ASCAN

ASCAN(a,[d])
a
array
[d]
direction argument ; 0 or omitted scan by array, -1 by rows, 1 by clms

Array SCAN, 3 in 1 function, SCAN by row, by column, by array

Xlambda

Well-known Member
Joined
Mar 8, 2021
Messages
832
Office Version
  1. 365
Platform
  1. Windows
ASCAN, Array SCAN, 3 in 1 function, SCAN by row, by column, by array. This is my take of tboulden's SCANBYROW/BYCOL.
Uses only new!! SCAN lambda helper function, no need of byrow,bycol,makearray, or lambda as arguments.
Excel Formula:
=LAMBDA(a,[d],
    LET(y,IF(d=1,TRANSPOSE(a),a),s,SCAN(0,y,LAMBDA(v,a,v+a)),r,ROWS(s),c,COLUMNS(s),sr,SEQUENCE(r)-1,
       x,s-IF(d,IFERROR(INDEX(INDEX(s,,c),sr)*sr^0,0),0),
       IF(d=1,TRANSPOSE(x),x)
   )
)
LAMBDA 1.1.3.xlsx
ABCDEFGHIJKLMNOPQRST
1d,omitted (by array)d,-1 (by rows)d,1 (by clms)
2sample 1a=ASCAN(A3:D6)=ASCAN(A3:D6,-1)=ASCAN(A3:D6,1)
3123413610136101234
45678152128365111826681012
5910111245556678919304215182124
613141516911051201361327425828323640
7
8d,omitted (by array)d,-1 (by rows)d,1 (by clms)
9sample 2a=ASCAN(A10#)=ASCAN(A10#,-1)=ASCAN(A10#,1)
10123413610136101234
115678152128365111826681012
12910111245556678919304215182124
1313141516911051201361327425828323640
14171819201531711902101735547445505560
15212223242312532763002143669066727884
16
17Note: Did not set an extra argument for any kind of "initial value", since the only thing it does is too simple,
18adds a constant value to the final outcome , like in 10+ASCAN(a)
19
ASCAN post
Cell Formulas
RangeFormula
F2,P9,K9,F9,P2,K2F2=FORMULATEXT(F3)
F3:I6F3=ASCAN(A3:D6)
K3:N6K3=ASCAN(A3:D6,-1)
P3:S6P3=ASCAN(A3:D6,1)
A10:D15A10=SEQUENCE(6,4)
F10:I15F10=ASCAN(A10#)
K10:N15K10=ASCAN(A10#,-1)
P10:S15P10=ASCAN(A10#,1)
Dynamic array formulas.
 
Upvote 0
Extra challenge: Extract only dups and nr. of dups for each row.
EMT1793.xlsx
ABCDEFGHIJKLMNOP
1
2Data1Data2Data3Data4Data5Data6Data7Data8Data9
36014913228197092922,92
423883514931643886 
5FredChinChantelMikiChantelJenoTyroneTyroneLim2,Chantel2,Tyrone
6FredChinChantelMikiDinoJenoBiggyTyroneLim 
7QuadQuadMBCarlotaQuadSunshineAspenCarlotaYanaki3,Quad2,Carlota
8QadCarlotaSunshineAspenYanakiSunsetSunspotBellenMB 
919637022529458441 
10518852184175138047 
11298570178132848398 
12801226508862271525 
13276266593897138457 
14244340298721992619 
1595372490101434712,1
169011657820336549972,65
171324462923383873712,38
1873976191293741123 
199927195853162448 
207662282146627322142,62
218741411670747669712,41
229550692593502850393,50
231190631720934886902,90
2492533219721514367 
25
26Formulas range L3:L24, a formula for each row
27=LET(x,B3:J3,u,UNIQUE(FILTER(x,ISNA(XMATCH(x,UNIQUE(x,1,1))),""),1),m,MAP(u,LAMBDA(y,SUM(--(y=x)))),IF(m,m&","&u,""))
28
1793 (3)
Cell Formulas
RangeFormula
L3:L4,L6,L8:L24,L7:M7,L5:M5L3=LET(x,B3:J3,u,UNIQUE(FILTER(x,ISNA(XMATCH(x,UNIQUE(x,1,1))),""),1),m,MAP(u,LAMBDA(y,SUM(--(y=x)))),IF(m,m&","&u,""))
B27B27=FORMULATEXT(L3)
Cells with Conditional Formatting
CellConditionCell FormatStop If True
B3:J24Expression=COUNTIFS($B3:$J3,B3)>1textNO
 
