Problem:
 Score : 100 points    Problem Statement There are N slimes lining up in a row.
Initially, the i -th slime from the left has a size of a_i .  Taro is trying to combine all the slimes into a larger slime.
He will perform the following operation repeatedly until there is only one slime:   Choose two adjacent slimes, and combine them into a new slime. The new slime has a size of x + y , where x and y are the sizes of the slimes before combining them. Here, a cost of x + y is incurred. The positional relationship of the slimes does not change while combining slimes.   Find the minimum possible total cost incurred.      Constraints  All values in input are integers.  2 \leq N \leq 400  1 \leq a_i \leq 10^9         Input Input is given from Standard Input in the following format:  N  a_1  a_2  \ldots  a_N       Output Print the minimum possible total cost incurred.        Sample Input 1 4
10 20 30 40      Sample Output 1 190  Taro should do as follows (slimes being combined are shown in bold):   ( 10 , 20 , 30, 40) → ( 30 , 30, 40)  ( 30 , 30 , 40) → ( 60 , 40)  ( 60 , 40 ) → ( 100 )        Sample Input 2 5
10 10 10 10 10      Sample Output 2 120  Taro should do, for example, as follows:   ( 10 , 10 , 10, 10, 10) → ( 20 , 10, 10, 10)  (20, 10 , 10 , 10) → (20, 20 , 10)  (20, 20 , 10 ) → (20, 30 )  ( 20 , 30 ) → ( 50 )        Sample Input 3 3
1000000000 1000000000 1000000000      Sample Output 3 5000000000  The answer may not fit into a 32-bit integer type.       Sample Input 4 6
7 6 8 6 1 1      Sample Output 4 68  Taro should do, for example, as follows:   (7, 6, 8, 6, 1 , 1 ) → (7, 6, 8, 6, 2 )  (7, 6, 8, 6 , 2 ) → (7, 6, 8, 8 )  ( 7 , 6 , 8, 8) → ( 13 , 8, 8)  (13, 8 , 8 ) → (13, 16 )  ( 13 , 16 ) → ( 29 )

Solution (Python):
def main():
    N = int(input())
    A = [int(a) for a in input().split()]
    INF = 10 ** 18
    dp = [[INF] * N for _ in range(N)]
    for i in range(N):
        dp[i][i] = 0
    acc = [0]
    for a in A:
        acc.append(acc[-1] + a)
    for w in range(2, N+1):
        for left in range(N):
            right = left + w - 1
            if right >= N:
                continue
            wsum = acc[right + 1] - acc[left]
            for mid in range(left, right):
                dp[left][right] = min(dp[left][right], dp[left][mid] + dp[mid+1][right] + wsum)
    print(dp[0][N-1])


if __name__ == '__main__':
    main()

Solution (Python):
n = int(input())
a = list(map(int, input().split()))
ruiseki = [0] * (n+1)
for i in range(n):
    ruiseki[i+1] = ruiseki[i] + a[i]

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

def solve(l, r):
    if dp[l][r] != -1:
        return dp[l][r]
    if r - l == 1:
        dp[l][r] = 0
        return dp[l][r]
    ans = 10**18
    for i in range(l+1, r):
        ans = min(ans, solve(l, i) + solve(i, r) + ruiseki[r] - ruiseki[l])
    dp[l][r] = ans
    return dp[l][r]

solve(0, n)
print(dp[0][n])

Solution (Python):
def f():
    import sys
    import numpy as np
    input=sys.stdin.readline
    n=int(input())
    a=np.array([0]+[int(j) for j in input().split()])
    np.cumsum(a,out=a)
    dp=np.zeros((n,n+1),np.int64)

    for i in range(1,n):
        l=np.arange(n-i)
        r=np.arange(i+1,n+1)
        m=(np.arange(1,i+1)+l[:,np.newaxis]).T
        dp[l,r]=np.amin(dp[l,m]+dp[m,r],0)+a[r]-a[l]
    print(dp[0][n])
f()

Solution (Python):
import sys
sys.setrecursionlimit(160000)

