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 (Python):
N,K=map(int,input().split())
H=list(map(int,input().split()))+[0]
h=[0]*(N+1)
h[0]=H[0]
for i in range(1,N):
    h[i]=max(H[i]-H[i-1],h[i])
for i in range(1,N+1):
    h[i]+=h[i-1]
data=[[0]*N for i in range(N)]
for L in range(N):
    for R in range(L,N):
        if L==0:
            data[L][R]=h[-1]-h[R+1]+H[R+1]
        else:
            data[L][R]=h[L-1]+h[-1]-h[R+1]+max(0,H[R+1]-H[L-1])
for L in range(N):
    for R in range(L,N):
        data[L][R]=h[-1]-data[L][R]
dp=[[0]*(K+1) for i in range(N+1)]
for i in range(1,N+1):
    for j in range(min(i+1,K+1)):
        dp[i][j]=dp[i-1][j]
        for k in range(j-1,-1,-1):
            if dp[i][j]<dp[i-1-j+k][k]+data[i-j+k][i-1]:
                dp[i][j]=dp[i-1-j+k][k]+data[i-j+k][i-1]
print(h[-1]-max(dp[N]))

Solution (Python):
N, K = map(int, input().split())
H = list(map(int, [0] + input().split() + [0]))
d = [[10**18]*(K+1) for _ in range(N+2)]
for i in range(K+1):
    d[0][i] = 0
for hi in range(N+1):
    hi+=1
    h = H[hi]
    for i in range(min(K+1, hi)):
        for k in range(i+1):
            d[hi][i] = min(d[hi][i], d[hi-k-1][i-k] + max(H[hi-k-1]-h, 0))
print(min(d[-1]))

Solution (Python):


import sys
import math
from bisect import bisect_right as br
from bisect import bisect_left as bl
sys.setrecursionlimit(2147483647)
from heapq import heappush, heappop,heappushpop
from collections import defaultdict
from itertools import accumulate
from collections import Counter
from collections import deque
from operator import itemgetter
from itertools import permutations
mod = 10**9 + 7
inf = float('inf')
def I(): return int(sys.stdin.readline())
def LI(): return list(map(int,sys.stdin.readline().split()))

"""
[解説AC]
塗っていくときにかかるコストはΣmax(0,h[i]-h[i-1])
k回まで高さを変えられる⇒k列は考えなくてよい(k列をその左と同じ高さにする)
残るのはn-k列のブロック
ある一列を残すと決めたとき、それにかかるコストはそれより前で残すと決めた列の高さに依存するため
dp[i][j] := i列目を残すとしたとき、i列目まででj列残す場合のコストの最小値とする
dp[i][j] = min(dp[i][j],dp[l][j-1] + max(0,h[i] - h[l])) (1<=l<i) (前回l列目を残し、今回i列目を残す場合)
ans = min(dp[i][n-k])
"""

n,k = LI()
h = [0] + LI()
dp = [[inf]*(n-k+1) for _ in range(n+1)]
dp[0][0] = 0
for i in range(1,n+1):
    for j in range(1,n-k+1):
        for l in range(i):
            dp[i][j] = min(dp[i][j],dp[l][j-1] + max(0,h[i]-h[l]))

ans = inf
for i in range(n+1):
    ans = min(ans,dp[i][n-k])
print(ans)

Solution (Python):


import sys
import math
from bisect import bisect_right as br
from bisect import bisect_left as bl
sys.setrecursionlimit(2147483647)
from heapq import heappush, heappop,heappushpop
from collections import defaultdict
from itertools import accumulate
from collections import Counter
from collections import deque
from operator import itemgetter
from itertools import permutations
mod = 10**9 + 7
inf = float('inf')
def I(): return int(sys.stdin.readline())
def LI(): return list(map(int,sys.stdin.readline().split()))

n,k = LI()
h = [0] + LI()

dp = [[inf]*(n-k+1) for _ in range(n+1)]
dp[0][0] = 0
for i in range(1,n+1):
    for j in range(1,n-k+1):
        for l in range(i):
            dp[i][j] = min(dp[i][j],dp[l][j-1] + max(0,h[i]-h[l]))

ans = inf
for i in range(n+1):
    ans = min(ans,dp[i][n-k])
print(ans)

Solution (Python):
import numpy as np
INF = 10**15
def solve(n, k, h):
    dp = np.full((n+1, n+1), INF, dtype=int)
    dp[0, 0] = 0
    h = np.array([0] + h, dtype=int)
    for i, h_i in enumerate(h[1:], 1):
        t = np.maximum(h_i - h[:i], 0)
        dp[i,1:] = np.min(dp[:i,:-1]+t[:,None], axis=0)
    return np.min(dp[:, n-k])

n, k = map(int, input().split())
h = list(map(int, input().split()))
print(solve(n, k, h))