If we can write a formula for each row, no matter how complex it looks, we can use the same construction as the lambda helper part in SPILLBYROWS => a single cell formula that spills.
EMT1793.xlsx
ABCDEFGHIJKLMNOPQRS
1
2Data1Data2Data3Data4Data5Data6Data7Data8Data9
36014913228197092922,92
423883514931643886
5FredChinChantelMikiChantelJenoTyroneTyroneLim2,Chantel2,Tyrone
6FredChinChantelMikiDinoJenoBiggyTyroneLim
7QuadQuadMBCarlotaQuadSunshineAspenCarlotaYanaki3,Quad2,Carlota
8QadCarlotaSunshineAspenYanakiSunsetSunspotBellenMB
919637022529458441
10518852184175138047
11298570178132848398
12801226508862271525
13276266593897138457
14244340298721992619
1595372490101434712,1
169011657820336549972,65
171324462923383873712,38
1873976191293741123
199927195853162448
207662282146627322142,62
218741411670747669712,41
229550692593502850393,50
231190631720934886902,90
2492533219721514367
25
26Single cell formula L3:
27=SPILLBYROWS(B3:J24,LAMBDA(x,LET(u,UNIQUE(FILTER(x,ISNA(XMATCH(x,UNIQUE(x,1,1))),""),1),m,MAP(u,LAMBDA(y,SUM(--(y=x)))),IF(m,m&","&u,""))))
28
1793 (3)
Cell Formulas
RangeFormula
L3:M24L3=SPILLBYROWS(B3:J24,LAMBDA(x,LET(u,UNIQUE(FILTER(x,ISNA(XMATCH(x,UNIQUE(x,1,1))),""),1),m,MAP(u,LAMBDA(y,SUM(--(y=x)))),IF(m,m&","&u,""))))
B27B27=FORMULATEXT(L3)
Dynamic array formulas.
Cells with Conditional Formatting
CellConditionCell FormatStop If True
B3:J24Expression=COUNTIFS($B3:$J3,B3)>1textNO
 
To do the same things using a construction BYROW(a,LAMBDA(x,MAP(UNIQUE(x,1),LAMBDA(y, .......
Because BYROW cannot spill we have to use TEXTJOIN
EMT1793.xlsx
ABCDEFGHIJKLMNOPQRST
1
2Data1Data2Data3Data4Data5Data6Data7Data8Data9
36014913228197092922,92
423883514931643886
5FredChinChantelMikiChantelJenoTyroneTyroneLim2,Chantel;2,Tyrone
6FredChinChantelMikiDinoJenoBiggyTyroneLim
7QuadQuadMBCarlotaQuadSunshineAspenCarlotaYanaki3,Quad;2,Carlota
8QadCarlotaSunshineAspenYanakiSunsetSunspotBellenMB
919637022529458441
10518852184175138047
11298570178132848398
12801226508862271525
13276266593897138457
14244340298721992619
1595372490101434712,1
169011657820336549972,65
171324462923383873712,38
1873976191293741123
199927195853162448
207662282146627322142,62
218741411670747669712,41
229550692593502850393,50
231190631720934886902,90
2492533219721514367
25
26Single cell formula L3:
27=LET(a,B3:J24,BYROW(a,LAMBDA(x,LET(m,MAP(UNIQUE(x,1),LAMBDA(y,LET(z,SUM(--(y=x)),a,z>1,b,FILTER(z,a,""),c,FILTER(y,a,""),r,b&","&c,r))),TEXTJOIN(";",,FILTER(m,m<>",",""))))))
28
1793 (3)
Cell Formulas
RangeFormula
L3:L24L3=LET(a,B3:J24,BYROW(a,LAMBDA(x,LET(m,MAP(UNIQUE(x,1),LAMBDA(y,LET(z,SUM(--(y=x)),a,z>1,b,FILTER(z,a,""),c,FILTER(y,a,""),r,b&","&c,r))),TEXTJOIN(";",,FILTER(m,m<>",",""))))))
B27B27=FORMULATEXT(L3)
Dynamic array formulas.
Cells with Conditional Formatting
CellConditionCell FormatStop If True
B3:J24Expression=COUNTIFS($B3:$J3,B3)>1textNO
 