N = int(input())
A = [int(a) for a in input().split()]

dp = [[0]*N for _ in range(N)]
flag = [[False]*N for _ in range(N)]
S = [0]*(N+1)

for i in range(N):
    flag[i][i] = True

S[0] = A[0]
for i in range(N):
    S[i+1] = S[i]+A[i]
    
def f(l, r):
    if flag[l][r]:
        return dp[l][r]
    flag[l][r] = True
    res = 10**18
    for m in range(l, r):
        res = min(res, f(l, m)+f(m+1, r))
    dp[l][r] = res+S[r+1]-S[l]
    return dp[l][r]

print(f(0, N-1))

Solution (Python):
def main(sample_file = ''):

    """ convenient functions
    
    
    
    
    
    """

    """convenient decorator
    
    
        
        
        
        
        
        
        
        
        
        
    """
    
    
    import sys
    sys.setrecursionlimit(10**7)
    from itertools import accumulate, combinations, permutations, product 
    
    from math import factorial, ceil, floor, sqrt
    def factorize(n):
        """return the factors of the Arg and count of each factor
        
        Args:
            n (long): number to be resolved into factors
        
        Returns:
            list of tuples: factorize(220) returns [(2, 2), (5, 1), (11, 1)]
        """
        fct = []  
        b, e = 2, 0  
        while b * b <= n:
            while n % b == 0:
                n = n // b
                e = e + 1
            if e > 0:
                fct.append((b, e))
            b, e = b + 1, 0
        if n > 1:
            fct.append((n, 1))
        return fct
    def combinations_count(n, r):
        """Return the number of selecting r pieces of items from n kinds of items.
        
        Args:
            n (long): number
            r (long): number
        
        Raises:
            Exception: not defined when n or r is negative
        
        Returns:
            long: number
        """
        
        if n < 0 or r < 0:
            raise Exception('combinations_count(n, r) not defined when n or r is negative')
        if n - r < r: r = n - r
        if r < 0: return 0
        if r == 0: return 1
        if r == 1: return n
        numerator = [n - r + k + 1 for k in range(r)]
        denominator = [k + 1 for k in range(r)]
        for p in range(2,r+1):
            pivot = denominator[p - 1]
            if pivot > 1:
                offset = (n - r) % p
                for k in range(p-1,r,p):
                    numerator[k - offset] /= pivot
                    denominator[k] /= pivot
        result = 1
        for k in range(r):
            if numerator[k] > 1:
                result *= int(numerator[k])
        return result
    def combinations_with_replacement_count(n, r):
        """Return the number of selecting r pieces of items from n kinds of items allowing individual elements to be repeated more than once.
        
        Args:
            n (long): number
            r (long): number
        
        Raises:
            Exception: not defined when n or r is negative
        
        Returns:
            long: number
        """
        if n < 0 or r < 0:
            raise Exception('combinations_with_replacement_count(n, r) not defined when n or r is negative')
        elif n == 0:
            return 1
        else:
            return combinations_count(n + r - 1, r)
    from bisect import bisect_left, bisect_right
    from collections import deque, Counter, defaultdict 
    from heapq import heapify, heappop, heappush, heappushpop, heapreplace,nlargest,nsmallest 
    from copy import deepcopy, copy 
    import operator
    from operator import itemgetter 
    
    
    from functools import reduce, lru_cache
    def chmin(x, y):
        """change minimum
        if x > y, x = y and return (x, True).
        convenient when solving problems of dp[i]
        
        Args:
            x (long): current minimum value
            y (long): potential minimum value
        
        Returns:
            (x, bool): (x, True) when updated, else (x, False)
        """
        if x > y:
            x = y
            return (x, True)
        else:
            return (x, False)
    def chmax(x, y):
        """change maximum
        if x < y, x = y and return (x, True).
        convenient when solving problems of dp[i]
        
        Args:
            x (long): current maximum value
            y (long): potential maximum value
        
        Returns:
            (x, bool): (x, True) when updated, else (x, False)
        """
        if x < y:
            x = y
            return (x, True)
        else:
            return (x, False)

    from fractions import gcd 
    def gcds(numbers):
        return reduce(gcd, numbers)
    def lcm(x, y):
        return (x * y) // gcd(x, y)
    def lcms(numbers):
        return reduce(lcm, numbers, 1)
    def make_divisors(n, reversed=False):
        """create list of divisors
        
        Args:
            number (int): number from which list of divisors is created
            reversed (bool, optional): ascending order if False. Defaults to False.
        