Solution (Python):
import sys
sys.setrecursionlimit(10**7)
INTMAX = 9223372036854775807
INTMIN = -9223372036854775808
DVSR = 1000000007
def POW(x, y): return pow(x, y, DVSR)
def INV(x, m=DVSR): return pow(x, m - 2, m)
def DIV(x, y, m=DVSR): return (x * INV(y, m)) % m
def LI(): return [int(x) for x in input().split()]
def LF(): return [float(x) for x in input().split()]
def LS(): return input().split()
def II(): return int(input())
def FLIST(n):
    res = [1]
    for i in range(1, n+1): res.append(res[i-1]*i%DVSR)
    return res


N,K=LI()
MP=[0] + LI()
LG = 10**15
DP=[[LG]*(N+1) for i in range(N-K+2)]

for i in range(1, N+1):
    DP[0][i] = 0
    DP[1][i] = MP[i]

for i in range(1, N-K):
    for j in range(1, N+1):
        for k in range(1, j):
            DP[i+1][j] = min(DP[i+1][j], DP[i][k] + max(0, MP[j] - MP[k]))

res = 10**15
for i in range(1, N+1):
    res = min(res, DP[N-K][i])
print(res)

Solution (Python):
N, K = map(int, input().split())
H = [0] + [int(i) for i in input().split()]

dp = [[float('inf')] * (N - K + 1) for _ in range(N + 1)]
dp[0][0] = 0


for i in range(1, N + 1) :
  for j in range(N - K + 1) :
    dp[i][j] = min(dp[k][j-1] + max(0, H[i] - H[k]) for k in range(i))

print(min(dp[i][N-K] for i in range(N + 1)))

Solution (Python):
n, m = list(map(int, input().split()))
if n == m:
  print(0)
  exit()
h = list(map(int, input().split()))
maxi = sum(h)
f = [e for e in h]

for i in range(n - m - 1):
  for j in range(n - 1, i, -1):
    res = maxi
    for k in range(i, j):
      res = min(res, f[k] + max(0, h[j] - h[k]))
    f[j] = res
  
print(min(f[n - m - 1:]))

Solution (Python):
import sys
sys.setrecursionlimit(2147483647)
INF=float("inf")
MOD=10**9+7
input=lambda:sys.stdin.readline().rstrip()
def resolve():
    n,k=map(int,input().split())
    H=[0]+list(map(int,input().split()))

    
    dp=[[INF]*(n-k+1) for i in range(n+1)]
    dp[0][0]=0

    for i in range(1,n+1):
        for j in range(1,n-k+1):
            dp[i][j]=min(dp[k][j-1]+max(0,H[i]-H[k]) for k in range(i))


    print(min(dp[i][n-k] for i in range(n+1)))
resolve()

Solution (Python):
n, k = map(int, input().split())
h = list(map(int, input().split())) + [0]


dp = [[[10**12 for _ in range(n+1)] for _ in range(k+1)] for _ in range(n+1)]
dp[0][0][0] = 0

for a in range(n):
	for b in range(k+1):

		for c in range(a+1):
			
			if b < k:
				dp[a+1][b+1][c] = min(dp[a+1][b+1][c], dp[a][b][c])

			
			dp[a+1][b][a+1] = min(dp[a+1][b][a+1], dp[a][b][c] + max(0, h[a] - h[c-1]))

print(min(dp[n][k]))

Solution (Python):
def solve():
    from sys import stdin
    f_i = stdin
    
    N, K = map(int, f_i.readline().split())
    H = tuple(map(int, f_i.readline().split()))
    
    if N == K:
        return 0
    
    dp1 = list(H)
    for i in range(1, N - K):
        dp2 = dp1[:i]
        for x, H_x in enumerate(H[i:], start=i):
            v = min(dp_j + max(0, H_x - H_j) for dp_j, H_j in zip(dp1[i-1:x], H[i-1:x]))
            dp2.append(v)
        dp1 = dp2
    return min(dp1[N-K-1:])

print(solve())

Solution (Python):
n, k = map(int, input().split())
h = list(map(int, input().split()))

if k == n:
    print(0)
    exit()

dp = [[0 for _ in range(n)] for _ in range(n-k)]

dp[0] = [] + h

for x in range(1, n-k):
    for y in range(n):
        temp = float('inf')
        for i in range(y):
            temp = min(temp, dp[x-1][i] + max(0, h[y] - h[i]))
        dp[x][y] = temp



print(min(dp[n-k-1]))

