Codeforces 448C Painting Fence

Bizon the Champion isn’t just attentive, he also is very hardworking.

Bizon the Champion decided to paint his old fence his favorite color, orange. The fence is represented as n vertical planks, put in a row. Adjacent planks have no gap between them. The planks are numbered from the left to the right starting from one, the i-th plank has the width of 1 meter and the height of ai meters.

Bizon the Champion bought a brush in the shop, the brush’s width is 1 meter. He can make vertical and horizontal strokes with the brush. During a stroke the brush’s full surface must touch the fence at all the time (see the samples for the better understanding). What minimum number of strokes should Bizon the Champion do to fully paint the fence? Note that you are allowed to paint the same area of the fence multiple times.

Input
The first line contains integer n (1 ≤ n ≤ 5000) — the number of fence planks. The second line contains n space-separated integers a1, a2, …, an (1 ≤ ai ≤ 109).

Output
Print a single integer — the minimum number of strokes needed to paint the whole fence.

Sample test(s)
input
5
2 2 1 2 1
output
3
input
2
2 2
output
2
input
1
5
output
1
Note
In the first sample you need to paint the fence in three strokes with the brush: the first stroke goes on height 1 horizontally along all the planks. The second stroke goes on height 2 horizontally and paints the first and second planks and the third stroke (it can be horizontal and vertical) finishes painting the fourth plank.

In the second sample you can paint the fence with two strokes, either two horizontal or two vertical strokes.

In the third sample there is only one plank that can be painted using a single vertical stroke.

解題思路：對於某一個區間分兩種策略去進行操作，第一種操作爲每個柵欄單獨刷，這樣最終的結果爲r-l+1。第二種策略爲用這個區間內的最小的高度橫着刷一次，然後對各個子區間分別採用這兩種方式進行最優值的求解，最終得到整個大區間的最優值。採用分治的方法進行求解。

#include <cmath>
#include <cstdio>
#include <cstdlib>
#include <cstring>
#include <iostream>
#include <string>
#include <vector>
#include <queue>
#include <stack>
#include <map>
#include <set>
#include <numeric>
#include <algorithm>
#include <functional>
using namespace std;
const int maxn = 5010;
int h[maxn];

int dfs(int l, int r) {
    if(l == r) return 1;
    int t1 = r - l + 1;
    int t2 = 0;
    int minh = 0x3f3f3f3f;
    for(int i = l; i <= r; ++i) {
        minh = min(minh, h[i]);
    }
    t2 += minh;
    int s = -1, e = -1;
    for(int i = l; i <= r; ++i) {
        h[i] -= minh;
        if(h[i] > 0) {
            if(s == -1) {
                s = i;
                e = i;
            } else {
                e = i;
            }
        } else {
            if(s > 0) {
                t2 += dfs(s, e);
            }
            s = -1;
            e = -1;
        }
    }
    if(s > 0) t2 += dfs(s, e);
    return min(t1, t2);
}

int main() {

    //freopen("aa.in", "r", stdin);

    int n;
    scanf("%d", &n);
    for(int i = 1; i <= n; ++i) {
        scanf("%d", &h[i]);
    }
    printf("%d\n", dfs(1, n));
    return 0;
}