bài tập bài toán chiếc túi xách

Bd6c 5: Cii det chddng trinh Program XauChung; uses crt; Var L:Array[0..

a Ph5t bidu bdi to5n:

Bii tQp 1: Bii toSn chi€'c triix5ch G\/

MOt c6i kho chfa n loai d6 v6t c6 kich thr/6c vd gi5 tri khiSc nhau Cu thd: Loai db vgt i

(i=1 n) c6:

- Kich cd m[i] e N.

- Gi5 tri c[i] e R

- Sd lrtOng: khdng han ch6

M6t t6n tr6m mang theo chi6c t[i c6 kich cd ld p e Nx V6y h6n ph6i chon lda mdt danh siich

ciic db vdt s6 mang di nhd th6 nio dd cho tdng gi5 tri t6y c5p dddc ti t6n nhdt

Tfc: Tim x[1], x[2],,,,, x[n] (vdi x[i] e N : sd lLtdng loai db v6t thf icen ldy) sao cho: ,;

Ix[i].mlil < p ve lx[i].c[i] dat gi5 tri ctrc dai

x Input: + n ld sd d6 v6t, kich thd6c cdc db khSc nhau.

Vdi m[i] e N' , c[i] e R

+ p lA cd trii

x Output: Tim (X[1], X[2] X[n]) (X[i ] :sdtoaidbv6t i, i=1 n)

5ao cno:

tI'*t,i.t,t-+ max

n

r' Vidt1: n = 5 ; p = 10, dtJdccho

x K€t guir: + Sd db virt 5, kich thd6c 1"0

+ Tdng gi5 tri nh6p dr/dc vdo t(i xSch: B

+ Sd lrrOng ldy theo th[r tlr nhd sau: 0 0 1 1 0

b Ph6n tich bii to6n:

Brl6c 1: Ph6n tich bii toSn:

Goi P(r, s) li bdi todn chi6c tfi x6ch, vdi:

r e Nx: kich cd chi6c t[i

s e N*: s6 c5c loai d6 v6t khdc nhau (bdi todn ban d6u td p(p, n))

C5c gi5 tri cEn tim:

t[r,s]: gi5 tricdc dai Ixlil,c[i] cia bditoSn p(r, s)

[r,s]:_s6 h/dng loaidb v6t s t6i uu c6n l6'y (tr?c: x[s]) ctia bditodn p(r, s)

Brfdc 2: ciii phSp ct€ quy:

Khis=1:

u[r, 1] = r div m[1]

Ilr, 1l = u[r, 1]*c[1]

Khis>1:

l[r, s] = max { k*c[s] + lfr - kxmfs], s-11 ]

0<k<rdivm[s]

= koxclsl + lfr - h*mls], s-11

ufr, s] = ks

Brldc 3: LQp bing

Procedure LapBang;

Begin

For s:=1 to n do

For r:=0 to p do

If s=1 then Tinh u[r, 1] vir l[r, 1]

else Tfnh u[r, s] vd l[r, s];

End;

Vi du

R

x x€'t qui: + Sd d6 vat s, kicfr thrrdc to

+ Tdng gi6 tr! nh6p dUdc vdo tfixiich: B

+ Sd luOng ldy theo thf/ tLr nhut sau: 0 0 1 1 0

D0 phrirc tap tinh to6n: O(np2)

BrJ6c 4: Tdng hqrp k€t qui

Procedure TongHop;

Begin

r: =pi

For s:=n downto 1 do

Begin

x[s]:= u[r,s];

r:= r - x[s],mfsl;

End;

End;

E6 phr?c t?e tinh to6n: O(n)

BrJ6c 5: Cei dit chddng trinh

Program TuiXach;

Uses crt;

Var n,p:word;

x,m:arrayf1., 10] of word;

c:arrayf1 10] of real;

l:array[0 10,1 10] of real;

u:array[0 10,1 10] of word;

Procedure NhapDL;

Var i:byte;f:text;

Begin

assign(f,'tuixach.inp'); reset(f);

read(f,n); readln(f,p);

End;

Procedure Lapbang;

Var r,s,k,k1 :word; max,tam : real;

Begin

for s:=1 to n do

for r:=0 to p do

if s=1 then Begin

u[r,1]:= r div m[1];

l[r,1]:=uIr,1]*cl1];