Solution (Python):
N, K = map(int, input().split())
H = [0] + list(map(int, input().split()))
dp = [[10 ** 100] * (N-K+1) for _ in range(N+1)]
dp[0][0] = 0
for x in range(1, N+1):
    for y in range(1, min(x+1, N-K+1)):
        dp[x][y] = min([dp[i][y-1] + max(H[x] - H[i], 0) for i in range(x)])
print(min([dp[i][N-K] for i in range(N+1)]))

Solution (Python):
N, K = map(int, input().split())
H = [0] + [int(a) for a in input().split()]
X = [[1<<100] * (N-K+1) for _ in range(N+1)]
X[0][0] = 0
for i in range(1, N+1):
    for j in range(1, min(i+1, N-K+1)):
        X[i][j] = min([X[ii][j-1] + max(H[i] - H[ii], 0) for ii in range(i)])

print(min([x[-1] for x in X]))

Solution (Python):
N, K = map(int, input().split())
H = list(map(int, input().split()))

N += 1
H = [0] + H

DP = [[float('inf')] * N for _ in range(N)]
DP[0][0] = 0
for i in range(1, N):
  DP[i][1] = H[i]
  for j in range(2, i + 1): 
    for k in range(1, i):
      DP[i][j] = min(DP[i][j], DP[k][j - 1] + max(0, H[i] - H[k]))

ans = float('inf')
for i in range(N):
    ans = min(ans, DP[i][N - K - 1])

print(ans)

Solution (Python):
N, K = map(int, input().split())
H = [0] + [int(a) for a in input().split()]
X = [[1<<100] * (N-K+1) for _ in range(N+1)]
X[0][0] = 0
for i in range(1, N+1):
    for j in range(1, min(i+1, N-K+1)):
        X[i][j] = min([X[ii][j-1] + max(H[i] - H[ii], 0) for ii in range(i)])

print(min([x[-1] for x in X]))

Solution (Python):
n, k = list(map(int, input().split()))
hs = [0] + list(map(int, input().split())) 


max_val = sum([max(hs[i + 1] - hs[i], 0) for i in range(n)])
dp = [[max_val for _ in range(n + 1)] for _ in range(n + 1)]

dp[0][0] = 0
for i in range(1, n + 1):
	for j in range(1, n + 1):	
		dp[i][j] = min([dp[i - 1][l] + max(hs[j] - hs[l], 0) for l in range(j)])

print(min([dp[n - k][l] for l in range(n + 1)]))

Solution (Python):
n,k=map(int,input().split())
h=list(map(int,input().split()))
h.insert(0,0)
dp=[[float("inf")]*(n-k+1) for _ in range(n+1)]
dp[0][0]=0
for i in range(1,n+1):
    for j in range(1,n-k+1):
        now=float("inf")
        for l in range(i):
            now=min(dp[l][j-1]+max(0,h[i]-h[l]),now)
        dp[i][j]=now

ans=float("inf")
for i in range(1,n+1):
    ans=min(ans,dp[i][n-k])

print(ans if n>k else 0)

Solution (Python):
N, K = map(int, input().split())
H = list(map(int, input().split()))


if N <= K:
    print(0)
    exit()


dp = [[float('inf')] * (N + 1) for i in range(N + 1)]
dp[0][0] = 0

for i, h in enumerate(H, start=1):
    dp[i][1] = h


for i in range(1, N + 1):
    for j in range(2, N + 1):
        for x in range(1, i):
            dp[i][j] = min(dp[i][j], dp[x][j - 1] + max(0, H[i - 1] - H[x - 1]))


ans = float('inf')
for i in range(N + 1):
    ans = min(ans, dp[i][max(0,  N - K)])

print(ans)

Solution (Python):
N, K = map(int, input().split())
H = list(map(int, input().split()))
H = [0] + H


dp = [[float('inf')] * (N + 1) for i in range(N + 1)]
dp[0][0] = 0

for i in range(1, N + 1):
    for j in range(1, N + 1):
        for x in range(i):
            dp[i][j] = min(dp[i][j], dp[x][j - 1] + max(0, H[i] - H[x]))


ans = float('inf')
for i in range(N + 1):
    ans = min(ans, dp[i][max(0,  N - K)])

print(ans)

Solution (Python):



N,K=map(int, input().split())
H=list(map(int, input().split()))
G=[0]
G.extend(H[:])

dp=[[0]*(N+1) for i in range(N-K+1)]


tempa=0
if K<N-1:
    for jtemp in range(N):
        j=jtemp+1
        dp[1][j]=G[j]
    for itemp in range(N-K-1):
        i=itemp+2
        for jtemp in range(N-(i-1)):
            j=jtemp+i
            temp=int(N*1e9)
            
            for ktemp in range(j-(i-1)):
                k=ktemp+i-1
                val=G[j]-G[k]
                if val<0:
                    val=0
                if temp>dp[i-1][k]+val:
                    temp=dp[i-1][k]+val
            dp[i][j]=temp
    tempa=dp[N-K][-1]
    for jtemp in range(N):
        j=jtemp+1
        if tempa>dp[N-K][j] and dp[N-K][j]!=0:
            tempa=dp[N-K][j]
elif N-K==1:
    tempa=min(H[:])
else:
    tempa=0
print(tempa)