        Returns:
            list: list of divisors
        """
        divisors = set()
        for i in range(1, int(n**0.5)+1):
            if n % i == 0:
                divisors.add(i)
                divisors.add(n//i)
        return sorted(list(divisors),reverse=reversed)
    
    
    
    INF = 10 ** 18
    MOD = 10 ** 9 + 7
    modpow = lambda a, n, p = MOD: pow(a, n, p) 
    def modinv(a, p = MOD):
        
        
        return modpow(a, p-2, p)
    def modinv_list(n, p = MOD):
        if n <= 1:
            return [0,1][:n+1]
        else:
            inv_t = [0,1]
            for i in range(2, n+1):
                inv_t += [inv_t[p % i] * (p - int(p / i)) % p]
            return inv_t
    def modfactorial_list(n, p = MOD):
        if n == 0:
            return [1]
        else:
            l = [0] * (n+1)
            tmp = 1
            for i in range(1, n+1):
                tmp = tmp * i % p
                l[i] = tmp
            return l
    def modcomb(n, k, fac_list = [], p = MOD):
        
        
        from math import factorial
        if n < 0 or k < 0 or n < k: return 0
        if n == 0 or k == 0: return 1
        if len(fac_list) <= n:
            a = factorial(n) % p
            b = factorial(k) % p
            c = factorial(n-k) % p
        else:
            a = fac_list[n]
            b = fac_list[k]
            c = fac_list[n-k]
        return (a * modpow(b, p-2, p) * modpow(c, p-2, p)) % p
    def modadd(a, b, p = MOD):
        return (a + b) % MOD
    def modsub(a, b, p = MOD):
        return (a - b) % p
    def modmul(a, b, p = MOD):
        return ((a % p) * (b % p)) % p
    def moddiv(a, b, p = MOD):
        return modmul(a, modpow(b, p-2, p))

    class UnionFindTree:
        """union find tree class
        TODO: fix this description...
        how to use (example):
        >>  uf = UnionFindTree(N) 
        >>  if uf.find_root(a) == uf.find_root(b):
        >>      do something
        >>  else:
        >>      do something
        >>      uf.unite(a, b)
        """
        def __init__(self, N):
            self.root = [-1] * (N+1)
            self.rank   = [0]  * (N+1)
            self.connected_num = [1] * (N+1)
    
        def find_root(self,x):
            root = self.root
            while root[x] != -1:
                x = root[x]
            return x
    
        def unite(self,x,y):
            root = self.root
            rank = self.rank
            connected_num = self.connected_num
            find_root = self.find_root
    
            rx = find_root(x)
            ry = find_root(y)
            if rx != ry:
                if rank[rx] < rank[ry]:
                    root[rx] = ry
                    rx,ry = ry,rx
                else:
                    if rank[rx] == rank[ry]:
                        rank[rx] += 1
                    root[ry] = rx       
                connected_num[rx] += connected_num[ry]

    
    
    
    
    

    def BellmanFord(N, M, ABC, vertex_start, vertex_end, value_if_inf = -1, find_shortest = False):
        """to calculate furthest or shortest length between vertex_start and vertex_end using BellmanFord algorithm
        
        Args:
            N (int): number of vertices
            M (int): number of edges
            ABC (list): [(ai, bi, ci) for _ in range(N)] where i-th edge is directed from vertex ai to vertex bi and the length is ci 
            vertex_start (int): start vertex. usually use 0.
            vertex_end (int): end vertex. usually use N-1.
            value_if_inf (int or string as you like, optional): value you want when the furthest (or shortest) distance is infinite (or -infinite). Defaults to -1.
            find_shortest (bool, optional): choose False to find furthest path. Defaults to False.
        
        Returns:
            int or string: normally int (but can be str if you set value_if_inf to str)
            
        Example:
                N, M, P = R()
                ABC = [R() for _ in range(M)]
                ABC = [(a-1, b-1, c-P) for a, b, c in ABC]
                print(BellmanFord(N, M, ABC, 0, N-1, value_if_inf = 'inf'))