End else Begin k1: =0;

max:= 0;

for k:=0 to r div m[s] do Begin

for i:=1 to n do read(f,mlil);

for i:=1 to n do read(f,c[i]);

writeln('So vat ',n,', kich thuoc

lieu trong file tuixach.inp');

close(f);

tui 'rp,', du

Tam : = kxclsl +lIr-kxm[s],s-11;

if tam>max then

Begin

Max:=tam; k1:=k;

end;

end;

lIr,s]:=max;

u[r,s]:=k1;

End;

End;

Procedure tonghop;

Var r,s:word;f:text;

Begin

assig n(f,'tuixach.out');

rewrite(f);

r:=pj

for s:= n downto 1 do

Begin

xlsl: =uIr,s];

r:=r-x[s]xm[s];

End;

End;

Procedure Inkq;

Var s:word; f:text;

Begin

assig n(f,'tu ixach.out' );

rewrite(f);

writein('Tong gia tri nhan duoc rrao tui xach

la: ',1[p,n]:4:1);

write('So luong lay theo thu tu nhu sau: ');

for s:=1 to n do

Begin

write(f,xIs]:3);

write(x[s]:3);

End;

writeln;

close(f);

End;

Procedure Inbang;

Var srr:word;

Begin

writeln;

for s:=1 to n do write(s:S,' ');

writeln;

for r:=0 to p do Begin

write(r);

for s:=1 to n do Begin

write(lIr,s] : 3 : 0,'\', u Ir,s],");

End;

writeln;

end;

End;

t - -)

BEGIN Clrscr;

NhapDL;

Lapbang;

Tonghop;

inbang;

Inkq;

Readln;

END.

{ - -}

BiitQp 2: ph6p nhAn td hdp nhi€u ma trQn (O", )

\J

a PhSt bidu bii to6n

CEn tinh M = M1xM2x ,xMn

Trong d6: M, Id ma tr6n c5'p m[i-1]xm[i] (i=1 n)

H5y xdc dinh thf tUthr/c hi6n cdc ph6p nh6n sao cho s6 ph6p tinh Ie t6ithidu

x Input: + C6'p cr]al ma tr6n

Vdi m[i] e N

x Output: X5c dinh thf td tinh: sd ph6p tinh > min

xVidg:TinhM= M1 * MZ " M3

| 10x201[20xs0] [s0xs]

(MrxM2)xM, c6 sd ph6p todn td:

10x20x50 + 10x50x5 = 12500 M1x(M2xM3 ) c6 sd ph6p todn ld:

10x20x5+20x50x5=6000

x K€'t qui: M1 x M2 x M, c6 sd ph6p todn lir: 6000

b PhAn tich bii to6n:

Bddc 1: Ph6n tich bii toin:

Goi P(r, s) ld bdi todn nhdn ma tr6n: MrxMr*rx xM' vdi r < s

cua n ma tr

(bai todn ban d6u td p(1, n))

Gi5 tric6n tim:

!lt,r]t vitri ph6p to5n thrrc hi6n cudi cing cia beitodn p(r, s)

(MrxMr*1x xMp-1) x (MpxMp*

1" rM5)

k = k[r,s] e [r+1, s]

[r, s]: sd ph6p tinh nh6n t6i uu cira baitodn p(r, s)

BtI6c 2; ciii ph5p dG quy:

Trr/o'ng hdp 1: Khis = r: l[r, r] = g

Trr/dng hgp.2t KhL5 = p1g.

lt r,Q t\< hf'- r fx m Jf.1 J I q 1

kfqv+11 =-1+1

Trddng hdp 3r Khi s > r<S:

l[r, s] = r+1 min <v<s { l[r, v-1] + m[r-1]*m[v-1]*mlsl + lfv, sl ]

(v lA c5c vi tri ph6p todn thdc hi6n cudi cirng khdc nhau)

= l[r, vL1] + mlr-11 * mlvll] {, m[s] + l[v', s]

(v' ld vi trit6i rru trong sd cdc vi tri cira v) k[r, s] = Y'

Nh6n X_6t: C6 thd gh6p trddng hdp 2 vAo trddng hdp 3l

Brfdc 3: Lflp bing

Procedure LapBang;

Begin

For s:=1 to n do

For r:=s downto 1 do

If r = s then lfr, r] := 0 End; else Tinh l[r' s] vi k[r' s];

Vi^!U: Tr/ vi du tr6n ta l6p dddc bing sau

56 ph6p to6n tdi thidu td: 6000

Thf t{thrJc hi6n ph6p nh6n: 3 2

r

D6 phr?c t?p tinh to6n: O(n3)

