Posted on 2007-04-16 20:47
oyjpart 閱讀(972)
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ACM/ICPC或其他比賽
Problem Statement
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You have been given a rows-by-cols chessboard, with a list of squares cut out. The list of cutouts will be given in a String[] cutouts. Each element of cutouts is a comma-delimited lists of coords. Each coord has the form (quotes for clarity) "r c". If coord "r c" appears in an element of cutouts, it means that the square at row r column c (0-based) has been removed from the chessboard. This problem will involve placing rooks on a chessboard, so that they cannot attack each other. For a rook to attack a target piece, it must share the same row or column as the target. Your method will return an int that will be the maximum number of rooks that can be placed on the chessboard, such that no pair of rooks can attack each other. Rooks cannot be placed on cut out squares. The cut out squares do not affect where the rooks can attack. |
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Constraints
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rows will be between 1 and 300 inclusive. |
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cols will be between 1 and 300 inclusive. |
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cutouts will contain between 0 and 50 elements inclusive. |
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Each element of cutouts will contain between 3 and 50 characters inclusive. |
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Each element of cutouts will be a comma delimited list of coords. Each coord will be of the form "r c", where
- r and c are integers, with no extra leading zeros,
- r is between 0 and rows-1 inclusive,
- and c is between 0 and cols-1 inclusive.
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Each element of cutouts will not contain leading or trailing spaces. |
Examples
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2
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2
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{"0 0","0 1","1 1","1 0"}
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Returns: 0
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| 2) |
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3
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3
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{"0 0","1 0","1 1","2 0","2 1","2 2"}
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Returns: 2
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看到這個題目有什么想法？
8皇后問題相信是大家入門搜索或其他算法的經典教材了 如果被砍掉部分格子呢？
看到row和col分別是300的時候相信想搜索的朋友們心里可能要嘀咕一下了
如果這樣分析一下：
由于在放置rook的時候要求這一行還有這一列一定只有這一個元素（注意是rook 不是queen 不要求斜行）
也就是說一個rook可以唯一的決定一行和一列
那么。。
這個rook似乎可以看成是某一行和某一列的一條邊
如果把rows作為一個集合 cols作為一個集合 把不是cut out的點作為row和col的連接
于是就轉化成了：二分圖匹配
按照最短路的增廣分析 時間復雜度不會超過o(n^3) 滿足題目要求
比如一個3*3的棋盤 被cut out掉了(0,0) (1,2) (2,2) 3個格子
row集合 0，1，2
col集合 0，1，2
可連接的邊為(0, 1), (0,2), (1, 0), (1,1), (2,0),(2,1)
執行最大匹配 將會得到如下結果
(0,2) (1,0), (2,1)
滿足題意