L09 Tree Balancing CX1007 Data Structures 2013/14 S2 Mark Yong Today • Importance of balance for BSTs • Balancing operaGons in self-‐balancing BSTs • Pseudocode + worked examples CX1007 Data Structures 2013/14 S2 2 Recall: Why use BSTs? • BSTs are a special form of BT L • At every
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4s + 12 s2 + 8s + 16 5s − 10 9s2 − 16 s+1 s−1 2. F (s) = 4. F (s) = 6. F (s) = 8. F (s) = s+2 s2 − 4s + 13 (s2 − 1)2 s5 2s − 1 s4 + s2 + 1 1 16 + 4s 1 − s2 1+s s 9. F (s) = log 10. F (s) = log 12. F (s) = 14. F (s) = 16. F (s) = 11. F (s) = cot−1 (s + 1) 13. F (s) = 15. F (s) = 17. F (s) = 19. F (s) = 21. F (s) = 23. F (s) = 25. F (s) = 1 − 2s3 8 s4 − 4s2 s2 4 + 4s 1 + a2 ) s4 1 s(s + a)3 e−2s s−5 se−2s s2 + π 2 1 + e−sπ/2 s2 + 4 se−as s2 + b 2 e−s (s − 1)(s − 2) s(s2 e−s 18
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APUNTES SOBRE EL MÉTODO SÍMPLEX DE PROGRAMACIÓN LINEAL Adriel R. Collazo Pedraja 2 INTRODUCCIÓN Este trabajo tiene como propósito proveer ayuda al estudiante para que pueda comprender y manejar más efectivamente el método símplex de programación lineal. Ilustraremos la aplicación a situaciones de maximización‚ minimización y análisis de sensibilidad. El Método Símplex como herramienta de programación lineal fue desarrollado para la época de los años cuarenta por George Dantzing‚ un joven matemático
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solution i = est or by the equivalent of substituting s2 for (d2i/dt2)‚ and s for (di/dt); thus 1 s + 2) ζ =0 jω jω 2 R s=0 + LC L n ζ =1 ζ→∞ σ ζ →∞ -jω ζ =0 n 1 s2 + + R s=0 LC L Characteristic equation: as2 + bs + c = 0 Here a b c -b ± √b2 – 4ac 2a 1 R L 1 LC s1‚ s2 = Muhammad Irfan Yousuf (Peon of Holy Prophet (P.B.U.H)) 2000-E-41 120 R L s1‚ s2 = ± R L 2 4(1) 1 LC 2(1) R L s1‚ s2 = 2 R L s1‚ s2 = 2 R = 2L ± ± ± R L 2 4(1) 1 LC 2
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length m [L] (c) Speed m/s [L]/ [T] (d) Displacement m/s2 [L]/ [T] 2 Ans. (d) 4. A car travels in a straight line covering a total distance of 90.0 miles in 60.0 minutes. Which one of the following statements concerning this situation is necessarily
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Operations Research Unit 4 Unit 4 Simplex Method Structure: 4.1 Introduction Objectives 4.2 Standard Form of LPP Fundamental theorem of LPP 4.3 Solution of LPP – Simplex Method Initial basic feasible solution of an LPP To solve an LPP in canonical form by simplex method 4.4 The Simplex Algorithm Steps 4.5 Penalty Cost Method or Big M-method 4.6 Two Phase Method 4.7 Solved Problems on Minimisation 4.8 Summary 4.9 Glossary 4.10 Terminal Questions 4.11 Answers 4.12 Case Study 4.1 Introduction
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References: site‚ Stavanger‚ Norway. Paper presented at the 9th International Congress of the FIP‚ Stockholm‚ Sweden‚ 1982. Proceedings of the 10th International Congress of the FIP‚ New Delhi‚ India‚ 1986‚ and FIP Notes 1987/2‚ p Hyde R.: Floating Concourses - Brighton Marina‚ Sussex. Paper presented at the 8th International Congress of the FIP‚ London‚ UK‚ 1978. PO.
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------------------------------------------------- To determine the enthalpy change of reaction for: ------------------------------------------------- Na2CO3(aq) + H2O(l) + CO2(g) → 2NaHCO3(aq) Given: S1— Anhydrous sodium carbonate (Na2CO3) S2— Anhydrous sodium hydrogen carbonate (NaHCO3) A1—Aqueous sulfuric acid (H2SO4)‚ 0.500mol dm-3 Apparatus | Uncertainty | Measuring cylinder | ± 0.5 ml | Electronic Balance | ± 0.001 g | Data logger | ±0.2 ℃ | Data Collection: S1 Weight
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basketballs X2 -- # of footballs Maximize Z = 12x1 + 16x2 Subject to: 3x1 + 2x2 ≤ 500 4x1 + 5x2 ≤ 800 X1‚ x2 ≥ 0 Transform this model to standard form. Maximize Z = 12x1 + 16x2 + 0s1 +0s2 3x1 + 2x2 + s1 = 500 4x1 +5x2 + x2 = 800 X1‚ x2‚ s1‚ s2 ≥ 0 a). Identify the amount of unused resources (slack) at each of the graphical points. 3x1 + 2x2= 500 4x1 + 5x2 = 800 X1 = 0‚ x2 = 250 X1 = 0‚ x2 = 160 X2 = 0‚ x1 = 500/3 X2 = 0‚ x1 = 200 Maximize Z = 12x1 + 16x2 At point A (0‚ 0) Z
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Work of Taylor and Fayol was complimentary. After going through the contribution made by both of these legends‚ we find that both of these are giving reflection of aiming increase in efficiency. Definitely the work of Taylor and Fayol is complimentary. Realizing the problem of human resource and their management at all levels they attributed this fact to be the key in the success of business. Both of them recognized the behavioral side of management; however they did not emphasize
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