point p is on line l if and only if point l∗is on line p∗. 1. Using the property above, prove the following properties: (a) If n points p1, ..., pnare on a common line l, then p∗1, p∗2, ..., p∗nintersect at a common point l∗. (b) If n lines l1, ..., lnintersect at a common point p, then l∗1, l∗2, ..., l∗nare on a common line p∗. 2. If we have a line segment s connecting two points p1 and p2, describe a region s∗corresponding to the dual of s in terms of p∗1 and p∗2. (No rigorous proof is needed.) 3. If a line l intersects the line segment s, prove that l∗is in the region s∗.

point p is on line l if and only if point l∗is on line p∗. 1. Using the property above, prove the following properties: (a) If n points p1, ..., pnare on a common line l, then p∗1, p∗2, ..., p∗nintersect at a common point l∗. (b) If n lines l1, ..., lnintersect at a common point p, then l∗1, l∗2, ..., l∗nare on a common line p∗. 2. If we have a line segment s connecting two points p1 and p2, describe a region s∗corresponding to the dual of s in terms of p∗1 and p∗2. (No rigorous proof is needed.) 3. If a line l intersects the line segment s, prove that l∗is in the region s∗.

C++ for Engineers and Scientists

4th Edition

ISBN:9781133187844

Author:Bronson, Gary J.

Publisher:Bronson, Gary J.

Chapter13: Structures

Section: Chapter Questions

Problem 4PP

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Q. Given a 2d grid map of '1's (land) and '0's (water),count the number of islands.An island is surrounded by water and is formed byconnecting adjacent lands horizontally or vertically.You may assume all four edges of the grid are all surrounded by water. Example 1: 11110110101100000000Answer: 1 Example 2: 11000110000010000011Answer: 3""" def num_islands(grid): count = 0 for i in range(len(grid)): for j, col in enumerate(grid[i]): if col == 1: dfs(grid, i, j) count += 1 Please code it. .
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