6044: POJ3250 - Bad Hair Day
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Description
Some of Farmer John's $N\ (1 ≤ N ≤ 80,000)$ cows are having a bad hair day! Since each cow is self-conscious about her messy hairstyle, FJ wants to count the number of other cows that can see the top of other cows' heads.
Each cow i has a specified height $h_i (1 ≤ h_i ≤ 1,000,000,000)$ and is standing in a line of cows all facing east (to the right in our diagrams). Therefore, cow $i$ can see the tops of the heads of cows in front of her (namely cows $i+1,\ i+2,$ and so on), for as long as these cows are strictly shorter than cow $i$.
Consider this example:
Cow#2 can see no cow's hairstyle
Cow#3 can see the hairstyle of cow #4
Cow#4 can see no cow's hairstyle
Cow#5 can see the hairstyle of cow 6
Cow#6 can see no cows at all!
Let $c_i$ denote the number of cows whose hairstyle is visible from cow $i$; please compute the sum of $c_1$ through $c_N$. For this example, the desired is answer $3 + 0 + 1 + 0 + 1 + 0 = 5$.
Each cow i has a specified height $h_i (1 ≤ h_i ≤ 1,000,000,000)$ and is standing in a line of cows all facing east (to the right in our diagrams). Therefore, cow $i$ can see the tops of the heads of cows in front of her (namely cows $i+1,\ i+2,$ and so on), for as long as these cows are strictly shorter than cow $i$.
Consider this example:
= = = = - = Cows facing right --> = = = = - = = = = = = = = = 1 2 3 4 5 6Cow#1 can see the hairstyle of cows #2, 3, 4
Cow#2 can see no cow's hairstyle
Cow#3 can see the hairstyle of cow #4
Cow#4 can see no cow's hairstyle
Cow#5 can see the hairstyle of cow 6
Cow#6 can see no cows at all!
Let $c_i$ denote the number of cows whose hairstyle is visible from cow $i$; please compute the sum of $c_1$ through $c_N$. For this example, the desired is answer $3 + 0 + 1 + 0 + 1 + 0 = 5$.
Input
Line $1$: The number of cows, $N$.
Lines $2..N+1$: Line $i+1$ contains a single integer that is the height of cow $i$.
Lines $2..N+1$: Line $i+1$ contains a single integer that is the height of cow $i$.
Output
Line $1$: A single integer that is the sum of $c_1$ through $c_N$.
Sample 1 Input
6
10
3
7
4
12
2
Sample 1 Output
5