        """

        def make_reachable_list(N, M, ABC, vertex_start, vertex_end):
            reachable_to_direct = defaultdict(list)
            reachable_from_direct = defaultdict(list)
            reachable_from_start = [False] * N
            reachable_to_end = [False] * N
            reachable_from_start[vertex_start] = True
            reachable_to_end[vertex_end] = True
            reachable_from_both_sides = [False] * N
            dfs_from_start = []
            dfs_to_end = []
            for a, b, c in ABC:
                reachable_to_direct[a].append(b)
                reachable_from_direct[b].append(a)
                if a == vertex_start:
                    dfs_from_start.append(b)
                    reachable_from_start[b] = True
                if b == vertex_end:
                    dfs_to_end.append(a)
                    reachable_to_end[a] = True
            while dfs_from_start:
                v = dfs_from_start.pop()
                for i in reachable_to_direct[v]:
                    if not reachable_from_start[i]:
                        reachable_from_start[i] = True
                        dfs_from_start.append(i)
            while dfs_to_end:
                v = dfs_to_end.pop()
                for i in reachable_from_direct[v]:
                    if not reachable_to_end[i]:
                        reachable_to_end[i] = True
                        dfs_to_end.append(i)
            for i in range(N):
                reachable_from_both_sides[i] = reachable_from_start[i] and reachable_to_end[i]
            return reachable_from_both_sides
        
        reachable_from_both_sides = make_reachable_list(N, M, ABC, vertex_start, vertex_end)
        
        if find_shortest:
            dist = [INF for i in range(N)]
        else:
            dist = [-INF for i in range(N)]
        
        dist[vertex_start] = 0
        for i in range(N):
            updated = False
            for a, b, c in ABC:
                if not reachable_from_both_sides[a]:
                    continue
                elif find_shortest:
                    update_condition = dist[a] + c < dist[b]
                else:
                    update_condition = dist[a] + c > dist[b]
                if dist[a] != INF and update_condition:
                    dist[b] = dist[a] + c
                    updated = True
                    if i == N-1:
                        return value_if_inf
            if not updated:
                break
        return dist[vertex_end]

    """ initialize variables and set inputs
    
        
        
            
            
    
        
        
        
        
        
        
        
    
        
        
        
        
    
        
        
    """

    
    r = lambda: sys.stdin.readline().strip()
    r_int = lambda: int(r())
    r_float = lambda: float(r())
    R = lambda: list(map(int, r().split()))
    R_map = lambda: map(int, r().split())
    R_float = lambda: list(map(float, r().split()))
    R_tuple = lambda: tuple(map(int, r().split()))

    """ how to treat input
    
    
    
    
    
    
    
    """

    
    if sample_file:
        sys.stdin = open(sample_file)
        
    
    

    N = r_int()
    A = R()
    
    dp = [[INF]*(N+1) for _ in range(N+1)]
    for i,a in enumerate(A):
        dp[i][i+1] = a
    for i in range(N):
        dp[i][i+1] = 0
    B = [0] + list(accumulate(A))
    for d in range(0,N+1):
        for i in range(0, N+1-d):
            for k in range(i+1, i+d):
                dp[i][i+d] = min(dp[i][k] + dp[k][i+d] + B[i+d] - B[i], dp[i][i+d])
                
    print(dp[0][N])


    
    
    

    """memo: how to use defaultdict of list
    
    Dic = defaultdict(list)
    
    Dic[x].append(y)
    
    for k, v in Dic.items():
    """
    
    """memo: how to solve binary problems
    
    >>> a = 5
    >>> bin_str_a = format(a, '
    >>> print(bin_str_a)
    0b0101 
    """
    
    """memo: how to solve the problem
    creating simple test/answer
    greed
    simple dp
    graph
    """

if __name__ == '__main__':
    main()

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

S = [0] * (N+1)
for i in range(N):
    S[i+1] = S[i] + a[i]

dp = [[float('inf') for _ in range(N)] for _ in range(N)]
for i in range(N):
    dp[i][i] = 0
for i in range(N-1):
    dp[i][i+1] = a[i] + a[i+1]
for d in range(2, N):
    for i in range(N - d):
        for k in range(d):
            dp[i][i+d] = min(dp[i][i+d], S[i+d+1] - S[i] + dp[i][i+k] + dp[i+k+1][i+d])

print(dp[0][N-1])