Extracting items byrow that appear exactly once, ascending order.
EMT1793.xlsx
ABCDEFGHIJKLMNOPQRSTU
1
2Data1Data2Data3Data4Data5Data6Data7Data8Data9=SPILLBYROWS(B3:J24,LAMBDA(x,SORT(UNIQUE(x,1,1),,,1)))
360149132281970929214192832607091
42388351493164388612331353849648688
5FredChinChantelMikiChantelJenoTyroneTyroneLimChinFredJenoLimMiki
6FredChinChantelMikiDinoJenoBiggyTyroneLimBiggyChantelChinDinoFredJenoLimMikiTyrone
7QuadQuadMBCarlotaQuadSunshineAspenCarlotaYanakiAspenMBSunshineYanaki
8QadCarlotaSunshineAspenYanakiSunsetSunspotBellenMBAspenBellenCarlotaMBQadSunsetSunshineSunspotYanaki
91963702252945844151922294145637084
10518852184175138047131841475152758088
11298570178132848398172932708183848598
12801226508862271525121525262750628088
13276266593897138457132738575962668497
14244340298721992619192124262940438799
15953724901014347110243743479095
1690116578203365499711203349789097
1713244629233838737113232429467173
187397619129374112331123296173749197
1999271958531624482624314871859599
2076622821466273221414212228467376
2187414116707476697116697071747687
22955069259350285039252839699395
2311906317209348869011172048638693
249253321972151436731415193253677292
25
1793 (3)
Cell Formulas
RangeFormula
L2L2=FORMULATEXT(L3)
L3:T24L3=SPILLBYROWS(B3:J24,LAMBDA(x,SORT(UNIQUE(x,1,1),,,1)))
Dynamic array formulas.
Cells with Conditional Formatting
CellConditionCell FormatStop If True
B3:J25Expression=COUNTIFS($B3:$J3,B3)>1textNO
 
Another formula that extracts unique byrow and spills, not as elegant and not good for large arrays because textjoin in limited in chars joining, but works:
EMT1793.xlsx
ABCDEFGHIJKLMNOPQRSTUVWXYZAAAB
1
2Data1Data2Data3Data4Data5Data6Data7Data8Data9=IFNA(TEXTSPLIT(TEXTJOIN(";",,BYROW(B3:J24,LAMBDA(x,TEXTJOIN(",",,SORT(UNIQUE(x,1),,,1))))),",",";"),"")
36014913228197092921419283260709192
42388351493164388612331353849648688
5FredChinChantelMikiChantelJenoTyroneTyroneLimChantelChinFredJenoLimMikiTyrone
6FredChinChantelMikiDinoJenoBiggyTyroneLimBiggyChantelChinDinoFredJenoLimMikiTyrone
7QuadQuadMBCarlotaQuadSunshineAspenCarlotaYanakiAspenCarlotaMBQuadSunshineYanaki
8QadCarlotaSunshineAspenYanakiSunsetSunspotBellenMBAspenBellenCarlotaMBQadSunsetSunshineSunspotYanaki
91963702252945844151922294145637084
10518852184175138047131841475152758088
11298570178132848398172932708183848598
12801226508862271525121525262750628088
13276266593897138457132738575962668497
14244340298721992619192124262940438799
159537249010143471110243743479095
169011657820336549971120334965789097
171324462923383873711323242938467173
187397619129374112331123296173749197
1999271958531624482624314871859599
207662282146627322141421222846627376
218741411670747669711641697071747687
2295506925935028503925283950699395
231190631720934886901117204863869093
249253321972151436731415193253677292
25
1793 (4)
Cell Formulas
RangeFormula
L2L2=FORMULATEXT(L3)
L3:T24L3=IFNA(TEXTSPLIT(TEXTJOIN(";",,BYROW(B3:J24,LAMBDA(x,TEXTJOIN(",",,SORT(UNIQUE(x,1),,,1))))),",",";"),"")
Dynamic array formulas.
Cells with Conditional Formatting
CellConditionCell FormatStop If True
B3:J25Expression=COUNTIFS($B3:$J3,B3)>1textNO
 
