DominoesFarmer John's son, Johnny is playing with some dominoes one afternoon.
His dominoes come in a variety of heights and colors.
Just like any other child, he likes to put them in a row and knock them over.
He wants to know something: how many pushes does it take to knock down all the dominoes?
Johnny is lazy, so he wants to minimize the number of pushes he takes.
A domino, once knocked over, will knock over any domino that it touches on the way down.
For the sake of simplicity, imagine the floor as a one-dimensional line, where 1 is the leftmost point. Dominoes will not slip along the floor once toppled. Also, dominoes do have some width: a domino of length 1 at position 1 can knock over a domino at position 2.
For the mathematically minded:
A domino at position x with height h, once pushed to the right, will knock all dominoes at positions x+1, x+2, ..., x+h rightward as well.
Conversely, the same domino pushed to the left will knock all dominoes at positions x-1, x-2, ..., x-h leftward.
InputThe input starts with a single integer N ≤ 100,000, the number of dominoes, followed by N pairs of integers.
Each pair of integers represents the location and height of a domino.
(1 ≤ location ≤ 1,000,000,000, 1 ≤ height ≤ 1,000,000,000)
No two dominoes will be in the same location.
NOTE: 60% of test data has N ≤ 5000.
OutputOne line, with the number of pushes required.
Push the domino at location 1 rightward, the domino at location 8 leftward.
| | | | | | | | | 1 2 3 4 5 6 7 8
Pushing 1 causes 2 and 3 to fall, while pushing 8 causes 6 to fall and gently makes 5 tip over as well.
Point Value: 25
Time Limit: 1.00s
Memory Limit: 64M
Added: Sep 26, 2008
- Data Structures
- Dynamic Programming
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