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CODE FESTIVAL 2015 ÓèßxA ½âÕh

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AtCoder Inc.

- The document contains code and explanations for solving optimization problems using dynamic programming, including calculating minimum costs using a 2D array to store results. - It describes applying dynamic programming to problems involving finding minimum costs for tasks that can be split into subtasks, with the overall cost determined by combining subtask costs. - The code provided shows initializing a 2D array and using nested for loops to iterate through values, calculate minimum costs based on previous results, and store them in the 2D array to build up an optimal solution.

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51 ?? ¡° 1 j s s h ?? ¡° 1 a a ¡°j D C Oh ?? O ¡° 1 j r r h ?? ok ¨C? sr at ?? Tc c ?? a?¡¯ j ?¡® V S T ¨C? 5 : A 5 5A A 5 : 4 ¨C? ¡° a Ot ?? Tc c ?? I ? ? ¡° _? a p n V S T ?? Lh ata?¡¯ j ?¡® had Ve
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?? ¨C? B LI L ¨C? I F95 V V ? L ¨C? < L=D <i T = BO F 9DD E ¨C L ?? B ?? ¨C? ? E < L=D <i T = BS ¨C? DD E 5 BV A B BO F9 BO i TTF ?? DD 9 SCF9 BO F 9 ? S ¨C? <2 BO =E B V
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?? ¨C? 2 DA EA D ll E l MMMMMm ¨C? X ?? ¨C? 9 ? ) DP[][]% %INF%l % DP[0][0]%=%0% for%(i%:%1...M)%for%(j%:%0...X[i]71)% %%for%(k%:%X[i]...N)% %%%%L%=%X[i]7j% %%%%R%=%k7X[i]% %%%%T%=%min(L*2+R,%L+R*2)% %%%%DP[i][k]%=%min(DP[i][k],%max(DP[i71][j],%T))%
?? ¨C? V + ?? ¨C? ?? = m[l l ¨C? ?? ( R l l S a N l l l ¨C? D [R l l S ?? 2 DA D [R l l SNm ?? DA L 2 D (A L (Nm ?? D ? ) ) -©\?? = mo m ?? mN2 DA DA mo
?? ¨C? V + ?? ¨C? ?? = m[l l ?? ¨C r * ) n ¨C? (lN [ Xo [ ¨C? ?? ( R l l S a N l l l
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?? ¨C? [ i ¨C? l ?? ¨C? 9 ? FIC)
?? ] m l ¨C? ?= ) ?= ) m m l ?? ¨C? 9 ? FIC

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CODE FESTIVAL 2015 ÓèßxA ½âÕh

  • 1. 5 ? 0 0+ 12. /
  • 2. 2 ?? E F Lh ¡° 1 O ih ?? j E F O r ?? ¨C? E 0+ 12. / F E 0+ 12. / F
  • 3. 51 ?? ¡° 1 j s s h ?? ¡° 1 a a ¡°j D C Oh ?? O ¡° 1 j r r h ?? ok ¨C? sr at ?? Tc c ?? a?¡¯ j ?¡® V S T ¨C? 5 : A 5 5A A 5 : 4 ¨C? ¡° a Ot ?? Tc c ?? I ? ? ¡° _? a p n V S T ?? Lh ata?¡¯ j ?¡® had Ve
  • 4. =A BD 21 ,3-©\?? ? 5 0 +1 ? ? +
  • 5. =A ?? ?2 ? ?+ ? E ?? ? ? ?5 ? ?2 ? D ?? ? [ 5 ?+ ?5 ? L ?5 ?VO A VCD D ?? 2 ? ?5 ? VT C AV ] ?? VT C A P ?? ¨C? ? ?2 ? ? ¨C? ? ?+ ? ? ¨C? E[ ? ? E C
  • 7. B ?? [ ? ? = O V Pi ?? -©\?? ¨C? D -©\?? E O ?? +-©\?? -©\?? * ¨C? ? ?? 5 ?+ ?5 ? L ?5 ?VO A ?? ?5 ? [ ?-©\?? 9 ? ?5 ? [ -©\?? 9 ? ?+ ? ?-©\?? 9 ?V O ¨C? ?? +-©\?? +-©\?? ? -©\?? ?? L ~¡« ? ? ?2 ? ? ? SCT NTCIV -©\?? 29 ? E V O ¨C? -©\?? 9 ? ? ?VNTFIV ? ? ? ? V L O
  • 9. ?? 2 E 9 9i T 9 L T N I ETF ?? S 5 N F9 T V V V D ?? N I E V ? N ?? ¨C? 2 ¨C? 5 ¨C?
  • 10. ?? ¨C? i T O E 5 V ?? ¨C? L O V 9 i T L ?? ¨C? E 9 E 5 BV T S ¨C? N O F9 O i TTF ¨C? 9<2 ? O =E B V ?? ¨C? < = S ?? S D S
  • 11. ?? ¨C? B LI L ¨C? I F95 V V ? L ¨C? < L=D <i T = BO F 9DD E ¨C L ?? B ?? ¨C? ? E < L=D <i T = BS ¨C? DD E 5 BV A B BO F9 BO i TTF ?? DD 9 SCF9 BO F 9 ? S ¨C? <2 BO =E B V
  • 12. 1923 3<=5 0 ) (+ 0
  • 13. ?? [ ?? r ND r D ?? rR SmR S[ ?? R S rT ?? R S r r o ?? o]m T [ ag o l rO ?? ¨C? ( V V ( , ¨C? ( V V ( + j V
  • 14. ?? ¨C? ( V V V ( ?? ¨C? [ j ?? r r o lN g r ?? r o lN r D x o mo ?? i ND [ N D x o ¨C? j ?? D D A m ag N Xo X [ ?? j N r D ? ) ) mo
  • 15. ?? ¨C? 2 DA EA D ll E l MMMMMm ¨C? X ?? ¨C? 9 ? ) DP[][]% %INF%l % DP[0][0]%=%0% for%(i%:%1...M)%for%(j%:%0...X[i]71)% %%for%(k%:%X[i]...N)% %%%%L%=%X[i]7j% %%%%R%=%k7X[i]% %%%%T%=%min(L*2+R,%L+R*2)% %%%%DP[i][k]%=%min(DP[i][k],%max(DP[i71][j],%T))%
  • 16. ?? ¨C? V + ?? ¨C? ?? = m[l l ¨C? ?? ( R l l S a N l l l ¨C? D [R l l S ?? 2 DA D [R l l SNm ?? DA L 2 D (A L (Nm ?? D ? ) ) -©\?? = mo m ?? mN2 DA DA mo
  • 17. ?? ¨C? V + ?? ¨C? ?? = m[l l ?? ¨C r * ) n ¨C? (lN [ Xo [ ¨C? ?? ( R l l S a N l l l
  • 18. ?? ¨C? D [R l l S ?? 2 DA D [R l l SNm ?? DA L 2 D (A L (Nm ?? D ? ) ) -©\?? = jN DA -©\?? D (A g X o m ¨C? D (A D [ ro ?? mN2 DA DA mo ¨C? ?? ( j a N ?? R( j a S r l P la o ¨C? [ DA ma ¨C mro g ?? ¨C? 9 ? FIC
  • 19. ?? ¨C? [ i ¨C? l ?? ¨C? 9 ? FIC)
  • 20. ?? ] m l ¨C? ?= ) ?= ) m m l ?? ¨C? 9 ? FIC