111111 1Y11111111 111)11111S 0000000000 0000000000 500000+000 000+0X=00P 1111111111 1111Y11#31 N(1111Q311 0000-00K00 100L0L000J 11111111U1 +112111111 0000000000 0000000000 000000Y0D0 111111O111 11111C)111 1111111V11 0000%00000 ,000000L0N 0Z00000000 0000000000 1111T11111 1111111111 00"0000000 008000\0## 0082005003 05L00N0000 1111111111 11@51111R1 1111111111 >!00000000 -00D00'0K0 00>0000000 11111#11Z9 000K;W000X 0000000S00 0000000000 11R1UZ111R 1111111111 00W0N00000 000[000000 000?0000A0 00000000X0 11!O111S11 1111=1K/11 11$1111111 000V000A00 0600000F&0 0000000000 0000G00000 000,000000 11B16U1111 11>!1111MT 1N11111101 111!111111 111G11111D 0B00000070 1111$11H11 51O1131111 0'Z(000000 000000000+ *0H0600'00 0000000000 1111111111 61111111A1 11U1111%11 1111111111 1111111111 0,00N0000> 0000\BE000 0!0000000G )111611111 :11111A@1: 0000000000 0000D(00-0 008000$000 1/111K1BI1 111A111111 1N1111111W 0E000F000G 000000:)00 00\0900:00 0000000000 1111111T1! 1111011111 1F3181\111 11MP111>I1 0000000000 0400000<05 0000000000 11111?1111 11+114)111 11111E1111 1111111111 1!1/1I1111 0000000000 000&000000 11111111P1 111U111111 S00Z00000# 0000000000 0000000000 J11\1%11B1 S1(111V11% 111111H111 N0"U000000 0000000000 1711#1-11R A11V1111[P 00E00,S000 0000T00000 0020008001 1111D*5111 0000000000 0000000000 Y9000)000+ 11$11111V" 1[111<11'1 1E1111X1U> 1111=$1E[1 00000>0000 0000000000 ?00300000) 0N02000900 300000/000 *111111111 1(G111111S 1151111111 1+11111111 $000"00000 05:00M0[00 N000000030 0000000000 0000000000 1111111Q11 111111[A.1 G1111L13$1 1111111?11 00000@0000 00Z00[0!#0 0000>00000 0000000020 L00000T000 1511111!11 11W1111F11 0000000000 0000000*00 0000000000 111:1N1111 1111'11111 111@111111 00%000!000 0000000000 0H'0000000 CN00000000 11#1111111 1111111112 1:Z161Z111 N1111111Z1 M11Z1C1111 0=09000000 60#00000&D ;111111111 0000000000 S0000;09/0 0S0<N00000 0:00:000DT 000000$00< 111111D111 040:0X0000 0U0DO00000 HU000000V0 1111111111 W00000/00@ 0O00R0W00G 000A80!000 000000A00H 0700005000 1111111111 00E00.0000 11#1111111 0000000029 000000000/ Y0000003-0 000000*008 111111111L 111111G")1 1<111'11=1 0000000000 3A0000000# 0000000000 000%00I004 11111/1111 1111111111 1111111111 O1111T=11$ 0@)0R00>00 00000000\0 0000000+Z0 000000T000 00000000(0 E113111*1V 111DQ111;# /00000[000 00000Y0000 0000000000 1J%111S11V 111<191111 G1C1+E1111 1111111111 UD00000JY0 4000U0E00N 00000000B0 1:1111&\11 1111111211 11111111Z1 11:11111/1 00\0000M00 0000000000 000000000> 1111111111 115111-1O+ 1111311111 11DL&%1111 0000000000 08000QR0.0 000"000000 0000000000 0070000P&M 1111111111 1111111116 0000000000 000V000F00 00000000.5 0000000000 0000000000 21(811,111 000000R+00 111N111111 11T1(11$11 1:11111J1B 1111\11111 1111<11"11 