Algorithmen und Problemlösungen mit C++ by Doina Logofatu

By Doina Logofatu

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P P"XP P"AP P"]P P"3P P"QP P"NP P""P P"PP ’Ž Š—Š›ȬŽ’—’’˜—œŠŽ’Ž— Ÿ˜—  ǻǀŒ¢™Žǯ‘ǁǼ ž— ƸƸ ǻǀŒŒ¢™ŽǁǼ œŽ••Ž— ž—”’˜Ȭ —Ž— ‹Ž›Ž’ǰ ž– –’ Ž’Œ‘Ž— £ž Š›‹Ž’Ž—ǯ ŽŽ ’ŽœŽ› ž—”’˜—Ž— Ž› Š›Ž Š•œ Š›Š–ŽŽ› ĤĖ ʲàćÀě½ÓšØ Ħ؏ EćàxʚÓÊãĎĦزšØ ÓÀě úú Ž’—Ž— ’—ȬŽ›ǰ Ž› Ž— ŽŽ›  ˜Ž› ž—œ’—Ž Œ‘Š› ’œ ž— •’ŽŽ› Ž’—Ž— ’—ȬŽ› £žȬ ›ûŒ”ǯ Ž‘˜Ž— Šžœ ǀŒ¢™Žǯ‘ǁ ž— ǀŒŒ¢™Žǁ ;AX ;AX ;AX ;AX ;AX Ž‘˜Ž ;R>F9G;AXH ;R[FF-QG;AXH ;R>D^-QG;AXH ;R+;6;XG;AXH ;R_+;6;XG;AXH ŽŽžž— žŒ‘œŠ‹Ž ›˜đ‹žŒ‘œŠ‹Ž ǻŠ‹Ž› ”Ž’— –•ŠžǼ •Ž’—‹žŒ‘œŠ‹Ž ǻŠ‹Ž› ”Ž’— –•Šž ˜Ž› đǼ Ž£’–Š•Ž ’Ž› ‘Ž¡ŠŽ£’–Š•Ž ’Ž› ŽŽ›£Ž’Œ‘Ž—ǰ Ž’Ž—Ÿ˜›œŒ‘ž‹ ǻȧǼǰ Ž’•Ž—›Ž——Ž› ǻȧ—Ǽǰ ŠŽ—›ûŒ”•Šž ǻȧ›Ǽǰ Š‹ž•Š˜›£Ž’Œ‘Ž— ǻȧǼǰ Ž›’”Š•Ȭ Š‹ž•Š˜› ǻȧŸǼ ŽžŽ›£Ž’Œ‘Ž— ǻ Ŗǰ ŗǰ ǯǯǯǰ řŗ ˜Ž› ŗŘŝǼ ’Œ‘‹Š›Žœ Ž’Œ‘Ž—ǰ –’ žœ—Š‘–Ž Ÿ˜— ŽŽ›£Ž’Œ‘Ž—ǰ žŒ‘œŠ‹Ž ˜Ž› ’Ž› Š•™‘Š—ž–Ž›’œŒ‘ ǻ’œŠ•™‘ŠǻǼ ˜Ž› ’œ’’ǻǼǼ ›žŒ”‹Š› ǻœ’Œ‘‹Š›Žœ Ž’Œ‘Ž—ǰ ŠžŒ‘ ŽŽ›£Ž’Œ‘Ž—Ǽ ’Œ‘‹Š›Žœ Ž’Œ‘Ž—ǰ ”Ž’— ŽŽ›£Ž’Œ‘Ž— Š—Ž• ( ’— Ž’—Ž— •Ž’—‹žŒ‘œŠ‹Ž— ž– Š—Ž• ( ’— Ž’—Ž— ›˜đ‹žŒ‘œŠ‹Ž— ž– ;AX ;RRF(-G;AXH ;AX ;R(AXQ>G;AXH ;AX ;RF[A(XG;AXH ;AX ;AX ;AX ;AX ;AX ;R>A[@G;AXH ;RFQ;AXG;AXH ;R6QF9G;AXH XD>D^-QG;AX (H XD[FF-QG;AX (H šž’ŸŠ•Ž—Ž ž—”’˜—Ž— û› ’Ž‘Š›Ȭ¢™Ž— ǻŘ ¢Žǰ £ǯ ǯ £ž› —Ž›—Š’˜—Š•’œ’Ž›ž— Ÿ˜— ™™•’”Š’˜—Ž—Ǽ œ’— ’— ǀŒ ¢™Žǁ ž— ǀ Œ¢™Žǯ‘ǁ £ž ’—Ž—ǯ Ĥ÷ ¿KěćÀزĎ÷ ’—Ž Ž’Œ‘Ž—”ŽŽǰ £ž– Ž’œ™’Ž• Ǯ Œ‘ ‹’— Ž’— ›’—ǯȄǰ ’œ Ž’— Ž’—’–Ž—œ’˜—Š•Žœ ››Š¢ǰ Šœ •Ž–Ž—Ž Žœ ¢™œ Œ‘Š› ‹Ž’—‘Š•Ž