Solution (Python):
n, k = map(int, input().split())
h = list(map(int, input().split()))
INF = 10**18

k = n - k

dp = [[INF]*(k+1) for i in range(n+1)]
dp[0][0] = 0


for i in range(n):
    
    for j in range(k):
        if j == 0:
            dp[i+1][j+1] = min(dp[0][j] + h[i], dp[i+1][j+1])
            continue
        
        for last_i in range(i):
            if last_i + 1 < j:
                continue
            dp[i+1][j+1] = min(dp[last_i+1][j] + max(h[i] - h[last_i], 0), dp[i+1][j+1])

ans = 10**18
for i in range(n+1):
    ans = min(dp[i][k], ans)

print(ans)

Solution (Python):











import sys
sys.setrecursionlimit(10**6)
input=sys.stdin.readline
from math import floor,ceil,sqrt,factorial,log 
from heapq import heappop, heappush, heappushpop
from collections import Counter,defaultdict,deque
from itertools import accumulate,permutations,combinations,product,combinations_with_replacement
from bisect import bisect_left,bisect_right
from copy import deepcopy
inf=float('inf')
mod = 10**9+7
def pprint(*A): 
    for a in A:     print(*a,sep='\n')
def INT_(n): return int(n)-1
def MI(): return map(int,input().split())
def MF(): return map(float, input().split())
def MI_(): return map(INT_,input().split())
def LI(): return list(MI())
def LI_(): return [int(x) - 1 for x in input().split()]
def LF(): return list(MF())
def LIN(n:int): return [I() for _ in range(n)]
def LLIN(n: int): return [LI() for _ in range(n)]
def LLIN_(n: int): return [LI_() for _ in range(n)]
def LLI(): return [list(map(int, l.split() )) for l in input()]
def I(): return int(input())
def F(): return float(input())
def ST(): return input().replace('\n', '')
def main():
    N,K = MI()
    H=LI()
    
    dp = [[0]+[inf]*(N) for _ in range(N)] 
    for i in range(N):
        dp[i][1] = H[i]
    dp[0][1]=H[0]
    for right in range(N):
        for size in range(2,N+1):

            for i in range(right):
                dp[right][size] = min(dp[right][size], dp[i][size-1]+max(0, H[right]-H[i]))
    ans = inf 
    for i in range(N):
        ans = min(ans,dp[i][N-K])
    
    print(ans)
if __name__ == '__main__':
    main()

Solution (Python):
N, K = map(int, input().split())
H = [0] + list(map(int, input().split())) + [0]


dp = [[float('inf') for i in range(K+1)] for j in range(N+2)]
dp[0] = [0 for i in range(K+1)]

def cost(i, j):
    return max(0, H[j] - H[i])

for i in range(1, N+2):
    for j in range(K+1):
        for d in range(j+1):
            if i-d-1 < 0: break
            dp[i][j] = min(dp[i][j], cost(i-d-1, i) + dp[i-d-1][j-d])
                
print(dp[-1][K])

Solution (Python):
N, K = list(map(int, input().split()))
H = list(map(int, input().split()))

N += 1
H = [0] + H

inf = 10 ** 15
DP = [[inf] * N for _ in range(N)]
DP[0][0] = 0
for i in range(1, N):
  DP[i][1] = H[i]
  for j in range(2, i + 1): 
    for k in range(1, i):
      DP[i][j] = min(DP[i][j], DP[k][j - 1] + max(0, H[i] - H[k]))

ans = inf
for i in range(N):
    ans = min(ans, DP[i][N - K - 1])

print(ans)

Solution (Python):
import sys,bisect
input = sys.stdin.readline

n,k = map(int,input().split())
h = list(map(int,input().split()))
hs = [0]+sorted(h)

if k==0:
    res = h[0]
    for i in range(1,n):
        res += max(0,h[i]-h[i-1])
    print(res)
    exit()


dp = [[[10**12]*(n+1) for i in range(k+1)] for j in range(n)]

kk = bisect.bisect_left(hs,h[0])
dp[0][0][kk] = h[0]
dp[0][1][0] = 0

for i in range(1,n):
    kk = bisect.bisect_left(hs,h[i])
    
    for j in range(k+1):
        tmp = 10**12
        for l in range(n):
            tmp = min(tmp,dp[i-1][j][l]+max(0,hs[kk]-hs[l]))
        dp[i][j][kk] = tmp

    
    for j in range(1,k+1):
        for l in range(n):
            dp[i][j][l] = min(dp[i][j][l],dp[i-1][j-1][l])

res = 10**12
for j in range(k+1):
    for l in range(n):
        res = min(res,dp[-1][j][l])
print(res)