0000000000 1111%1(:11 1111111111 1111111S1Z 111*111111 [D1111)111 0>00000X0K 0000000000 00000000N0 !'0000;000 00B0000X00 1@1111M111 1111115111 T111111;11 11111:118( 1*11111111 0000<X00(0 \0W00(0P00 1111111111 6E?11111D1 1*>11$6111 111511X111 1111O"1111 000000ET./ 0L\0000000 10711B1&11 <000002000 000&000000 0000000000 00U000Z00N 00%00$00;6 113?)11131 1181111111 1A1(11%111 11111!1111 X121211151 0000000000 0000000000 0000R@2000 00.0000000 00&00R(00E 1MN1111G12 0000100+0* 000K400%00 1111111611 11;+11+411 1141111111 111111.111 ,1(1111111 V000000000 0000000@Q0 0000000000 0000000(00 1111-11111 B11,111UN1 1111111111 $0$100000& 006&000000 000%00>"0" G0000000B0 1111:/1?11 WS111111.U 117,111111 11111/1111 0000000000 ).0800%000 000C(0=000 11W@111111 1111111111 1*1111111I IX1H11111= 1111131111 00(0?I0003 Z1F1111I21 1111111111 111H111111 (00Y0V0$00 0V00[0<500 00*00!D600 0000Y00$00 000000000I /E11?1$111 0#0?000C00 00%20!0000 11111111C1 11WR11N1=1 11N11B111$ 1"1111E1U1 11411111*1 0000000000 0LE0000&00 000FN00000 1P1111,11Y M111113911 H11111JJ<1 05000M0000 L000200000 11H11/-111 11118112*1 -11111111" 11Y1=E111% 111FA111U\ 0000000000 0000000400 000:000000 00U/00\K00 000000M0;0 111E111111 1.11111811 111N111111 000M0T000T >Q00V00000 0000000000 07000F0&0: 000900000& 1I11N11E19 ;1111111Z7 1111111111 1111711111 0C0000H000 0000000000 #O0000000< 1111111111 311131W111 1111111L11 151118111$ 000000[000 00000000)0 0000000000 0000080.00 1M11B$1111 #111111111 1S21111711 07\0000000 D000004000 %0H00Z0#00 E11111+1UJ P411111111 11K<111111 111K111111 1111111111 00>0000000 0(00000000 00000000\0 000K00L000 000&<00000 111X.11>"1 1111111111 1111SA1111 11W111111S 000000000. 1111111111 1117X1'111 00$8/00000 0000000000 11111111M4 11>11L;111 000000.M0% 000-0000W0 000004B0P0 0000000000 0000000000 1111111111 1111111111 0'000?00G0 0=00000000 0000000000 11111111E1 1171111111 11@K111111 111111111( 11I1111-11 V00000S)X0 0000P00000 1111111111 0000=0000E 0000000000 00Y00K000F 0@000000Q$ 000)000000 1111111111 U0000C>0X0 000000000X 0T0000/"00 ?000000000 1111111111 111111S1$1 000)00%008 511E11111' 111111-1(1 1T111,1311 000T40900B 0!0XO00S00 1111111111 1111111111 111114C1&? 11$11:11%1 :000000000 111111H1U1 1111M1111) 11"1L11LC1 1111111111 /0000::002 D1111111J1 11151=1011 1111111)11 T111111-11 1111111111 00L0000000 000P$DO000 0000000000 11111Y1C43 &1211Q11B1 111D11F111 1111111111 020+00;000 707000E0)0 0000X000:> 000#00000\ "1111WG611 %Q11111111 111L11111L 1111111111 0700E%F000 0000000S%% 00+000000> 0000000000 11111111W1 1#11111111 1182111+01 0000000000 000000I06P 0000070000 0000000000 1111P111D1 1AW18K1111 1111111111 1?11111111 08+0S0K000 000K000000 G000000000 000YJ00000 1)11111111 000000Y000 00000000O0 00B00000X0