ž— –’ Ž– Ž’Œ‘Ž— ȅȧŖȂ Š‹œŒ‘•’Žđǯ  ‹’ŽŽ ”Ž’—Ž ™Ž›Š˜›Ž—ǰ ž– ›’—œ £ž –Š—’™ž•’Ž›Ž—ǯ Šœ ŽœŒ‘’Ž‘ –’ Ž’Ž›— ˜Ž› Ž‘˜Ž— Šžœ Ž› Š—Š›‹’‹•’˜‘Ž” ǀœ›’—ǯ‘ǁǯ ’Ž Š– ‘§ž’œŽ— ŸŽ› Ž—ŽŽ— Ž‘˜Ž— ™›§œŽ—’Ž› ’Ž —§Œ‘œŽ Š‹Ž••Žǯ ’› —Ž‘–Ž— Š—ǰ Šœœ œǰ œŗǰ ž— œŘ Ž— ¢™ Œ‘Š›Ș ‘Š‹Ž—ǰ Œ ’œ Ÿ˜– ¢™ Œ‘Š› ž— — Ÿ˜– ¢™ œ’£Žȏǯ §ž’ ŸŽ› Ž—ŽŽ Ȭ›’—ȬŽ‘˜Ž— ¢—Š¡ (9Q RXQ(XGRE* RZH (9Q RXQ(9QGR* (H ŽŽžž— û ’Ž Ž’Œ‘Ž—”ŽŽ œŘ Š– —Ž Ÿ˜— œŗ Ž’— ž— •’ŽŽ› œŗ £ž›ûŒ” ’ŽŽ› Ž’—Ž— Ž’Ž› Šž Šœ Ž›œŽ Œ ’— œ ˜Ž› ǰ Š••œ Œ —’Œ‘ Žž—Ž— ’› ğ cšÀ‚½šØȚěěšØ ;AX RXQ(@FGRE* RZH ;AX RXQ;(@FGRE* RZH (9Q RXQ(F`GRE* RZH R;a-\X RXQ>-AGRH (9Q RXQA(XGRE* RZ* AH ;AX RXQA(@FGRE* RZ* AH ;AX RXQA;(@FGRE* RZ* AH (9Q RXQA(F`GRE* RZ* AH (9Q RXQQ(9QGR* (H Ĥĕ Ž›•Ž’Œ‘ ’Ž Ž’Œ‘Ž—”ŽŽ— œŗ ž— œŘ •Ž¡’”˜›ŠȬ ™‘’œŒ‘ǰ ˜‹Ž’ £ ’œŒ‘Ž— ›˜đȬ ž— •Ž’—œŒ‘›Ž’Ȭ ‹ž— ž—Ž›œŒ‘’ŽŽ— ’› ǻŒŠœŽ œŽ—œ’’ŸŽǼDz •’ŽŽ› Ž’—Ž— Ž› ”•Ž’—Ž› Ŗǰ Ž—— œŗǀœŘǰ Ŗǰ Ž—— œŗƽƽœŘ ž— Ž’—Ž— Ž› ›ãđŽ› Ŗǰ Ž—— œŗǁœŘ ’Ž RXQ(@F GRE* RZHǰ Š‹Ž› £ ’œŒ‘Ž— ›˜đȬ ž— •Ž’—œŒ‘›Ž’‹ž— ’› —’Œ‘ ž—Ž›œŒ‘’ŽŽ— ǻŒŠœŽ ’—œŽ—œ’’ŸŽǼ Ž’Œ‘Ž—”ŽŽ œŘ ’— œŗ ”˜™’Ž›Ž—ǰ ’—”•žœ’ŸŽ ȅȧŖȂDz •’ŽȬ Ž› œŗ ’ŽŽ› ’Ž §—Ž Ÿ˜— œ ǻ˜‘—Ž ȁȧŖȂǼ û –Š¡’–Š• — Ž’Œ‘Ž— Ÿ˜— œŘ –’ Ž’—Ž– ȁȧŖȂ Š– —Ž Ÿ˜— œŗ Ž’— ž— •’ŽŽ› œŗ Ž›•Ž’Œ‘ –Š¡’–Š• — Ž’Œ‘Ž— Ÿ˜— œŗ ž— œŘ •Ž¡’Ȭ ”˜›Š™‘’œŒ‘ ǻŒŠœŽ œŽ—œ’’ŸŽǼDz •’ŽŽ› Ž’—Ž— Ž› ”•Ž’—Ž› Ŗǰ Ž—— œŗǀœŘǰ Ŗǰ Ž—— œŗƽƽœŘ ž— Ž’—Ž— Ž› ›ãđŽ› Ŗǰ Ž—— œŗǁœŘ ’Ž RXQA(@F GRE* RZ* AHǰ Š‹Ž› ŒŠœŽ ’—œŽ—œ’’ŸŽ ˜™’Ž› –Š¡’–Š• — Ž’Œ‘Ž— Ÿ˜— œŘ ’— œŗDz •’ŽŽ› œŗǯ ’ ȅȧŖȂ Šžû••Ž—ǰ Ž—— œŘ Ž—’Ž› Š•œ — Ž’Œ‘Ž— ‘Šǯ ’ŽŽ› Ž’—Ž— Ž’Ž› Šž Šœ •Ž£Ž Œ ’— œ ˜Ž› ǰ Š••œ Œ —’Œ‘ Žž—Ž— ’› ğ÷ úú¿KěćÀزĎ÷ — ƸƸ §•• Ž› –Š— –’ ›’—œ •Ž’Œ‘Ž› Š•œ ’— ǰ Ž’• ’Ž ƸƸȬ •ŠœœŽ œDZDZœ›’— ’Ž ™Ž’Œ‘Ž›ŸŽ› Š•ž— œŽ•‹œ Ž›•Ž’ ž— ’––Ž› Ž’đǰ ’Ž •Š— ’Ž Ž—‘Š•Ž—Ž— ›’—œ œ’—ǯ û› ›’—œ ’‹ Žœ ’Ž û› ˜—Š’—Ž› Ž›  Ž’—Ž Ž›Š˜›Ȭ Œ‘—’œŽ••Žǰ ǯ‘ǯ –Š— ”Š—— Šž œ’Ž ’Ž •˜›’‘–Ž— Ž›  Š— Ž—Ž—ǯ Ž› –™•ŽȬ –Ž—’Ž›ž— Ÿ˜— ›’—œ •’Ž ’Ž Ž–™•ŠŽ”•ŠœœŽ ‹Šœ’Œȏœ›’—ǀǁ £ž›ž—Žǰ ’Ž Ž— ŽȬ Ž› –’ Ž› ŞȬ‹’ ˜–™˜—Ž—Ž Œ‘Š› ˜Ž› Ž› ŗŜȬ‹’ ˜–™˜—Ž—Ž ȏŒ‘Š› £ž› —œŠ—£’’ŽȬ ›ž— Ÿ˜— ›’—œ £ž– ’—œŠ£ ”˜––ǯ žđŽ›Ž– –žœœ ‹Ž’ Ž› —œŠ—£’’Ž›ž— ’Ž •ŠœœŽ Œ‘Š›ȏ›Š’œǀǁ Š—Žû‘› Ž›Ž—ǰ Ž—— œ’Ž ‹Ž’—‘Š•Ž Š••Ž ›’—Ȭœ™Ž£’’œŒ‘Ž— ’Ž—œŒ‘ŠŽ— Ž› Ž’Œ‘Ž—œ§£Žǰ ’Ž ž›Œ‘ Œ‘Š› ž— ȏŒ‘Š› ›Ž™›§œŽ—’Ž› Ž›Ž—ǯ žȬ œ§£•’Œ‘ ’—Ž –Š— ’— Œ‘Š›ȏ›Š’œǀǁ —˜Œ‘ ¢™Ž’—’’˜—Ž— ’Ž ™˜œȏ¢™Ž ž— Œ‘Š›ȏ¢™Ž ž— ž—”’˜—Ž— £ž› Ž’Œ‘Ž—Ȭ ž— ›’—–Š—’™ž•Š’˜— ǻ
˜™’Ž›Ž—ǰ ˜›’Ž›Ž—ǰ §—Ž ‹Žœ’––Ž—ǰ dzǼǯ žœœŒ‘•’Žđ•’Œ‘ –’ ’ŽœŽ› •ŠœœŽ ”ã——Ž— Ž’Œ‘Ž—”ŽŽ— ŸŽ›Š›‹Ž’Ž Ž›Ž—ǯ Š–’ ‹•Ž’‹ ’Ž ‹’—§›Ž Š›œŽ••ž— Ž› Ž’Œ‘Ž— û› Ž— — ’Œ”•Ž› ŸŽ›‹˜›Ȭ Ž—ǯ Ĥ¡ ʲàćÀě½ÓšØ Ħ؏ EćàxʚÓÊãĎĦزšØ ÓÀě úú ’Ž •ŠœœŽ œDZDZœ›’— Ž’—’Ž› –Ž‘›Ž›Ž Ž–‹Ž›ž—”’˜—Ž—ǰ Ÿ˜— Ž—Ž— ’Ž –Ž’œ‹ŽȬ —ž£Ž— —ž— Ÿ˜›ŽœŽ•• Ž›Ž—ǯ Ž’œŸŽ› Ž—ŽŽ ž—”’˜—Ž— û› ’Ž ƸƸȬ›’—œ Š–Ž  ¢—Š¡ ž— — Ž—ž— ’› ˜‘—Ž —’’Š•’œ’Ž›ž—œ Ž› Ž’—’Ž›ǰ ’— ’ŽœŽ– Š•• ’œ Ž› Ž› Ž’—Ž •ŽŽ›Ž Ž’Œ‘Ž—”ŽŽ –’ §—Ž ž••DZ RXQ;A6 RE* RZS  ˜™’Ž— Ÿ˜— œ›’—Ȭ’Ž›Š•Ž—DZ RXQ;A6 RY 1 N;>>=D@@-A2 NS RXQ;A6 R5GN;- 6-9X -R +;QMNHS —’’Š•’œ’Ž›ž— ǻ
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