Solution (Python):
def f_laminate(INF=float('inf')):
    
    N, K = map(int, input().split())
    H = [0] + list(map(int, input().split()))

    
    dp = [[INF] * (N - K + 1) for _ in range(N + 1)]
    dp[0][0] = 0
    for x in range(1, N + 1):
        for y in range(1, N - K + 1):
            for i in range(x):
                dp[x][y] = min(dp[x][y], dp[i][y - 1] + max(0, H[x] - H[i]))

    ans = INF
    for i in range(N + 1):
        ans = min(ans, dp[i][N - K])
    return ans

print(f_laminate())

Solution (Python):
import numpy as np

n, k = map(int, input().split())
hhh = list(map(int, input().split()))
hhh = np.array([0] + hhh, dtype=np.int64)
INF = 10 ** 18
dp = np.full((n + 1, k + 1), fill_value=INF, dtype=np.int64)
dp[0, 0] = 0
for i, h in enumerate(hhh[1:], start=1):
    ndp = np.full((n + 1, k + 1), fill_value=INF, dtype=np.int64)
    ndp[:n, 1:] = dp[:n, :-1]
    ndp[i] = (dp + np.maximum(0, h - hhh)[:, np.newaxis]).min(axis=0)
    dp = ndp

print(dp.min())

Solution (Python):
import sys
input = sys.stdin.readline

N,K = map(int,input().split())
H = [0]+list(map(int,input().split()))+[0]

DP=[[1<<60]*(K+1) for i in range(N+2)]

for k in range(K+1):
    DP[0][k]=0

for i in range(1,N+2):
    
    for k in range(K+1):
        for j in range(k+1):
            DP[i][k]=min(DP[i][k],DP[i-j-1][k-j]+max(0,H[i]-H[i-j-1]))
        
print(min(DP[-1]))

Solution (Python):
def main():
    N, K = map(int, input().split())
    H = [0] + list(map(int, input().split()))
    dp = [[float("inf")] * (N+1) for _ in range(N+1)]
    dp[0][0] = 0
    for i in range(1, N+1):
        for j in range(i):
            diff = max(H[i] - H[j], 0)
            for k in range(min(N-K, j+1)):
                dp[i][k+1] = min(dp[i][k+1], dp[j][k] + diff)
    ans = float("inf")
    for i in range(N+1):
        ans = min(ans, dp[i][N-K])
    print(ans)


if __name__ == "__main__":
    main()

Solution (Python):
import sys
sys.setrecursionlimit(2147483647)
INF=float("inf")
MOD=10**9+7
input=lambda :sys.stdin.readline().rstrip()
def resolve():
    n,k=map(int,input().split())
    H=[0]+list(map(int,input().split()))

    dp=[[INF]*(n-k+1) for _ in range(n+1)]
    dp[0][0]=0

    for x in range(1,n+1):
        for y in range(1,n-k+1):
            dp[x][y]=min(dp[x0][y-1]+max(0,H[x]-H[x0]) for x0 in range(x))

    print(min(dp[x][n-k] for x in range(n+1)))
resolve()

Solution (Python):
import sys
sys.setrecursionlimit(2147483647)
INF=float("inf")
MOD=10**9+7
input=lambda :sys.stdin.readline().rstrip()
def resolve():
    n,k=map(int,input().split())
    H=[0]+list(map(int,input().split()))

    dp=[[INF]*(n-k+1) for _ in range(n+1)]
    dp[0][0]=0

    for x in range(1,n+1):
        for y in range(1,n-k+1):
            dp[x][y]=min(dp[x0][y-1]+max(0,H[x]-H[x0]) for x0 in range(x))

    print(min(*(dp[x][n-k] for x in range(n+1))))
resolve()

Solution (Python):
import numpy as np

n, k = map(int, input().split())
h = np.array(input().split(), dtype=np.int)

if k < n:
  dp = np.zeros((n - k, n), dtype=np.int)
  dp[0] = h
  for i in range(n - k - 1):
    for j in range(i + 1, n):
      dp[i+1, j] = np.min(dp[i][i:j] + np.maximum(h[j] - h[i:j], 0))
  print(dp[n-k-1, n-k-1:].min())
else:
  print(0)

