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pankajkumar

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    algorithm

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  1. derive the transformation matrix which will rotate an object through 45 degree about a line passing through (2,3,4) and (3,5,7)
  2. Show that f1(n)+f2(n)= o(m4*(g1(n),g2(n)) where f1(n)= o(g1(n)) and f2(n)=o(g2(n))? o is small o asymptotic notation and question is related to time complexity
  3. Show that f1(n)+f2(n)= o(m4*(g1(n),g2(n)) where f1(n)= o(g1(n)) and f2(n)=o(g2(n))? o is small o asymptotic notation and question is related to time complexity
  4. ya homework. i want solution i want recurrence relation of below equation by master method
  5. Ques.1 If P1/W1 is less than P2/W2...less than Pn/Wn, prove greedy generate optimal solution to knapsack prob.? Ques.2 time complexity of- for i:= 1 to n do for j:= i+1 to n do for k:= j+1 to n do z= z+1
  6. find the optimal sequence and minimum number of operations required for the following chain matrix multiplication using dynamic programming. A(30,40) B(40,5) C(5,15) D(15,6)
  7. explain divide and conquer strategy that multiply two nxn matrices using O(n^3) operations. determine the precise number of multiplications and additions.
  8. 1. T(n)=3T(n/u)+nlogn 2. T(n)=2T(n/2)+n^3
  9. how to find pixels required for generating a line from(0,0) to (10,5) initial calculation- x=0 y=0 Δx=x2-x1 = 10-0= 10 Δy=y2-y1, 5-0, 5→2Δy=10 m= Δy/Δx = 5/10 = 1/2 2Δy-2Δx = 10-20 = -10 first plot(0,0) now incrementing through main loop yields next plots. now how to find next plot. i am confuse here
  10. show that f1(n)+f2(n)= o(m4*(g1(n),g2(n)) where f1(n)= o(g1(n)) and f2(n)=o(g2(n))? o is small o asymptotic notation and question is related to time complexity
  11. time complexity of- for i:= 1 to n do for j:= i+1 to n do for k:= j+1 to n do if P1/W1 is less than P2/W2...less than Pn/Wn, prove greedy generate optimal solution to knapsack prob.
  12. the adjacency list representation of a graph G, which has 7 vertices and 10 edges is, a:- d,e,b,g b:- e,c,a c;- f,e,b,d d:- c,a,f e:- a,c,b f:- d,c g:- a 1. show the tree produced by depth first search when it is run on the graph G, using vertex a as the source 2. In the DFS of item 1, show the edges of the graph G which is not present in DFS tree by dashed line
  13. give asymptotic upper bounds for t(n), bounds should be as tight as possible, assume n is power of 2. 1. t(n)=t(2)=1 t(n)=t(n-2)+1 if n>2 2. t(1)=1 t(n)=t(n/2)+1 if n>1
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