To overcome the limitation of textjoining the whole array in a single cell we can use ATEXTSPLIT, a function that splits each row "analogical"
EMT1793.xlsx
ABCDEFGHIJKLMNOPQRSTUVWX
1step 1step 2
2Data1Data2Data3Data4Data5Data6Data7Data8Data9=BYROW(B3:J24,LAMBDA(x,TEXTJOIN(",",,SORT(UNIQUE(x,1),,,1))))=ATEXTSPLIT(L3#,",")
360149132281970929214,19,28,32,60,70,91,921419283260709192
4238835149316438861,23,31,35,38,49,64,86,8812331353849648688
5FredChinChantelMikiChantelJenoTyroneTyroneLimChantel,Chin,Fred,Jeno,Lim,Miki,TyroneChantelChinFredJenoLimMikiTyrone
6FredChinChantelMikiDinoJenoBiggyTyroneLimBiggy,Chantel,Chin,Dino,Fred,Jeno,Lim,Miki,TyroneBiggyChantelChinDinoFredJenoLimMikiTyrone
7QuadQuadMBCarlotaQuadSunshineAspenCarlotaYanakiAspen,Carlota,MB,Quad,Sunshine,YanakiAspenCarlotaMBQuadSunshineYanaki
8QadCarlotaSunshineAspenYanakiSunsetSunspotBellenMBAspen,Bellen,Carlota,MB,Qad,Sunset,Sunshine,Sunspot,YanakiAspenBellenCarlotaMBQadSunsetSunshineSunspotYanaki
9196370225294584415,19,22,29,41,45,63,70,8451922294145637084
1051885218417513804713,18,41,47,51,52,75,80,88131841475152758088
1129857017813284839817,29,32,70,81,83,84,85,98172932708183848598
1280122650886227152512,15,25,26,27,50,62,80,88121525262750628088
1327626659389713845713,27,38,57,59,62,66,84,97132738575962668497
1424434029872199261919,21,24,26,29,40,43,87,99192124262940438799
1595372490101434711,10,24,37,43,47,90,95110243743479095
1690116578203365499711,20,33,49,65,78,90,971120334965789097
1713244629233838737113,23,24,29,38,46,71,731323242938467173
18739761912937411233,11,23,29,61,73,74,91,9731123296173749197
1999271958531624482,6,24,31,48,71,85,95,992624314871859599
2076622821466273221414,21,22,28,46,62,73,761421222846627376
2187414116707476697116,41,69,70,71,74,76,871641697071747687
2295506925935028503925,28,39,50,69,93,9525283950699395
2311906317209348869011,17,20,48,63,86,90,931117204863869093
24925332197215143673,14,15,19,32,53,67,72,9231415193253677292
25
26Extracting unique byrow ascending orderExtracting unique that appear only once, byrow, ascending order
27single cellsingle cell
28=ATEXTSPLIT(BYROW(B3:J24,LAMBDA(x,TEXTJOIN(",",,SORT(UNIQUE(x,1),,,1)))),",")=ATEXTSPLIT(BYROW(B3:J24,LAMBDA(x,TEXTJOIN(",",,SORT(UNIQUE(x,1,1),,,1)))),",")
29141928326070919214192832607091
301233135384964868812331353849648688
31ChantelChinFredJenoLimMikiTyroneChinFredJenoLimMiki
32BiggyChantelChinDinoFredJenoLimMikiTyroneBiggyChantelChinDinoFredJenoLimMikiTyrone
33AspenCarlotaMBQuadSunshineYanakiAspenMBSunshineYanaki
34AspenBellenCarlotaMBQadSunsetSunshineSunspotYanakiAspenBellenCarlotaMBQadSunsetSunshineSunspotYanaki
355192229414563708451922294145637084
36131841475152758088131841475152758088
37172932708183848598172932708183848598
38121525262750628088121525262750628088
39132738575962668497132738575962668497
40192124262940438799192124262940438799
4111024374347909510243743479095
42112033496578909711203349789097
43132324293846717313232429467173
443112329617374919731123296173749197
4526243148718595992624314871859599
46142122284662737614212228467376
47164169707174768716697071747687
4825283950699395252839699395
49111720486386909311172048638693
503141519325367729231415193253677292
51
1793 (5)
Cell Formulas
RangeFormula
L2,N2,N28,B28L2=FORMULATEXT(L3)
L3:L24L3=BYROW(B3:J24,LAMBDA(x,TEXTJOIN(",",,SORT(UNIQUE(x,1),,,1))))
N3:V24N3=ATEXTSPLIT(L3#,",")
B29:J50B29=ATEXTSPLIT(BYROW(B3:J24,LAMBDA(x,TEXTJOIN(",",,SORT(UNIQUE(x,1),,,1)))),",")
N29:V50N29=ATEXTSPLIT(BYROW(B3:J24,LAMBDA(x,TEXTJOIN(",",,SORT(UNIQUE(x,1,1),,,1)))),",")
Dynamic array formulas.
Cells with Conditional Formatting
CellConditionCell FormatStop If True
B3:J25,B26,I26:J26Expression=COUNTIFS($B3:$J3,B3)>1textNO
 