Output

189

Validator 6 Validator

Input

602 0111111111 0000000$00 11111O1(11 300600[060 &9OD000000 "00O0000EW 000000U000 1111111111 1M111:11FQ ?00)0S0000 000000[0>0 0000!0E000 0:0S000000 C11'11[11O 1111111111 111/V111M2 0000000000 0000000000 0000000000 0200001.0) 11\1111111 1111111<11 1111000000 11H1111J+W 1@11311111 6111=11JO1 0(00>0$000 00000%0000 1N11111111 1111111111 000000000X 0IH0(000T0 [000000I09 1111111N1[ 11$1111111 11111111Z1 111C0D111# >,S111111. S100000011 1111111111 1F@111:11T 11111111T1 11111111<1 0000000000 07O0B00000 00000<00G0 0080006000 0000000000 1?11[11111 5000000000 0000000000 0J00000000 11=1111111 11111<1111 11111JZ11I 1111111111 11M11Z1KM1 0000000000 0000000000 000#H)000Z 11111311,1 0000M?0000 0000000000 11111-1111 111111E111 11N1111111 11;7111"10 #1111X1111 0000000000 03K00H=000 11<L11[111 1111O11V1; +)[111111! 000JI00#L0 0000000000 W0!0000400 000000000< 000000000/ 1311111111 Z1[611111) 11111111Y1 1111111111 1S111\S171 0[00(000N0 0:00000000 1111111E1R 111W11M111 11=7111!1, 0000000000 0000400000 00'0000I:/ 00@0000000 ,111111,18 111157'111 1111111111 &111711811 @O1111*111 0C00000000 000Z000000 000800$$0; 0000000000 111%-*1111 R111111111 0000000000 00Z#00>000 $000K0$040 00A0000000 1111111111 111111111[ 1T1111"11Y 0V00000000 0000000000 0;0L00040Q 0000000.00 11111B11:K 1111111111 1111111111 1+'11G1A11 11$111211M 0000000000 $00700080! 1111111"\1 0000000000 0000010000 00000M0JG! 1111[1''10 111-T11111 1111111111 11161:1UU1 1111111161 0000000000 S0000000/0 0000000000 Z0#0000=00 M111111111 11111%1111 0000000000 0000000004 0=000%00V0 1111111111 1111111111 1111111111 111111W111 1111111111 0000000000 00000#0000 000L0000ZM 1W1+11J111 1111111111 1111111111 111'118161 OX00000\Y0 0000+000A, 00E0000=00 000000!00, K11=111111 115%111111 2111?1111L 1111"11111 1111R11111 0T>00800?0 V*80000000 1111111:M8 11111111V1 11111=111M 1>1J1.1211 1111111111 000000!0B0 11E51111,1 1111111111 111111111( 111Z1#Y111 0000000000 0709000"00 11$11=1111 11111111)$ 1111111111 1111111111 11041111/1 000F000000 00K0000600 0000000Z00 116Y1L11/1 111111HD+1 11=1111P15 11=1(R1111 .!00000<00 11I1111111 1111W1=711 1111111111 11A1111+11 00;00<000S 000000+000 400+[0000A 0H00900000 0040000000 11111111H1 1111111111 B1111)@114 00000000)0 #20P000D00 00S0000IQ0 1111111111 111111(1K1 1111111111 0(0+0000.# 0000&0D090 0000000000 0000000000 1111>11111 1!1111111Q 1111111117 0000000000 0000000000 0000000000 0000000000 1111.211)1 0000009;0: 1;1Z1H#111 011Z111;11 1211J111U1 ,1111IKV11 0000020000 0000000000 0[>000'000 0000000Z00 1";1111"1. 1111111111 111;1M11&Y 191112115G 1111111B11 0<C000-Q00 (00(0000O0 0000000000 08000#<:00 11.1"11111 2111111111 1111111111 0000000000 7111111111 1(1)111111 0060000000 0000000M0W 00000W00O0 0$@0D00000 0000E09000 Z11:111111 0000000000 1111111111 0[000'0070 EY0J00000! 00(0000000 00000<0000 000030000' 1115Z%1111 0000000000 0000000000 1)<11=111P C1111111Y1 00000T0000 0-000!0000 0000000000 /00000300N \00000000I 11M11V1Q17 111G1&1,A1 11W*111Z13 *P0000000K 0000000R00 <000000-00 %1114111\1 1111111111 000000000G 1111O#1111 111;141111 J>00000000 0000000000 0000000000 00$0W00E0D 00000P0Y00 1111F11?1! 