Tutorial4 - 1-1COMP170 – Tutorial 4Cartesian Coordinate...

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Unformatted text preview: 1-1COMP170 – Tutorial 4Cartesian Coordinate Path ProblemProof of Distributive Laws2-1Cartesian Coordinate Path ProblemIn a Cartesian coordinate system,how many paths are therefrom the origin to the point with integer coordinates (m,n)if the paths are built up of exactly m+n horizontal andvertical line segments, each of length 1?2-2Cartesian Coordinate Path ProblemYou should assume that all of the horizontal edges go fromleft to right and all the vertical edges from bottom up.You should also assume that m, n>0.In a Cartesian coordinate system,how many paths are therefrom the origin to the point with integer coordinates (m,n)if the paths are built up of exactly m+n horizontal andvertical line segments, each of length 1?2-3Cartesian Coordinate Path ProblemThat is, you start at point (0, 0) and each edge either goes(i)vertically, from (i, j) to (i, j +1) or(ii)horizontally, from (i, j) to (i+1, j).You should assume that all of the horizontal edges go fromleft to right and all the vertical edges from bottom up.You should also assume that m, n>0.In a Cartesian coordinate system,how many paths are therefrom the origin to the point with integer coordinates (m,n)if the paths are built up of exactly m+n horizontal andvertical line segments, each of length 1?3-1Cartesian Coordinate Path Problem (Example)(0, 0)# of ways from (0, 0) to (4, 3)??(4, 3)3-2Cartesian Coordinate Path Problem (Example)(0, 0)(4, 3)Method 1Step 1: VerticalStep 2: HorizontalStep 3: HorizontalStep 4: HorizontalStep 5: VerticalStep 6: VerticalStep 7: Horizontal3-3...
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This note was uploaded on 08/25/2010 for the course COMP COMP170 taught by Professor M.j.golin during the Spring '10 term at HKUST.

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Tutorial4 - 1-1COMP170 – Tutorial 4Cartesian Coordinate...

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