2014 Canadian Computing Competition, Stage 1
Problem S4: Tinted Glass Window
You are laying N rectangular pieces of grey-tinted glass to make a stained glass window. Each piece of glass adds an integer value "tint-factor". Where two pieces of glass overlap, the tint-factor is the sum of their tint-factors.
You know the desired position for each piece of glass and these pieces of glass are placed such that the sides of each rectangle are parallel to either the x-axis or the y-axis (that is, there are no "diagonal" pieces of glass).
You would like to know the total area of the finished stained glass window with a tint-factor of at least T.
The first line of input is the integer N (1 ≤ N ≤ 1000), the number of pieces of glass. The second line of input is the integer T (1 ≤ T ≤ 1 000 000 000), the threshold for the tint-factor. Each of the next N lines contain five integers, representing the position of the top-left and bottom-right corners of the i-th piece of tinted glass followed by the tint-factor of that piece of glass. Specifically, the integers are placed in the order xl yt xr yb ti, where the top-left corner is at (xl, yt) and the bottom-right corner is at (xr, yb), and tint-factor is ti. You can assume that 1 ≤ ti ≤ 1 000 000. The top-most, left-most co-ordinate where glass can be placed is (0, 0) and you may assume 0 ≤ xl < xr ≤ K and 0 < yt < yb ≤ K, and
The following additional constraints will apply.
- At least 10% of the marks will be for test cases where N ≤ 100 and K ≤ 100;
- at least 30% of the marks will be for test cases where N ≤ 1000 and K ≤ 1000;
- at least 40% of the marks will be for test cases where N ≤ 100 and K ≤ 1 000 000 000;
- the remaining marks will be for test cases where N ≤ 1000 and K ≤ 1 000 000 000.
Output the total area of the finished stained glass window which has a tint-factor of at least T. All output will be less than 264, and the output for some test cases will be larger than 232.
4 3 11 11 20 15 1 13 8 14 17 2 17 8 18 17 1 12 12 19 13 1
There are 4 pieces of glass used. There are two regions of glass which have a tint-factor greater than or equal to 3: one region between (13, 11) and (14, 15) (which has tint-factor of 3, except for a unit square with tint-factor 4), and another region between (17, 12) and (18, 13) (with tint-factor 3). In total, these two regions have 5 square units of glass with tint-factor greater than or equal to 3, as shown on the diagram below.
Point Value: 15 (partial)
Time Limit: 2.00s
Memory Limit: 64M
Added: Feb 27, 2014
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