00'0008V0E 000N0?0000 (0000G0000 0000@0000\ 00[[00FG00 11"1-11Y11 Z111111311 0E*0&0D000 11111*11V1 1110111111 1R11""1111 0000000000 0000000Z00 0000000000 0000<00100 00Y0000S00 1P1111O111 %611((1111 1111111111 X11;111111 0000Z[90Q0 0900000000 11111F1111 000$0:0000 F0,0B000N0 050<00\00Q 11111111+= 1111111111 8J1111*111 1111111111 0000000000 0K700000)8 1111111111 1M1T111117 1111111111 0000000000 0#00000G00 11111!1111 1111111R11 11S1111N1Q 111H111111 000B00?000 000000-D00 0000000000 0\0\0000H0 0Z(00000&0 1111111111 1111(11111 1111111111 11U111111+ 0U00*00(:0 0000000000 0000000000 11(.Q111+1 1<111111;1 11H1111111 1111111C11 08000000Y/ 0'00007200 K111HW1111 1E1G111>11 4111111161 1111111111 0000000000 )0F0000000 0000000QV0 11111111X1 1111111111 000000W000 0000000000 000@000000 11H9111Z1) 1*11111111 0000000000 0000000000 111111\111 1111111111 1111111111 111L111111 G000P000-0 1111111111 1A1111111N 111*1S411D 111111=111 0000000000 008000I000 11T-11>11E 1N11111RC1 @1111111K1 1111111111 =11D11111J 0000000000 0000000000 0000D0.D/0 0000003000 11Z1111KH2 1111111111 1111G1L111 11111JU1=1 1T11911111 000AK00K0% .11111;11: 111111+111 /000X+:000 0000000000 00000000V0 000V0000UI 0080000000 11J1111111 0000000000 00.S%00000 0>0000FG00 0000000000 11);1"11Y1 O111111111 X1L1111191 00E=000000 90000000W0 000=00000, 5?00000000 1111111111 >000000;00 000+00C003 020600N0G0 11115111Q1 1111W11+11 1211*>1141 0000000000 00C000-000 00%00I000J 11111>11Y1 +7/111111T 0000000000 0O000Z0$0= 0000000800 111111G1,1 1111111111 11111-11+1 0000000000 H000000GC0 0020000000 0000000000 07"=000000 /111111111 11111G1311 ",000.F000 0000005(00 [<B11111=1 00L0000000 0000000000 I0000Z00:0 0-00<00S'0 11V1111111 1111111111 1111111.1P 005000;000 000$000000 0000000000 000000000P 1111111111 \111\)11U1 0L00000000 0@00&000Q0 00000"0000 0E0[0($000 0000000000 ?11&111111 D>0G0D0000 0000(00J(0 -00'000000 1111111111 111&1111P1 Y00040+I00 1111111I11 1(11?1>11* 1F11:111>1 1111111111 0%00Y000W0 010$0/00(0 0000000000 111111'111 0&40000000 0000000000 0I00#0000N S000000000 000000000Y 1111111!11 11111111A1 0000000000 811C111J11 +00H0*0000 O000000[0B 111A1T1111 000'0R&00J 0000000000 0-00000000 000%000000 111/1%[1V1 11NC1:1>11 1111W11111 1111111111 111111111G 0000Z00000 1111111111 1\11[11111 1111111111 R000000000 1111111111 11#1111111 11?1111111 1)11L11111 11T1111111 0000000300 0000000000 15111$1111 1+11111111 (111111111 1<1U1J1(11 0;000000T: 0009S00000 0000:000"0 VM0000000G 0000[+0+60 11W1111111 )11"WF1111 1M1D11?11[ 0000&$0Y00 0000005000 11111111Q1 '1.C111111 111111111? 111\7W111B 1111111111 (0000#S005 0000000000 D000000000 00P0500010 1111111111 111111F1E1 1111Q111#M 1111111111 11T1YZ1111 0000000000 1111111$11 00Y0@00000 '0D0000H00 1111111111 1111AW11HO 11101.111\ 000'0D00/0 000S0!00!1 000E00T00< 000;000000 Z111111111 000000000+ 0000YPI000 F00RD0"000 1111111111 1M11181131 G111181$11 1111[11111 0000V00000 111;1X1111 000D000000 1$1"!111H1 (5000C0000 111D11111B 111611!<1O 11%1111&&0 1!#1111@>1 1V11111111 00B0000000 000000000% A000M000T" 0000000000 :0(00>0000 1E115"D111 000L00000T 00000JU00W 00000000M0 0000000000 11=(1&11A1 111111111G 1111111111 0U00P0&000 00000,0A00 11%11W,111 00#&0N0000 0Z/000000: 0000000000 11111A1111 000H000000 Z0P000[0F0 0000000000 N+11111111 1>1111(1C1 1111111211 11111!1111 0000)0[008 0000000000 0000000000 0000000000 1111111111 1>111&;119 1141111.11 1'6+1K1111 0000000050 0S0*\00M00 01[000X0&0 000K00B000 1111113111 111/1#1111 N1111111F1 /E00P0000X 000.00:000 0040V30@00 0000000000 W00000000V 11<1R11111 1111111111 1111111111