Solution (Python):
import itertools
inf=float("inf")
n=int(input())
a=list(map(int,input().split()))
for i in range(1,n):
    a[i]+=a[i-1]
a.append(0)
dp=[[0]*n for i in range(n)]
for l in range(1,n):
    for right in range(l,n):
        left=right-l
        num=inf
        for mid in range(left,right):
            num=min(num,dp[left][mid]+dp[mid+1][right])
        dp[left][right]=num+a[right]-a[left-1]
print(dp[0][n-1])

Solution (Python):
N = int(input())
slimes = [int(c) for c in input().split()]

cum_sum = [0]
for s in slimes:
    cum_sum.append(cum_sum[-1] + s)
dp = [[0] * N for _ in range(N)]
for L in range(N, -1, -1):
    for R in range(L, N):
        if R - L == 0:
            dp[L][R] = 0
        else:
            dp[L][R] = float('infinity')
            for i in range(L, R):
                dp[L][R] = min(dp[L][R], dp[L][i] + dp[i+1][R] + cum_sum[R+1] - cum_sum[L])

print(dp[0][N-1])

Solution (Python):
N = int(input())
A = list(map(int,input().split()))
A.insert(0,0)
B = [0 for _ in range(N+2)]
for i in range(N+1):
    B[i+1] = B[i]+A[i]
dp = [[0 for _ in range(N+2)] for _ in range(N+2)]
for i in range(N):
    dp[i][i+2] = A[i]+A[i+1]
for k in range(3,N+1):
    for i in range(1,N-k+2):
        dp[i][i+k] = dp[i][i+1]+dp[i+1][i+k]
        for j in range(i+2,i+k):
            dp[i][i+k] = min(dp[i][i+k],dp[i][j]+dp[j][i+k])
        dp[i][i+k] += B[i+k]-B[i]
print(dp[1][N+1])

Solution (Python):
n = int(input())
a = [int(x) for x in input().strip().split()]

c = [[None for i in range(n)] for j in range(n)]
s = [[0 for i in range(n)] for j in range(n)]

for i in range(n):
    c[i][i] = 0
    s[i][i] = a[i]

for i in range(n):
    for j in range(i+1,n):
        s[i][j] = s[i][j-1]+a[j]

def solve(i,j):
    if c[i][j] is not None:
        return c[i][j]
    mn = 10**100
    for k in range(i,j):
        mn = min(mn,solve(i,k)+solve(k+1,j)+s[i][k]+s[k+1][j])
    c[i][j] = mn
    return c[i][j]


print(solve(0,n-1))

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

dp = [[float('inf')] * n for _ in range(n)]
s = [0] * (n + 1)
for i in range(n):
    s[i + 1] += s[i] + a[i]
for L in range(n - 1, -1, -1):
    for R in range(L, n):
        if L == R:
            dp[L][R] = 0
        else:
            for i in range(L, R):
                dp[L][R] = min(dp[L][R], dp[L][i] + dp[i + 1][R] + s[R + 1] - s[L])
print(dp[0][n - 1])

Solution (Python):
def p_n():
    from itertools import accumulate
    n = int(input())
    *a, = map(int, input().split())
    ac = list(accumulate(a)) + [0]
    dp = [[0] * (n + 1) for _ in range(n + 1)]
    for i in range(2, n + 1):
        for j in range(n - i + 1):
            dp[i][j] = ac[j + i - 1] - ac[j - 1] + min(dp[k][j] + dp[i - k][j + k] for k in range(1, i))
    print(dp[-1][0])


if __name__ == '__main__':
    p_n()

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


n=int(input())
a=list(map(int, input().split()))
b=itertools.accumulate(a)
b=[0]+list(b)
dp=[[0]*(n) for i in range(n)]

x=float('inf')
for i in range(n-1,-1,-1):
    for j in range(i+1,n):
        if j>=i+2:
            for k in range(i,j):
                x=min(dp[i][k]+dp[k+1][j],x)
            dp[i][j]=x+(b[j+1]-b[i])
            x=float('inf')
        else:
            dp[i][j]=b[j+1]-b[i]
print(dp[0][-1])

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

sums = [[None for i in range(N)] for j in range(N)]
for i in range(N):
    for j in range(i, N):
        sums[i][j] = sum(slimes[i:j+1])

dp = [[-1 for i in range(N)] for j in range(N)]

def recurse(i, j):
    if i == j: return 0
    
    if dp[i][j] != -1:
        return dp[i][j]

    cost = float('inf')
    for s in range(i, j):
        cost = min(cost, sums[i][j] + recurse(i, s) + recurse(s+1,j))

    dp[i][j] = cost
    return cost

print(recurse(0, N - 1))