Solution (Python):
N,K = map(int, input().split())
H = [int(h) for h in input().split()]

dp = [[10**13]*N for _ in range(N)]
dp[0][0] = H[0]
    
for i in range(1, N):
    for j in range(i+1):
        if j == 0:
            dp[i][j] = H[i]
            continue
        for k in range(i):
            dp[i][j] = min(dp[i][j], dp[k][j-1]+max(0, H[i]-H[k]))
            
if N == K:
    ans = 0
else:
    ans = 10**13
    for i in range(N):
        ans = min(ans, dp[i][N-K-1])
        
print(ans)

Solution (Python):
inpl = lambda: list(map(int,input().split()))
N, K = inpl()
H = [0] + inpl() + [0]
dp = [[0]*(K+1) for _ in range(N+2)]
for n in range(1,N+2):
    for k in range(K+1):
        if k >= n-1:
            dp[n][k] = H[n]
        else:
            dp[n][k] = min(dp[n-1-l][k-l] + max(0,H[n]-H[n-1-l]) for l in range(k+1))
print(dp[-1][-1])

Solution (Python):
N, K = [int(s) for s in input().split(' ')]
H = [int(s) for s in input().split(' ')]



dp = [[] for _ in range(N)]

for n, h in enumerate(H):
  if n == 0:
    before = [{0: 0}] + [{} for _ in range(K)]
  else:
    before = dp[n-1]
  
  dp[n] = [{}] + before[:-1]
  current = dp[n]
  
  for k in range(K+1):
    
    for h_before, count in before[k].items():
      candidate = current[k].get(h, float("inf"))
      if h_before >= h:
        current[k][h] = min(candidate, count)
      else:
        current[k][h] = min(candidate, count + h - h_before)
      
  

print(min([v for d in dp[-1] for v in d.values()]))

Solution (Python):

import sys
input = sys.stdin.readline
MOD = 10**9 + 7
INF = 10**13

n, K = [int(item) for item in input().split()]
h = [0] + [int(item) for item in input().split()]


dp = [[[INF] * (n + 1) for _ in range(n + 1)] for _ in range(n + 1)]
for i, item in enumerate(h):
    if i == 0:
        dp[0][0][0] = 0
        continue
    for j in range(n-1, -1, -1):
        for k in range(n-1, -1, -1):
            if dp[i-1][j][k] == INF:
                continue
            
            dp[i][j+1][k] = min(dp[i][j+1][k], dp[i-1][j][k])
            
            dp[i][j][i] = min(dp[i][j][i], dp[i-1][j][k] + max(0, h[i] - h[k]))
            
ans = INF
for j in range(n+1):
    ans = min(ans, dp[n][K][j])

print(ans)

Solution (Python):
import sys

sys.setrecursionlimit(10 ** 6)
int1 = lambda x: int(x) - 1
p2D = lambda x: print(*x, sep="\n")

def main():
    inf = 10 ** 16
    n, k = map(int, input().split())
    hh = [0] + list(map(int, input().split()))
    dp = [[0] * (k + 1) for _ in range(n + 1)]
    for i in range(1, n + 1):
        h = hh[i]
        for j in range(k + 1):
            v = inf
            for nd in range(k + 1):
                if i - 1 - nd < 0 or j - nd < 0: break
                v = min(v, dp[i - 1 - nd][j - nd] + max(0, h - hh[i - 1 - nd]))
            dp[i][j] = v
    print(min(dp[n-d][k-d] for d in range(min(n+1,k+1))))

main()

Solution (Python):
def solve(n, k, h_list):
    if k == n:
        return 0
    
    large = sum(h_list) + 1
    dp = [[large] * n for _ in range(n + 1)]
    dp[1][0] = h_list[0]
    
    for i in range(1, n):
        for s in range(2, n + 1):
            dp[s][i] = min([dp[s - 1][j] + max(0, h_list[i] - h_list[j]) for j in range(i)])
        dp[1][i] = h_list[i]
    
    return min(dp[n - k])


def main():
    n, k = map(int, input().split())
    h_list = list(map(int, input().split()))
    res = solve(n, k, h_list)
    print(res)


def test():
    assert solve(4, 1, [2, 3, 4, 1]) == 3
    assert solve(6, 2, [8, 6, 9, 1, 2, 1]) == 7
    assert solve(10, 0, [1, 1000000000, 1, 1000000000, 1, 1000000000, 1, 1000000000, 1, 1000000000]) == 4999999996


if __name__ == "__main__":
    
    main()

