Problem:
Score : 600 points

Problem Statement

We will create an artwork by painting black some squares in a white square grid with 10^9 rows and N columns.

The current plan is as follows: for the i-th column from the left, we will paint the H_i bottommost squares and will not paint the other squares in that column.

Before starting to work, you can choose at most K columns (possibly zero) and change the values of H_i for these columns to any integers of your choice between 0 and 10^9 (inclusive).

Different values can be chosen for different columns.

Then, you will create the modified artwork by repeating the following operation:

Choose one or more consecutive squares in one row and paint them black. (Squares already painted black can be painted again, but squares not to be painted according to the modified plan should not be painted.)

Find the minimum number of times you need to perform this operation.

Constraints

1 \leq N \leq 300

0 \leq K \leq N

0 \leq H_i \leq 10^9

All values in input are integers.

Input

Input is given from Standard Input in the following format:

N K
H_1 H_2 ... H_N

Output

Print the minimum number of operations required.

Sample Input 1

4 1
2 3 4 1

Sample Output 1

3

For example, by changing the value of H_3 to 2, you can create the modified artwork by the following three operations:

Paint black the 1-st through 4-th squares from the left in the 1-st row from the bottom.

Paint black the 1-st through 3-rd squares from the left in the 2-nd row from the bottom.

Paint black the 2-nd square from the left in the 3-rd row from the bottom.

Sample Input 2

6 2
8 6 9 1 2 1

Sample Output 2

7

Sample Input 3

10 0
1 1000000000 1 1000000000 1 1000000000 1 1000000000 1 1000000000

Sample Output 3

4999999996

Solution in Java (OpenJDK 11.0.6) (judge verdict: Accepted)

import java.io.FileInputStream;
import java.util.Arrays;
import java.io.InputStream;
import java.io.FileNotFoundException;
import java.util.InputMismatchException;
import java.io.PrintWriter;
import java.io.IOException;

public class Main {
    InputStream is;

    int __t__ = 1;
    int __f__ = 0;
    int __FILE_DEBUG_FLAG__ = __f__;
    String __DEBUG_FILE_NAME__ = "src/F1";

    FastScanner in;
    PrintWriter out;

    public void solve() {
        int n = in.nextInt();
        int K = in.nextInt();
        long[] h = new long[n+2];
        for (int i = 1; i <= n; i++) {
            h[i] = in.nextLong();
        }

        long INF = 1L << 60;
        long[][] dp = new long[n+1][n+1];
        for (int i = 0; i <= n; i++) {
            Arrays.fill(dp[i], INF);
        }
        dp[0][0] = 0;
        for (int i = 1; i <= n; i++) {
            for (int j = 1; j <= n; j++) {
                for (int x = 0; x < i; x++) {
                    dp[i][j] = Math.min(dp[i][j], dp[x][j-1] + Math.max(0, h[i] - h[x]));
                }
            }
        }
        long res = INF;
        for (int i = 0; i <= n; i++) {
            res = Math.min(res, dp[i][n-K]);
        }
        System.out.println(res);
        /*
        long INF = 1L << 60;
        long[][][] dp = new long[n+1][n+1][K+1];
        for (int i = 0; i <= n; i++) {
            for (int j = 0; j <= n; j++) {
                Arrays.fill(dp[i][j], INF);
            }
        }
        dp[0][0][0] = 0;
        for (int i = 0; i < n; i++) {
            for (int j = 0; j <= i; j++) {
                for (int k = 0; k <= K; k++) {
                    if (dp[i][j][k] == INF) {
                        continue;
                    }
                    dp[i+1][i+1][k] = Math.min(dp[i+1][i+1][k], dp[i][j][k] + Math.max(0, h[i+1] - h[j]));
                    if (k < K) {
                        dp[i + 1][j][k + 1] = Math.min(dp[i + 1][j][k + 1], dp[i][j][k]);
                    }
                }
            }
        }
        long res = INF;
        for (int j = 0; j <= n; j++) {
            for (int k = 0; k <= K; k++) {
                res = Math.min(res, dp[n][j][k]);
            }
        }
        System.out.println(res);

         */
        /*
        long[][] cost = new long[n][n];
        TreeSet<Integer> ts = new TreeSet<>();
        PriorityQueue<Integer> pq = new PriorityQueue<>(Comparator.comparingLong(i -> h[i]));
        for (int l = 0; l < n; l++) {
            for (int r = l; r < n; r++) {
                ts.clear();
                ts.add(0);
                ts.add(n + 1);
                pq.clear();
                for (int i = l; i <= r; i++) {
                    pq.add(i + 1);
                }
                while (!pq.isEmpty()) {
                    int u = pq.poll();
                    int left = ts.lower(u);
                    int right = ts.higher(u);
                    ts.add(u);
                    cost[l][r] += h[u] - Math.max(h[left], h[right]);
                }
            }
        }
        long[][] dp = new long[n+1][K+1];
        for (int i = 0; i <= n; i++) {
            Arrays.fill(dp[i], 1L << 60);
        }
        dp[0][0] = 0;
        for (int i = 0; i < n; i++) {
            for (int k = 0; k < K; k++) {
                dp[i+1][k+1] = Math.min(dp[i+1][k+1], dp[i][k]);
                for (int j = i; j < n; j++) {
                    dp[j+1][k] = Math.min(dp[j+1][k], dp[i][k] + cost[i][j]);
                }
            }
        }
        long res = 1L << 60;
        for (int k = 0; k <= K; k++) {
            res = Math.min(res, dp[n][k]);
        }
        System.out.println(res);
         */
    }

    public void run() {
        if (__FILE_DEBUG_FLAG__ == __t__) {
            try {
                is = new FileInputStream(__DEBUG_FILE_NAME__);
            } catch (FileNotFoundException e) {
                e.printStackTrace();
            }
            System.out.println("FILE_INPUT!");
        } else {
            is = System.in;
        }
        in = new FastScanner(is);
        out = new PrintWriter(System.out);

        solve();
    }

    public static void main(final String[] args) {
        new Main().run();
    }
}


class FastScanner {
    private InputStream stream;
    private byte[] buf = new byte[1024];
    private int curChar;
    private int numChars;

    public FastScanner(InputStream stream) {
        this.stream = stream;
        // stream = new FileInputStream(new File("dec.in"));
    }

    int read() {
        if (numChars == -1)
            throw new InputMismatchException();
        if (curChar >= numChars) {
            curChar = 0;
            try {
                numChars = stream.read(buf);
            } catch (IOException e) {
                throw new InputMismatchException();
            }
            if (numChars <= 0)
                return -1;
        }
        return buf[curChar++];
    }

    public boolean isSpaceChar(int c) {
        return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
    }

    public boolean isEndline(int c) {
        return c == '\n' || c == '\r' || c == -1;
    }

    public int nextInt() {
        return Integer.parseInt(next());
    }

    public int[] nextIntArray(int n) {
        int[] array = new int[n];
        for (int i = 0; i < n; i++)
            array[i] = nextInt();

        return array;
    }

    public int[][] nextIntMap(int n, int m) {
        int[][] map = new int[n][m];
        for (int i = 0; i < n; i++) {
            map[i] = nextIntArray(m);
        }
        return map;
    }

    public long nextLong() {
        return Long.parseLong(next());
    }

    public long[] nextLongArray(int n) {
        long[] array = new long[n];
        for (int i = 0; i < n; i++)
            array[i] = nextLong();

        return array;
    }

    public long[][] nextLongMap(int n, int m) {
        long[][] map = new long[n][m];
        for (int i = 0; i < n; i++) {
            map[i] = nextLongArray(m);
        }
        return map;
    }

    public double nextDouble() {
        return Double.parseDouble(next());
    }

    public double[] nextDoubleArray(int n) {
        double[] array = new double[n];
        for (int i = 0; i < n; i++)
            array[i] = nextDouble();

        return array;
    }

    public double[][] nextDoubleMap(int n, int m) {
        double[][] map = new double[n][m];
        for (int i = 0; i < n; i++) {
            map[i] = nextDoubleArray(m);
        }
        return map;
    }

    public String next() {
        int c = read();
        while (isSpaceChar(c))
            c = read();
        StringBuilder res = new StringBuilder();
        do {
            res.appendCodePoint(c);
            c = read();
        } while (!isSpaceChar(c));
        return res.toString();
    }

    public String[] nextStringArray(int n) {
        String[] array = new String[n];
        for (int i = 0; i < n; i++)
            array[i] = next();

        return array;
    }

    public String nextLine() {
        int c = read();
        while (isEndline(c))
            c = read();
        StringBuilder res = new StringBuilder();
        do {
            res.appendCodePoint(c);
            c = read();
        } while (!isEndline(c));
        return res.toString();
    }

    public int[][] nextPackedIntArrays(int packN, int size) {
        int[][] res = new int[packN][size];
        for (int i = 0; i < size; i++) {
            for (int j = 0; j < packN; j++) {
                res[j][i] = nextInt();
            }
        }
        return res;
    }
}