Cool example to share.
Mike asked me on the comments section of his latest YT:
"a formula that will enact a running sub-count for consecutive numbers. I have a none spill formula like this:

G10 contains: 2
and I use this formula in Column H starting in cell H10: =IF(G10=G9,H9+1,1) to get: 1
G11 contains: 1
and I use this formula in Column H starting in cell H10: =IF(G11=G10,H10+1,1) to get: 1
G12 contains: 3
and I use this formula in Column H starting in cell H10: =IF(G12=G11,H11+1,1) to get: 1
G13 contains: 1
and I use this formula in Column H starting in cell H10: =IF(G13=G12,H12+1,1) to get: 1
G14 contains: 3
and I use this formula in Column H starting in cell H10: =IF(G14=G13,H13+1,1) to get: 1
G15 contains: 3
and I use this formula in Column H starting in cell H10: =IF(G15=G14,H14+1,1) to get: 2
G16 contains: 2
and I use this formula in Column H starting in cell H10: =IF(G16=G15,H15+1,1) to get: 1
G17 contains: 2
and I use this formula in Column H starting in cell H10: =IF(G17=G16,H16+1,1) to get: 2 "


Since it will be a SCAN/REDUCE lambda formula scenario like so many other examples here, belongs to this thread.
1 on 1 as requested:
Cell Formulas
RangeFormula
H10:H17H10=IF(G10=G9,H9+1,1)
I10:I17I10=FORMULATEXT(H10)
H20H20=FORMULATEXT(H21)
H21:H28H21=LET(a,G10:G17,SCAN(1,SEQUENCE(ROWS(a)),LAMBDA(v,i,IF(i=1,v,IF(INDEX(a,i-1)=INDEX(a,i),v+1,1)))))
Dynamic array formulas.
 
Happy New Year 2023 All !! ✌️🎆🥳
Last post 2022, inspired by a question on YT comment section. latest Mike's YT. Excel LAMBDA function – Every Single Things You Ever Wanted To Know - 365 MECS 10
Running totals for 2 columns array.
Lambda formulas, 3 scenarios:
Book1
ABCDEFGHIJKLMNOP
1Running totals double column array
2
3sales 1sales 2=LET(a,B4:C10,r,REDUCE(0,SEQUENCE(ROWS(a)),LAMBDA(v,i,VSTACK(v,INDEX(v,i)+INDEX(a,i)))),DROP(r,1))
41204512045
52302335068
643083780151
7520451300196
8712892012285
9439562451341
10492372943378
11
12Running totals single column , 2 values joined
13
14=LET(a,C15#,r,REDUCE(0,SEQUENCE(ROWS(a)),LAMBDA(v,i,VSTACK(v,INDEX(v,i,)+TEXTSPLIT(INDEX(a,i,1),",")))),DROP(r,1))
15120,4512045
16230,2335068
17430,83780151
18520,451300196
19712,892012285
20439,562451341
21492,372943378
22
23Running totals, cumulative 2 clms
24
25=SCAN(0,B4:C10,LAMBDA(v,i,v+i))
26120165
27395418
28848931
2914511496
3022082297
3127362792
3232843321
33
Sheet1
Cell Formulas
RangeFormula
E3,E25,E14E3=FORMULATEXT(E4)
E4:F10E4=LET(a,B4:C10,r,REDUCE(0,SEQUENCE(ROWS(a)),LAMBDA(v,i,VSTACK(v,INDEX(v,i)+INDEX(a,i)))),DROP(r,1))
C15:C21C15=B4:B10&","&C4:C10
E15:F21E15=LET(a,C15#,r,REDUCE(0,SEQUENCE(ROWS(a)),LAMBDA(v,i,VSTACK(v,INDEX(v,i,)+TEXTSPLIT(INDEX(a,i,1),",")))),DROP(r,1))
E26:F32E26=SCAN(0,B4:C10,LAMBDA(v,i,v+i))
Dynamic array formulas.
 