Solution (Python):

from collections import defaultdict,deque
from heapq import heappush, heappop
from bisect import bisect_left, bisect_right
import sys, random, itertools, math
sys.setrecursionlimit(10**5)
input = sys.stdin.readline
sqrt = math.sqrt
def LI(): return list(map(int, input().split()))
def LF(): return list(map(float, input().split()))
def LI_(): return list(map(lambda x: int(x)-1, input().split()))
def II(): return int(input())
def IF(): return float(input())
def LS(): return list(map(list, input().split()))
def S(): return list(input().rstrip())
def IR(n): return [II() for _ in range(n)]
def LIR(n): return [LI() for _ in range(n)]
def FR(n): return [IF() for _ in range(n)]
def LFR(n): return [LI() for _ in range(n)]
def LIR_(n): return [LI_() for _ in range(n)]
def SR(n): return [S() for _ in range(n)]
def LSR(n): return [LS() for _ in range(n)]
mod = 1000000007
inf = float('INF')
from copy import deepcopy


def solve():
    n, k = LI()
    h = [0] + LI()
    d = defaultdict(int)
    d[(0, 0)] = 0
    for i in range(1, n + 1):
        nd = defaultdict(lambda: inf)
        for key, value in d.items():
            a, b = key
            if nd[(i, b)] > value + (h[i] - h[a] if h[i] > h[a] else 0):
                nd[(i, b)] = value + (h[i] - h[a] if h[i] > h[a] else 0)
            if b + 1 > k:
                continue
            if nd[(a, b + 1)] > value:
                nd[(a, b + 1)] = value
        d = nd
    ans = inf
    for i in range(n + 1):
        for j in range(k + 1):
            ans = min(ans, d[(i, j)])
    print(ans)
    return



if __name__ == '__main__':
    solve()

Solution (Python):

from collections import defaultdict,deque
from heapq import heappush, heappop
import sys
import math
import bisect
import random
def LI(): return [int(x) for x in sys.stdin.readline().split()]
def I(): return int(sys.stdin.readline())
def LS():return [list(x) for x in sys.stdin.readline().split()]
def S():
    res = list(sys.stdin.readline())
    if res[-1] == "\n":
        return res[:-1]
    return res
def IR(n):
    return [I() for i in range(n)]
def LIR(n):
    return [LI() for i in range(n)]
def SR(n):
    return [S() for i in range(n)]
def LSR(n):
    return [LS() for i in range(n)]

sys.setrecursionlimit(1000000)
mod = 1000000007

def solve():
    n,k = LI()
    h = LI()
    h.insert(0,0)
    dp = [[float("inf")]*(n+1) for i in range(n+1)]
    dp[0][0] = 0
    for i in range(n):
        ni = i+1
        hi = h[ni]
        for s in range(n):
            ns = s+1
            for j in range(ni):
                hj = h[j]
                nd = dp[j][s]+max(0,hi-hj)
                if nd < dp[ni][ns]:
                    dp[ni][ns] = nd
    ans = min([dp[i][n-k] for i in range(n+1)])
    print(ans)
    return


if __name__ == "__main__":
    solve()

Solution (Python):
import sys


N,K = map(int,input().split())

if N == K:
    print (0)
    sys.exit()

H = list(map(int,input().split()))


dp = [[None] * (N-K+1) for i in range(N) ]

for i in range(N):

    nh = H[i]

    dp[i][1] = nh

    for j in range(i):
        for k in range(N-K):

            if dp[j][k] != None:

                if dp[i][k+1] == None:
                    
                    dp[i][k+1] = dp[j][k] + max(0, H[i]-H[j])

                else:

                    dp[i][k+1] = min(dp[i][k+1] , dp[j][k] + max(0, H[i]-H[j]))

ans = float("inf")
for i in range(N):

    if dp[i][-1] != None:
        ans = min(ans,dp[i][-1])

print (ans)

Solution (Python):
import sys
import math
from collections import defaultdict

sys.setrecursionlimit(10**7)
def input():
    return sys.stdin.readline()[:-1]

mod = 10**9 + 7

def I(): return int(input())
def II(): return map(int, input().split())
def III(): return list(map(int, input().split()))
def Line(N,num):
    if N<=0:
        return [[]]*num
    elif num==1:
        return [I() for _ in range(N)]
    else:
        read_all = [tuple(II()) for _ in range(N)]
        return map(list, zip(*read_all))



N,K = II()
H = III()

if N==K:
    print(0)
    exit()

dp = [[float('inf')]*(N-K+1) for _ in range(N)]

for x in range(N):
    for y in range(N-K+1):
        if x+1<y:
            continue
        elif y==0:
            dp[x][y] = float('inf')
        elif y==1:
            dp[x][y] = H[x]
        else:
            val = float('inf')
            for i in range(x):
                now = dp[i][y-1] + max(0,H[x]-H[i])
                if now<val:
                    val = now
            dp[x][y] = val

ans = float('inf')
for i in range(N):
    if dp[i][N-K]<ans:
        ans = dp[i][N-K]

print(ans)