Brf6c 4: Tdng hep k6t quJ

Procedure TongHop;

Begin

writetn('Sd ph6p tinh le t6i thidu:,, l[1, n]);

i:=r'ti

1-imW(1, n); {NhEm lEn [fdt xiic dinh cdc gi5 tri x[i]: vi tri ph6p nhSn cEn thuc hi6n trong tEn

nh6n thf i(i=1 n-1))

writeln('Thr? t{ thttc hi6n cdc ph6p nh6n :,);

For i:=1 to n-1 do writeln(xfil);

End;

Trong d6 th[r tuc TimW dr/dc x6y dqfng d9 quy nhf sau:

Procedure TimW(r, s);

Begin

If (r < s) then

Begin

i:=i-1;

vt:= k[r, s];

xlil:= vt;

TimW(r, vt-1);

TimW(vt, s);

End;

End;

Bddc5: CAi d{t chtldng trinh

Program Matran;

Uses Crt;

Var n:word;

m :array[0 20] of word;

x:arrayf1 20] of word;

k,l :arrayf1 20,1 20] of integer;

{ -}

Procedure NhapDl;

Var i:byte;f:text;

Begin

assign(f,'matran, inp'); reset(f);

readln(f,n);

for i:=0 to n do

Begin

read(f,mIi]);

write(mIi]:3);

End;

writeln;

close(f);

End;

{ -}

Procedure Lapbang;

Var r,srvrvmax:word;

Begin

for s:=1 to n do

for r:=s downto l" do

if s=r then

Begin

lIr,r]:=0;

klr,rl:=r;

End

else

Begin

VmaX:=f + 1;

l[r,s]:=l[r,r]+mIr-llxmIr]xm[s] +lIr+ 1,s];

for v:=r+2 to s do

if

l[r,s]>l[r,v-1]+m[r-1]xm[v-llxm[s]+l[v,s] then

Begin

VMaX:=V;

llr,sl : = lIr,v- 1] +mIr-1]

xmlv-llxm[s]+l[v,s];

End;

k[r,s]:=vmax;

End;

End;

{ -}

Proced ure timvt( r,s :word) ;

Var vt,i:word;

Begin

if r<s then

Begin

i:=i-1;

vt:=k[r,s];

xlil:=vt;

timvt(r,vt-1);

timvt(vt,s);

End;

End;

t -)

Procedure tonghop;

Var i:word;f:text;

Begin assign(f,'matra n.out'); rewrite(f);

writeln('so phep toan toi thieu la: ',1[1,n]);

writeln(f,'so phep toan toi thieu la: ',1[1,n]);

i:=rtj timvt(1,n);

write('thu tu thuc hien cac phep nhan:'); writeln(f,'thu tu thuc hien cac phep nhan:'); for i:=1 to n-1 do

Begin

write(xIi]:3);

write(f,xIi],' ');

End;

Close(f);

End;

{ - -}

Procedure Inbang;

Begin

for s:=1 to n do write(s:10,' '); -j writeln;

for s:=1 to n do Begin

write(sr' ');

for r:=1 to s do t

Begin

write(lIr,s]:5 ,'f' ,klt,s],' ');

End;

writeln;

end;

End;

BEGIN

Clrscr;

NhapDL;

Lapbang;

Tonghop;

Inbang;

Readln;

END.

Bii tdp 3: Tim x6u trong cdc dai.

a PhSt bidu bii to6nr

Bei toSn x6u t1o1s cr"lc dqi: s ld x6u trong cia T n6u s nh6n dddc bSng cSch xo5 di m6t sd t<f

ttl nAo d6 Vidu: 'ABC, ld x6u trong cria.GAHEBOOC,

Bei todn: cho 2 x6u T1, T2 Tim m6t x6u S ld x6u trong chung cria T1 vd T2 co d6 ddi ct;c dAi,

'-"r -"errJ vev

'r ve

Vi du: TI='ABCDAE'vd T2='XYACADK' c6 x6u 'AcD' le x6u trong chung vdi d6

ddi cdc dai

* Input: X6u T1 vd T2

* output: X6u s li x6u trong chung cira T1 vir T2 c6 d6 dei cdc dai

b PhAn tich bii tof n:

Budc 1: phin tich bii toin:

Goi n lA d6 dei cria x6u T1

m ld d6 ddi c[ra x6u T2

Ta cEn xdc dinh x6u con chung S ddi nh6't c0a 2 x6u T1 vd T2

Gi6 sir L(i,j) c6 d6 dei x5u con chung ldn nh6't crla z x6u T1 c6 d6 dii i vd x6u T2 c6 d6 ddij

(i<=n, j<=m).