Solution (Python):
mod = 10**9+7
N = int(input())
a = list(map(int, input().split()))
S = [0]*(N+1)
for i in range(1, N+1):
    S[i] = S[i-1]+a[i-1]
memo = [[-1]*(N+1) for _ in range(N)]
def dp(i, j):
    if memo[i][j]>=0:
        return memo[i][j]
    if j-i == 1:
        memo[i][j] = 0
        return 0
    memo[i][j] = min(dp(i, k)+dp(k, j)+S[j]-S[i]for k in range(i+1, j))
    return memo[i][j]
print(dp(0, N))

Solution (Python):
mod = 10**9+7
N = int(input())
a = list(map(int, input().split()))
S = [0]*(N+1)
for i in range(1, N+1):
    S[i] = S[i-1]+a[i-1]
dp = [[float('inf')]*(N+1) for _ in range(N)]
for i in range(N):
    dp[i][i+1] = 0
for l in range(2, N+1):
    for i in range(N-l+1):
        j = i+l
        for ll in range(1, l):
            k = i+ll
            dp[i][j] = min(dp[i][j], dp[i][k]+dp[k][j]+S[j]-S[i])
print(dp[0][-1])

Solution (Python):
def main():
    N = int(input())
    A = list(map(int, input().split()))
    dp = [[0] * (len(A) - i) for i in range(len(A))]

    for i in range(1, len(A)):
        s = sum(A[:i])
        for j in range(len(A) - i):
            s += A[i + j]
            dp[i][j] = min(dp[k][j] + dp[i - k - 1][j + k + 1] for k in range(i)) + s
            s -= A[j]
    print(dp[-1][0])


main()

Solution (Python):
def main():
    N = int(input())
    a = list(map(int, input().split()))
    l = [[10**9+1] * (N+1) for _ in range(N+1)]
    s = [[0] * (N+1) for _ in range(N+1)]
    for i in range(N-1):
        for j in range(i+1, N+1):
            s[i][j] = s[i][j-1] + a[j-1]
    for i in range(N):
        l[i][i+1] = 0
    for j in range(2, N+1):
        for i in range(N):
            m = i + j
            if m > N:
                continue
            l[i][m] = min(l[i][k] + l[k][m] for k in range(i+1, m)) + s[i][m]
    return l[0][-1]

print(main())

Solution (Python):
import sys

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

def main():
    def cost(l, r):
        if l + 2 == r:
            return aa[l] + aa[l + 1]
        if l + 1 == r:
            return 0
        if dp[l][r] != -1:
            return dp[l][r]
        res = 10 ** 16
        for m in range(l + 1, r):
            res = min(res, cost(l, m) + cost(m, r))
        res += cumsum_aa[r] - cumsum_aa[l]
        dp[l][r] = res
        return res

    n = int(input())
    aa = list(map(int, input().split()))
    dp = [[-1] * (n + 1) for _ in range(n + 1)]
    cumsum_aa = [0]
    for i, a in enumerate(aa):
        cumsum_aa.append(cumsum_aa[i] + a)
    print(cost(0, n))

main()

Solution (Python):
def solve(n, a):
    from itertools import accumulate

    inf = (400 ** 2) * (10 ** 9) + 10

    acc = (0,) + tuple(accumulate(a))
    cost = [[inf] * (n + 1) for _ in range(n + 1)]
    for i in range(n):
        cost[i][i + 1] = 0

    for l in range(n - 1, -1, -1):
        for r in range(l + 2, n + 1):
            for c in range(l + 1, r):
                cost[l][r] = min(cost[l][r], cost[l][c] + cost[c][r])
            cost[l][r] += acc[r] - acc[l]

    return cost[0][n]


if __name__ == '__main__':
    n = int(input())
    a = tuple(map(int, input().split()))
    print(solve(n, a))