Solution (Python):
import sys
input=sys.stdin.readline

def main():
    n,k=map(int,input().split())
    H=[0]+list(map(int,input().split()))
    DP=[[10**12]*(n-k+1) for _ in range(n+1)]
    DP[0][0]=0
    for x in range(1,n+1):
        for y in range(1,n-k+1):
            for i in range(x):
                DP[x][y]=min(DP[x][y],DP[i][y-1]+max(0,H[x]-H[i]))
    print(min(DP[i][-1] for i in range(n+1)))

if __name__=='__main__':
    main()

Solution (Python):

import sys
sys.setrecursionlimit(10**6)
readline = sys.stdin.readline 




n,k = [int(i) for i in readline().split()]
a = [0]+[int(i) for i in readline().split()]

n += 1

INF = 10**18

K = n-k-1

dp = [[INF]*n for _ in range((K+1))]
dp[0][0] = 0



for i in range(1,n):
    ndp = [c[:] for c in dp]
    
    for l in range(min(i,K)):
        for now in range(0,i):
            ndp[l+1][i] = min(ndp[l+1][i], ndp[l][now]+max(0,a[i]-a[now]))
    
    dp = ndp
    


print(min(dp[-1]))

Solution (Python):
N,K = map(int,input().split())
H = list(map(int,input().split()))
H = [0]+H
dp = [[10**12]*(N+1) for _ in range(N+1)]
dp[0][0] = 0
for x in range(N+1):
    for y in range(1,N+1):
        for z in range(x):
            dp[x][y] = min(dp[x][y],dp[z][y-1]+max(H[x]-H[z],0))

ans = 10**12
for x in range(N+1):
    ans = min(dp[x][N-K],ans)

print(ans)

Solution (Python):
import sys
N, K = map(int, input().split())
H = list(map(int, input().split()))
if N<=K:
    print(0)
    sys.exit()
dp = [[[float('inf')]*(K+2) for i in range(N+2)] for j in range(N+1)]
dp[0][0][0] = H[0]
dp[0][-1][1] = 0
for i in range(N-1):
    for j in range(i+1):
        for k in range(K+1):
            if H[j]>H[i+1]:
                dp[i+1][j][k+1] = min(dp[i][j][k], dp[i+1][j][k+1])
                dp[i+1][i+1][k] = min(dp[i][j][k], dp[i+1][i+1][k])
            else:
                dp[i+1][i+1][k] = min(dp[i+1][i+1][k], dp[i][j][k]+H[i+1]-H[j])
                dp[i+1][j][k+1] = min(dp[i][j][k], dp[i+1][j][k+1])
    for k in range(K):
        dp[i+1][-1][k+1] = min(dp[i][-1][k], dp[i+1][-1][k+1])
        dp[i+1][i+1][k] = min(dp[i+1][i+1][k], dp[i][-1][k]+H[i+1])

ans = float('inf')
for i in range(K+1):
    res = min(dp[N-1][j][i] for j in range(N))
    ans = min(ans, res)
print(ans)

Solution (Python):
from collections import defaultdict

n, k = map(int, input().split())
hhh = list(map(int, input().split()))
INF = 10 ** 18
dp = defaultdict(lambda: INF)
dp[0] = 0
mask1 = (1 << 10) - 1
mask2 = ((1 << 63) - 1) ^ mask1

for h in hhh:
    ndp = defaultdict(lambda: INF)
    h_key = h << 10
    for changed_prev_h, operate in dp.items():
        changed = changed_prev_h & mask1
        prev_h = changed_prev_h >> 10
        if h == prev_h:
            key = h_key + changed
            ndp[key] = min(ndp[key], operate)
        elif h > prev_h:
            key = h_key + changed
            ndp[key] = min(ndp[key], operate + h - prev_h)
            if changed < k:
                key = changed_prev_h + 1
                ndp[key] = min(ndp[key], operate)
        else:
            key = h_key + changed
            ndp[key] = min(ndp[key], operate)
            if changed < k:
                key = changed_prev_h + 1
                ndp[key] = min(ndp[key], operate)
    
    
    
    dp = ndp
print(min(dp.values()))

Solution (Python):



N, K = map(int, input().split())
H = [0] + list(map(int, input().split())) + [0]
N += 1
inf = 10**18
dp = [[inf]*(K+1) for _ in range(N+1)]
dp[0][0] = 0
for i, h in enumerate(H[1:], 1):
    for j in range(K+1):
        for k in range(K+1):  
            if i-k-1 < 0 or j-k < 0:
                continue
            h_p = H[i-k-1]
            dp[i][j] = min(dp[i][j], dp[i-k-1][j-k] + max(0, h - h_p))



print(min(dp[-1]))