Btt6c2= ciii ph6p d6 quy:

+ Ndu i=0 thi L(0,1;:9, Ndu j=g thi L(i,0)=0

+ Ndu i>0 vd j>O va T1;=72-thi L(ij)'= i + L(i_1j_1)

+ N6u i>0 vd j>0 vd T1i<>T2j tni L(i;l = rvaxiLli,j_rj,l1i_r,i;;

Brf6c 3: L6p bing;

Procedure LapBang;

Begin

For i:=1 to n do

L[1,0]; =0;

For j:=1 to m do

L[O,j]: =0;

For i:=1 to n do

For j:=1 to m do

if T1[i] = T2[] then

L[i,j]:= 1 + Lli_1,j_11 else

L[i,j] := maxab(L[i,j_1], L[i_1,j]);

End;

Vi du: cho hai x6u T1='ABCDAE'vd T2-'XyACADK, Tim

x6u con chung c6 d6 dii rdn nh6.t.

BA

I

L * c.D

4

,

G -, \T;

A

TZ

l 1

?=

,&

Kdt qu6 x6u chung ddi nh6't ld: ACD

D0 phr?c tap tinh to5n: O(n.m)

Brl6c 4: Tdng h{p k6t qui:

Procedure Tonghop;

Begin

i:=hi j:=m; S:=";

While (L[i,j]>0) do

Begin

if T1[i]=T2Dlthen

Begin

S:=T2Ul + S;

:._; {,

l,=1;'

End else

if L[i, j]= Lli-1, jl then

i:=i-1

else

j: =j- 1;

End;

Writeln('Xau chung dai nhat:', S);

End;

D6 phfc tap tinh to6n: O(n).

Bd6c 5: Cii det chddng trinh

Program XauChung;

uses crt;

Var

L:Array[0 100,0 100] of Byte;

s1,s2,kq: String;

m,n: Byte;

{ -}

Function maxab(a,b: byte) : byte;

Begin

if a>b then

maxab: =a

else

maxab: =b;

End;

{ -}

Procedure NhapDL;

Var f : Text;

Begin

Assign(f,'xauchung, inp'); Reset(f);

Readln(f, s1);

Readln(f, s2);

m:=Length(s1);

n: =Length(s2);

Close(f);

End;

{ -}

Procedure LapBang;

Var i,j: Byte;

Begin

For i:=1 to n do

lIi,0]:=0;

For j:=1 to m do

ll0,jl:=0;

For i:=1 to m do For j:=1 to n do

if sllil = s2ljl then

L[i,j]:= 1 + L[i-1,j-1]

else

L[i,j]:= maxab(L[i,j-1]

1,il);

End;

{ -}

Procedure Tonghop;

Var

i,j:byte; f:text;

Begin Assi gn(f,'xauchung out' ); Rewrite(f);

i: =mi

j: =n;

kq:="'

While (L[i,j]>0) do Begin

if s1[i]=s2Ulthen

Begin

kq:=s2[] + kq;

i:=i-1;

j:=j-L;

End else

if L[i, j]= L[i, j-1] then

,

else

i:=i-1;

End;

Writeln(f,'s1 - ',s1),

Writeln(f,'s2 = ',s2);

Writeln(f,'Xau chung dai nhat;', kq);

Close(f);

End;

{ -}

Procedure Inkq;

Begin

Writeln('s1 = ',sl)i

Writeln('s2 - ',s2),

Writeln('Xau chung dai nhat:', kq);

End;

t -) i

Procedure Inbang;

var i,j:byte;

writeln(' - LAp BANG -\;

write(");

for j:=1 to m do write(s2[]:4);

writeln;

for i:=1 to n do begin

wrlte(s1[i]);

for j:=1 to m do write(lli,jl:4);

writeln;

end;

End;

{ -}

BEGIN

Clrscr;

NhapDL;

Lapbang;

Tonghop;

Inbang;

Inkq;

Readln;

END.

\

a phSt bidu bii to6n: Bii tQp 5; Bii to5n ngr/di du lich

M6t ngfdi di tt/ thdnh phd 0 ddn thdnh ph6 n vd c6 thd di qua n-l thanh phd kh5c 1, 2,.,.,

n-1, theo 16trinh: 0-+ i1 - i2 _+ i;,-+ n, trong d6: O < t i t ik n,

Gi5 v6 c0a xe ditr/thdnh phd id6n thdnh ph6 j ta cgi,i1.