Solution (Python):
def solve(n, a):
    from itertools import accumulate

    inf = (400 ** 2) * (10 ** 9) + 10

    
    def dfs(l, r):
        if memo[l][r] != -1:
            return memo[l][r]
        if r - l == 1:
            return 0
        res = inf
        for c in range(l + 1, r):
            
            res = min(res, dfs(l, c) + dfs(c, r))
        res += acc[r] - acc[l]
        memo[l][r] = res
        return res

    acc = (0,) + tuple(accumulate(a))
    memo = [[-1] * (n + 1) for _ in range(n + 1)]

    return dfs(0, n)


if __name__ == '__main__':
    n = int(input())
    a = tuple(map(int, input().split()))
    print(solve(n, a))

Solution (Python):
import sys

n = int(input())
INF = 10**20
a_ls = [int(i) for i in sys.stdin.readline().split()]
memo_ls = [[0 for j in range(n)] for i in range(n)]
for _ in range(1,n):
    for i in range(n-_):
        j = i + _
        sum_ij = sum(a_ls[i:j+1])
        memo_ls[i][j] = sum_ij
        res = INF if j - i > 1 else 0
        for k in range(i,j):
            res = min(memo_ls[i][k] + memo_ls[k+1][j], res)
        memo_ls[i][j] += res
for i in range(n):
    memo_ls[i][i] = a_ls[i]
print(memo_ls[0][-1])

Solution (Python):
import sys
read = sys.stdin.buffer.read
readline = sys.stdin.buffer.readline
readlines = sys.stdin.buffer.readlines

import numpy as np

N = int(readline())
A = np.array(read().split(),np.int64)

INF = 10**18


size = np.full((N,N),INF,np.int64)
for n in range(N):
    size[n,:N-n] = A[n:].cumsum()

dpl = np.zeros((N,N),np.int64)
dpr = np.zeros((N,N),np.int64)

for n in range(1,N):
    x = np.min(dpl[:N-n,:n] + dpr[n:N,:n][:,::-1],axis=1)
    x += size[:N-n,n]
    dpl[:N-n,n] = x
    dpr[n:N,n] = x

answer = dpl[0,-1]
print(answer)

Solution (Python):
import sys
sys.setrecursionlimit(2147483647)
INF=float("inf")
MOD=10**9+7
input=lambda :sys.stdin.readline().rstrip()
def resolve():
    n=int(input())
    A=list(map(int,input().split()))
    S=[0]*(n+1)
    for i in range(n): S[i+1]=S[i]+A[i]
    dp=[[INF]*(n+1) for _ in range(n+1)]

    def dfs(L,R):
        if(R-L==1): return 0
        if(dp[L][R]!=INF): return dp[L][R]
        res=INF
        for h in range(L+1,R):
            res=min(res,dfs(L,h)+dfs(h,R)+S[R]-S[L])
        dp[L][R]=res
        return res

    print(dfs(0,n))
resolve()

Solution (Python):
import sys
sys.setrecursionlimit(10**8)
n = int(input())
a = list(map(int,input().split()))

a_data = [0]
now = 0
for i in a:
    now += i
    a_data.append(now)

dp = [[10**18 for _ in range(n+1)] for i in range(n)]

def solve(i,j):
    if dp[i][j] != 10**18:
        return dp[i][j]
    if i+1 == j:
        dp[i][j] = 0
        return dp[i][j]
    dp[i][j] = a_data[j] - a_data[i]
    x = 10**18
    for k in range(i+1,j):
        s = solve(i,k)
        t = solve(k,j)
        x = min(x,s+t)
    dp[i][j] += x
    return dp[i][j]

ans = solve(0,n)
print(ans)

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

CSUM = [0 for _ in range(N)]
CSUM[0] = A[0]
for i in range(1,N):
  CSUM[i] = CSUM[i-1] + A[i]

def csum(i,j):
  if i == 0:
    return CSUM[j]
  else:
    return CSUM[j]-CSUM[i-1]

dp = [[0 for _ in range(N)] for _ in range(N)]

for k in range(1,N):
  for i in range(N-k):
    j = i+k
    tmp = 10**18
    for l in range(i,j):
      tmp = min(tmp,dp[i][l]+dp[l+1][j] + csum(i,j))
    dp[i][j] = tmp

print(dp[0][N-1])

Solution (Python):
N = int(input())
a = list(map(int, input().split()))
dp = [[0] * (N) for _ in range(N)]
ans = int(0)



for l in range(1,N):
    for i in range(N-l):
        j = i + l
        dpcandi = [0] * (j-i)
        Sdp = int(0)
        for k in range(i,j+1):
            Sdp += a[k]
        for k in range(0,j-i):
            dpcandi[k] = dp[i][i+k] + dp[i+k+1][j]


        dp[i][j] = min(dpcandi) + Sdp

ans = dp[0][N-1]

print(ans)