Output

204

Trap Test

Input

12 1111111111 1111111111 1111111111 1111111111 1111111111 1111111111 1111111111 1111111111 1111111111 1111111111 1111111111 1111111111

Output

Validator 7 Validator

Input

16 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000

Output

Solution language

Solution

Stub generator input

Comments

13 Comments

CodinBot Unnamed CodinGamer

almost 4 years ago

This contribution hasn’t received enough positive votes from the community. The "REVERSE" option has therefore been deactivated.

Deltaspace Unnamed CodinGamer

about 4 years ago

✅ Approved the contribution. Comment: it's very cool

PoowisChatsakunpen Unnamed CodinGamer

✅ Approved the contribution. Comment: The code is very straightforward once you figured out the trick

Niako Unnamed CodinGamer

✅ Approved the contribution. Comment: Looks good to me.

Edited to improve a few formatting details. In my opinion you need at least 2 more cases such as the 3rd one to make it reasonable for reverse mode (because obviously the 4th case is too large to help, and this case should also probably be moved to the very end to avoid some painful scrolling in reverse mode). The 4th consideration (about rounding) could also be removed as it's useless and even confusing considering the statement previously explicitly mentions that you're expected to "count the number of transitions".

XorZy Unnamed CodinGamer

I have updated the contribution, thank you for your feedback

Bruhhuhr Unnamed CodinGamer

over 4 years ago

Cool clash! I have some suggestions, to trim down the instructions leave out the first two "considerations" since they are to be expected. They other two could be combined with the "To compute..." line. To get a better feeling for the clash I tried to get a shortest in ruby: l=c=-1;gets.to_i.times{x=gets.count(?0)/6;c+=1if x!=l;l=x};p c Also, dandy name :)

Hey CodinGamer! Your contribution has unfortunately not been moderated on time and will temporarily be removed from the system... But no worries! You can republish it anytime to give it another chance! :)

float Unnamed CodinGamer

I really like this. I agree with Raimon that the problem statement is a bit too long, so try reducing it. The important part seems to be that there's "less errors than valid characters". Definitely emphasize that, since that's a super key part of the algorithm (figuring out if there's a state change between the last line to the current). +1 Definitely has potential! edit: here's python solution: n = int(input()) lastState = False stateChanges = 0 for i in range(n): line = input() isFast = line.count('1') > line.count('0') if i == 0: lastState = isFast elif lastState != isFast: stateChanges += 1 lastState = isFast print(stateChanges)

Shurixe Unnamed CodinGamer

You don't need the if statement if stateChanges starts at -1

Raimon Unnamed CodinGamer

I like the idea, though i think for CoC this would be well served by reducing the size of the instructions.

[CG]Recher Unnamed CodinGamer

Cool. You should add specific test about the "dendro-errors", to catch people who would not handle these errors correctly. Put it to the limit, with 6 ones and 4 zeros, or 6 zeros and 4 ones. For example: "0110101110" must be considered as a ring with ones. But if you only check the first and/or the last character, you miss it. "0000111111" and "0000001111" may also be interesting to test.

Thank your for your feedback! Actually the "very old tree" test case was generated randomly but within the limits specified in the statement. Therefore it includes lines such as : N(1111Q311 WS111111.U E11111+1UJ 400+[0000A 011Z111;11 On so on But I reckon I could add a simpler test first to better demonstrate the idea