Tim m6t 16 trinh ttJ thdnh phd 0 d6n thdnh pr'ro n-rul"."r.)o tdng chi phf v€ gi5 v6 dat cdc tidu,

* Input: +:- ld thtinh ph6xudt phdt lrrr vrrr vs vro

+ s li dfch

+ Ma tr6n cli,jl (i,j =0 n) tuu trii chi phf

x output: L6 trinh ngSn nh6't trr thdnh prr6 o o8n tnirnh phd n.

b Ph6n tich bii todn:

Brl6c 1: Ph6n tich bii to6n:

x Goi P(r,s) lA bei todn du lich, vdi:

- r e N: dinh xudt phdt

- s e N: dinh cEn d6n

(bei todn ban dEu: p(0,n))

x C5c gi5 tri c6n tim:

- l[l,s] : chi phi nhd nh6't d6 di ti/ r _> s c0a bei todn p(r,s)

- ufr,sl : dinh k6 cu6i tr6n dL/dng di tf r-> s cira odi toJn p(r,s)

BtI6c2= Giii ph6p d€ qui:

-Khir=s:

l[r's] = 6

u[r,s] = -1 -Khi r + s:

l[r,s] = min(l[r,k] + c[k,s]) = l[r,ko]+c[ko,sJ

(r-<k<s) ulr,s] = ko

Brfdc 3: LAp bing:

Procedure Lapbang;

Begin

Fors:=0tondo

Forr: =0tosdo

Ifr=sThen

Begin

l(r, r): = 0;

u(r, r) = -1'

Else Tinh l(r,s)) vir u(r,s);

End;

Dfdng di tU thenh phd 0 ddn thdnh ph6 4 c6 t6 trinh: 0 >1 >2 >4

Chi phi nh6 nhdt dd di tiJ thdnh phd 0 ddn thdnh ph6 4: 15

D6 phr?c t?p tinh to6n: O(n3)

Brl6c 4: Tdng hdp:

Procedure Tong hop(d,c :word );

Begin

i:=0; x[0]:=c; k:=ci

while k<>d do

Begin

i:=i+1i xlil:=u[d,k];

k:=u[d,k];

End;

End;

D6 phr?c tap tinh to5n: O(n)

Brl6c 5: Cii d{c chr.tdng trinh

Program DuLich;

Uses cft;

Const max=100;

Var n:word;

x:array[0 max] of integer;

c,l,u:array[O max,O max] of integer;

{ - -}

Procedure NhapDL;

Var i,j:byte;f:text;

Begin

assign(f,'C: \d u lich inp'); reset(f);

readln(f,n);

for i:=0 to n do

for j:=0 to n do

read(f,cIi,j]);

close(f);

End;

Procedure Lapbang;

Var r,s,k,k0:word;

Begin

for s:=0 to n do

for r:=0 to s do

if s=r then

Begin

lIr,s]:=0;

u Ir,s]: =- 1;

End else Begin k0: =s-1;

lIr,s] : = lIr,s-1] +c[s- 1,s];

for k:=r to s-1 do

if l[r,s] > l[r,k]+c[k,s] then Begin

k0: = k;

lIr,s] : = lIr,k] +c[k,s];

End;

u[r,s]:=k0;

End;

End;

{ - -}

Procedure tonghop(d,c:word);

Var i,k,j,t:word;f:text;

Begin assig n(f,'C: \dulich.out');

rewrite(f);

i:=0;

s

-1

0

o -1

1

5

1

0 -1

0

7

1

4

2

0 -1

2

8

2

3

2

4

3

o -1

x[0]:=c; k:=c;

while k<>d do

Begin

i:=i+1;

x[i]:=u[d,k];

k: =u[d,k];

End;

writeln(f,'Duong di tu Tp ', d,, den Tp ',c,, chi

nho nhat la:');

for j:=i downto 0 do

Begin

write(f,x[]);

if j>0 then write(f,' >,);

End;

writeln(f);

write(f,'chi phi la: ',1[d,c]);

close(f);

End;

{ - -}

Procedure Inkq;

Var f:text; ch:string;

Begin

Assign(f,'C: \DuLich.Out'); reset(f);

readln(f,ch);write(ch);

readln(f,ch);writeln(ch);

read I n(f,ch);write(ch);

close(f);

End;

{ - -}

Procedure InBang;