Solution (Python):
def resolve():
    N = int(input())
    a = list(map(int,input().split()))
    DP = [[2 ** 63 -1  for _ in range(N+1)] for _ in range(N)]
    SUM = [[0 for _ in range(N+1)] for _ in range(N+1)]
    RANGE = [[0 for _ in range(N+1)] for _ in range(N+1)]

    SUM[0][0] = 0
    for i in range(N):
        for j in range(i,N):
            SUM[i][j+1] = SUM[i][j] + a[j]
            if i < j:
                SUM[i+1][j] = SUM[i][j] - a[i]

    for i in range(N):
        j = i+1
        DP[i][j] = 0
        RANGE[i][j] = i

    for w in range(2,N+1):
        for i in range(N+1-w):
            j = i + w
            for k in range(RANGE[i][j-1],RANGE[i+1][j]+1):
                s = DP[i][k]+DP[k][j]+SUM[i][j]
                if DP[i][j] > s:
                    DP[i][j] = s
                    RANGE[i][j] = k
    print(DP[0][N])
resolve()

Solution (Python):
def resolve():
    N = int(input())
    a = list(map(int,input().split()))
    DP = [[2 ** 63 -1  for _ in range(N+1)] for _ in range(N)]
    SUM = [[0 for _ in range(N+1)] for _ in range(N+1)]

    SUM[0][0] = 0
    for i in range(N):
        for j in range(i,N):
            SUM[i][j+1] = SUM[i][j] + a[j]
            if i < j:
                SUM[i+1][j] = SUM[i][j] - a[i]

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

    for w in range(2,N+1):
        for i in range(N+1-w):
            j = i + w
            for k in range(i,j):
                DP[i][j] = min(DP[i][k]+DP[k][j]+SUM[i][j],DP[i][j])
    print(DP[0][N])
resolve()

Solution (Python):























def f(A):
    n = len(A)
    inf = float("inf")
    dp = [[(inf, inf)] * n for _ in range(n)]
    for i in range(n):
        dp[i][i] = (A[i], 0)

    for h in range(1, n):
        for v in range(h, -1, -1):
            for j in range(v, h):
                
                
                
                
                left, lv = dp[v][j]
                right, rv = dp[j + 1][h]
                sum_ = left + right

                cost = lv + rv + sum_
                if cost < dp[v][h][1]:

                    dp[v][h] = (sum_, lv + rv + sum_)


    return dp[0][n-1][1]

assert f([10, 10, 10, 10, 10]) == 120
assert f([10, 20, 30, 40]) == 190
assert f([1000000000, 1000000000, 1000000000]) == 5000000000
assert f([7, 6, 8, 6, 1, 1]) == 68

n = input()
A = list(map(int, input().split()))
ans = f(A)
print(ans)

Solution (Python):


import sys
from itertools import accumulate

def input(): return sys.stdin.readline().strip()
def list2d(a, b, c): return [[c] * b for i in range(a)]
def list3d(a, b, c, d): return [[[d] * c for j in range(b)] for i in range(a)]
def list4d(a, b, c, d, e): return [[[[e] * d for j in range(c)] for j in range(b)] for i in range(a)]
def ceil(x, y=1): return int(-(-x // y))
def INT(): return int(input())
def MAP(): return map(int, input().split())
def LIST(N=None): return list(MAP()) if N is None else [INT() for i in range(N)]
def Yes(): print('Yes')
def No(): print('No')
def YES(): print('YES')
def NO(): print('NO')
sys.setrecursionlimit(10 ** 9)
INF = float('inf')
MOD = 10 ** 9 + 7

N = INT()
A = LIST()


acc = [0] + list(accumulate(A))

dp = list2d(N+1, N+1, INF)
for i in range(N):
    dp[i][i+1] = 0
for d in range(2, N+1):
    for l in range(N+1-d):
        r = l + d
        for m in range(l+1, r):
            dp[l][r] = min(dp[l][r], dp[l][m]+dp[m][r])
        
        dp[l][r] += acc[r] - acc[l]
print(dp[0][N])