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Bi ton ng i ca robot to thnh s nh phn ln nht

Cho mtbng vung m dng, n ct (2

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V d:

Ta c s 1011 (gi tr thp phn l 11)+ Ghp thm s 1 vo s l 10111 (gi tr mi l 23 = 2*11+1)+ Ghp thm s 0 vo s l 10110 (gi tr mi l 22 = 2*11+0)

Ti (i,j) ch c th n t (i-1, j) hoc (i, j-1), gi tr thu cl ln nhtth phi n t c gi tr ln hn,nh vy cng thc truy hi s l:

F[i, j] = 2 * max( F[i, j-1], F[i-1, j] ) + A[i, j]

2. Tnh bng phng n

thun tin ta cn t hng ro: ct 0 v dng 0 ca c A v F u t gi tr -1.Ring A[1, 0] hoc A[0, 1] cn t gi tr 0 bt u tnh th F[1,1] = A[1, 1].

3. Truy vt

Bng th tc quy: Bt u t (m,n), qu trnh truy vt kt thc khi tatruy nn (1,1) v ra gi tr F[m,n], ti mi bc truy vtta s truy vt c gi tr lnhn trong 2 : (m-1,n) v (m,n-1).

Ci t bng ngn ng Pascal:

PROGRAM robot;

VAR A:ARRAY[0..30,0..30] OF BYTE;

F:ARRAY[0..30,0..30] OF LONGINT;

m,n:INTEGER;

PROCEDURE Enter;

VAR i,j:INTEGER;

BEGIN

readln(m,n);

FOR i:=1 TO m DO

BEGINFOR j:=1 TO n DO read(A[i,j]);

readln;

END;

FOR i:=0 TO m DO A[i,0]:=-1;

FOR j:=0 TO n DO A[0,j]:=-1;

END;

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FUNCTION Max(a,b:LONGINT):LONGINT;

BEGIN

IF (a>b) THEN Max:=a ELSE Max:=b;

END;

PROCEDURE Optimize;

VAR i,j:INTEGER;

BEGIN

FOR i:=0 TO m DO F[i,0]:=-1;

FOR j:=0 TO n DO F[0,j]:=-1;

F[0,1]:=0;

FOR i:=1 TO m DO

FOR j:=1 TO n DOF[i,j]:=2*Max(F[i,j-1],F[i-1,j])+A[i,j];

END;

PROCEDURE Trace(i,j:INTEGER);

BEGIN

IF (i=1) AND (j=1) THEN

writeln(F[m,n])

ELSE

BEGIN

IF F[i,j-1]>F[i-1,j] THEN

Trace(i,j-1)

ELSE

Trace(i-1,j);

writeln(i,' ',j);

END;

END;

BEGIN

Assign(Input,'Robot.inp'); Reset(Input);Assign(Output,'Robot.out'); Rewrite(Output);

Enter;

Optimize;

Trace(m,n);

close(Input);

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close(Output);

END.

Ci t bng ngn ng C++

#include

#include

using namespace std;

int F[31][31],A[31][31],m,n;

ofstream fo("robot.out");

ifstream fi("robot.inp");

void Enter()

{

fi>>m>>n;

fi.ignore();

int i,j;

for (i=1; iA[i][j];

fi.ignore();}

for (i=0; i

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F[1][0]=0;

for (i=1; i