Var i,j:Byte;

Begin

phi for i:=0 to n do write(i:g);writeln;

for j:=0 to n do

Begin

write(;':4,' ');

for i;=0 to j do

write(uIi,j],'/,,1[i,j],' ');

writeln;

End;

End;

BEGIN

Clrscr;

NhapDL;

Lapbang;

Tonghop(0,4);

Inbang;

Inkq;

Readln;END.

a phSt bidu bai toSn: Bia tip 5: Bii toSn sinh vi6n 6n thi,

Bei todn sinh vi6n 6n thi: M6t sinh.vi6n cdn

T ngdy dd 6n thi n m6n Theo kinh nghi6m cia anh ta, ndu 6n m6n j trong i ngdy thi drdc oidr'H J1i,;1 cia stJ

cho nia a a[i,j] (vdi

a[i,j] < =a[i+ 1,j])

Tim b6 xUl (sd ngdy 6n m6n j, v6i j=1,.n) sao cho Ix[1=, vd sinh vi€n dat tdng didm idn

nhdt (IalxUl, jl-+max)

x Input: + n ld sd m6n

+ m td s6 ngdy

+ aIij] didm crla 6n thi m6n j trong i ngiry (ali,jl<=a[i+1,j])

x out put: -,, r"J,]rJiT;';f; i'r,=I n) *o *orx[]=, va sinh vi6n dat tdns didm rdn

nhdt (IalxUl, jl-+max),

b Ph6n tich biito5n:

Brldc 1: ph6n tich bii to6n:

x Goi p(r,s) ld bii toiin SV 6n thi r m6n trong s ngEy

(bai to6n ban d6u s6 ld : p(n,m)) "

* Cdc gi5 tri cEn tim lir:

bait"drl[i;rrj.tunn sd didm ldn nh6't mir sinh vi6n c6 thd dat dudc khi 6n thi r m6n trons s ngdy cria _ ufr,gJ : 56 ngdy tdi uu cEn d6 6n m6n r c0a bii todn p(r,s)

Bttdc2: ciii phip dQ qui:

-flrif = 1:l[1,r] =a[s,1], u[1,s] = I

-Khi

i> 1:l[r,s] = max(attit it;r-r,s_t1;

a[h,r] + llr-1, s-ksl

Brf6c 3: L6p bing: u[r's] = ko

Procedure Lapbang;

Begin

for s:=1 to m do

for r:=0 to n do

End;

if (s =.1) then Tinh lf1,sl vd ufl,sl

else Tinh l[r,s] vi u[r,s]

vf du: c6 3 m6n thi 6n trong 5 ngdy vir didm cdc m6n tr/dng r?ng cdc ngdy nhf sau:

K6t qu6 l6p b6ng

Tdng didm ldn nh6't ld: 24.0

E0 phr?c t?p tinh to5n:

Brldc 4: Tdng hfp k6t qui:

Procedure Tonghop;

Begin

f: = ITli

for s:= n downto 1 do

begtn

x[s]:= ulr,s];

r:= r - x[s]i

End;

End;

D6 pht?c tap tinh to6n: O(n)

BrJdc 5: Cii dic chr^fdng trinh:

Program sinhvienonthi;

Uses Cft;

Const max=50;

Var n,m:word;td:real;

x:array[1 max] of word;

a :arrayfO.,max,0 max] of real;

l:array[0 max,0 max] of real;

u :array[0 max,0 max] of word;

{ - -}

Procedure NhapDL;

Var i,j:byte;f:text;

Begin

assign(f,'sinhvien, inp'); reset(f);

read(f,n); readln(f,m);

writeln('So mon ',n,'on trong ',m,' ngay');

writeln('Diem tuong ung on cac mon la:');

for i:=0 to m do

begin

for j:=1 to n do

begin

read(f,aIi,j]);

write(aIi,j]:4:0);

end;

readln(f);

writeln;

end;

close(f);

End;

{ - -}

Procedure Lapbang;

Var r,s,k,k0:word;

Begin

for s:=0 to m do

for r:=1 to n do

if r=1 then Begin

u[1,s]:= s;

l[ 1,s]: =a [s,1];

End else Begin k0: =0; l[r,s] : =l[r-1,s]; for k:=0 to s do

if lIr,s] <lIr-1,s-k]+a[k,r] then Begin

k0: =k;

I Ir,s] : = l[r-l,s-k] +a Ik,r] ; End;

u[r,s]:=k0;

End;

r

o(