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{SECT 0 {EXCHG {PARA 18 "" 0 "" {TEXT -1 19 "Epreuve de l'X 2002" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "restart;with(plots):" }}
{PARA 7 "" 1 "" {TEXT -1 50 "Warning, the name changecoords has been r
edefined\n" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 37 "n:=10: a:=[se
q(rand(10)(), k=1..10)];" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"aG7,\"
\"\"\"\"!\"\"(\"\"$\"\"'\"\")\"\"&F+F&\"\"*" }}}{EXCHG {PARA 0 "> " 0 
"" {MPLTEXT 1 0 169 "amplitude:=proc(a::list)\nlocal mi, ma, k;\n  mi:
=a[1]; ma:=a[1];\n  for k from 2 to n do\n    if a[k]<mi then mi:=a[k]
 fi;\n    if a[k]>ma then ma:=a[k] fi\n  od;\nma-mi;\nend:" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "amplitude(a);" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#\"\"*" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 109 "[2
, 1]:\n#l'amplitude est un majorant des gains et des pertes maximaux, \+
\351gale au maximum de ces deux quantit\351s" }}}{EXCHG {PARA 0 "> " 
0 "" {MPLTEXT 1 0 238 "gain:=proc(a::list)\nlocal n, i, j, gm, iopt, j
opt;\n  n:=nops(a);\n  gm:=0; iopt:=1; jopt:=1;\n  for i from 1 to n d
o\n    for j from i to n do\n      if a[j]-a[i]>gm then gm:=a[j]-a[i];
 iopt:=i; jopt:=j; fi\n    od\n  od;\ngm, [iopt, jopt];\nend:" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 259 "gain1:=proc(a::list)\nlocal
 n, i, mi,  gc, gm, iopt, jopt;\n  n:=nops(a);\n  mi:=a[1]; gm:=0; iop
t:=1; jopt:=1;\n  for i from 2 to n do\n    if a[i]<mi then mi:=a[i]; \+
iopt:=i; \n    else if a[i]-mi>gm then gm:=a[i]-mi; jopt:=i fi\n    fi
\n  od;\ngm, [iopt, jopt];\nend:" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 18 "gain(a);\ngain1(a);" }}{PARA 11 "" 1 "" {XPPMATH 20 "
6$\"\"*7$\"\"#\"#5" }}{PARA 11 "" 1 "" {XPPMATH 20 "6$\"\"*7$\"\"#\"#5
" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 277 "gain2:=proc(a::list)\n
local n, i, g1, g2, g, gm, p1, p2;\n  n:=nops(a);\n  gm:=0; p1:=[1,1];
 p2:=[1,1];\n  for i from 2 to n do\n    g1:=gain1(a[1..i]); g2:=gain(
a[i..n]);\n    g:=g1[1]+g2[1];\n    if g>gm then gm:=g; p1:=g1[2]; p2:
=map(x->x+i-1, g2[2]) fi   \n  od;\ngm, [p1, p2];\nend:" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 9 "gain2(a);" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6$\"#;7$7$\"\"#\"\"'7$\"\"*\"#5" }}}{EXCHG {PARA 0 "> " 
0 "" {MPLTEXT 1 0 134 "tps:=op([]):\nfor n from 100 by 5 to 550 do\n  \+
a:=[seq(rand(100)(), k=1..n)]:\n  tps:=tps, [log(n), log(time(gain(a))
)];\nod:\nplot([tps]);" }}{PARA 13 "" 1 "" {GLPLOT2D 878 298 298 
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" {MPLTEXT 1 0 145 "tps1:=op([]):\nfor n from 1000 by 1000 to 60000 do
\n  a:=[seq(rand(100)(), k=1..n)]:\n  tps1:=tps1, [log(n), log(time(ga
in1(a)))];\nod:\nplot([tps1]):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 
1 0 137 "tps2:=op([]):\nfor n from 1 by 5 to 151 do\n  a:=[seq(rand(10
0)(), k=1..n)]:\n  tps2:=tps2, [log(n), log(time(gain2(a)))];\nod:\npl
ot([tps2]):" }}}}{MARK "2 0 0" 7 }{VIEWOPTS 1 1 0 1 1 1803 1 1 1 1 }
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