...one year later..first post 2023
When comes to running totals for multiple columns we have 3 ways,3 different techniques/concepts
- main function of this thread ASCAN
- adding row by row
- scanning column by column
last post 2022 ASCAN.xlsx
ABCDEFGHIJKLMNOPQRSTUVWX
1defined function, any scenario, very eficient
2=RANDARRAY(10,10,10,99,1)=ASCAN(B3#,1)
37050935852594727726370509358525947277263
42535948335411435141895851871418710061628681
577918271825668871887172176269212169156129149104168
663374381809828605526235213312293249254157209159194
717727790992621879849252285389383348280178296257243
862824718453375875858314367436401393313253383315301
999306911267646544454413397505412419389299437359355
1019435436171962774261432440559448436408361514401416
1166901683185421255979498530575531454462382539460495
1211994398416622766017509629618629495528404615520512
13
14
15lambda formula when nr of columns way larger than the number of rows
16=LET(a,B3#,r,REDUCE(0,SEQUENCE(ROWS(a)),LAMBDA(v,i,VSTACK(v,INDEX(v,i)+INDEX(a,i)))),DROP(r,1))
1770509358525947277263
1895851871418710061628681
19172176269212169156129149104168
20235213312293249254157209159194
21252285389383348280178296257243
22314367436401393313253383315301
23413397505412419389299437359355
24432440559448436408361514401416
25498530575531454462382539460495
26509629618629495528404615520512
27
28lambda formula when nr. of rows way larger than nr. of columns
29=LET(a,B3#,LET(s,LAMBDA(x,SCAN(0,x,LAMBDA(v,i,v+i))),r,REDUCE(0,SEQUENCE(COLUMNS(a)),LAMBDA(v,i,HSTACK(v,s(INDEX(a,,i))))),DROP(r,,1)))
3070509358525947277263
3195851871418710061628681
32172176269212169156129149104168
33235213312293249254157209159194
34252285389383348280178296257243
35314367436401393313253383315301
36413397505412419389299437359355
37432440559448436408361514401416
38498530575531454462382539460495
39509629618629495528404615520512
40
Sheet2
Cell Formulas
RangeFormula
B2,M2B2=FORMULATEXT(B3)
B3:K12B3=RANDARRAY(10,10,10,99,1)
M3:V12M3=ASCAN(B3#,1)
J16J16=FORMULATEXT(M17)
M17:V26M17=LET(a,B3#,r,REDUCE(0,SEQUENCE(ROWS(a)),LAMBDA(v,i,VSTACK(v,INDEX(v,i)+INDEX(a,i)))),DROP(r,1))
D29D29=FORMULATEXT(M30)
M30:V39M30=LET(a,B3#,LET(s,LAMBDA(x,SCAN(0,x,LAMBDA(v,i,v+i))),r,REDUCE(0,SEQUENCE(COLUMNS(a)),LAMBDA(v,i,HSTACK(v,s(INDEX(a,,i))))),DROP(r,,1)))
Dynamic array formulas.
 
Hi Xlambda,

regarding to Running totals for 2 columns array,I tried to do with the function TAKE, I think you can develop this without the need for recursion.
=MAP(TAKE(B4:C10,SEQUENCE(7,,1,1)),LAMBDA(x,SUM(INDEX(x,,1))))

TAKE(B4:C10,SEQUENCE(7,,1,1)) ,
Creates the cumulative amount.

David
 

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