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)



Sample input:
4
10 20 30 40


Sample output:
190

Submission status: Accepted

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

    """ convenient functions
    # for i, a in enumerate(iterable)
    # q, mod = divmod(a, b)
    # divmod(x, y) returns the tuple (x//y, x%y)
    # Higher-order function: reduce(operator.mul, xyz_count, 1)
    # manage median(s) using two heapq https://atcoder.jp/contests/abc127/tasks/abc127_f
    """

    """convenient decorator
    # @functools.lru_cache():
    # to facilitate use of recursive function
        # ex:
        # from functools import lru_cache
        # import sys
        # sys.setrecursionlimit(10**9)
        # @lru_cache(maxsize=None)
        # def fib(n):
        #     if n < 2:
        #         return n
        #     return fib(n-1) + fib(n-2)
        # print(fib(1000))
    """
    
    # import numpy as np
    import sys
    sys.setrecursionlimit(10**7)
    from itertools import accumulate, combinations, permutations, product # https://docs.python.org/ja/3/library/itertools.html
    # accumulate() returns iterator! to get list: list(accumulate())
    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 = []  # prime factor
        b, e = 2, 0  # base, exponent
        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
        """
        # TODO: How should I do when n - r is negative?
        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 # https://docs.python.org/ja/3/library/collections.html#collections.deque
    from heapq import heapify, heappop, heappush, heappushpop, heapreplace,nlargest,nsmallest # https://docs.python.org/ja/3/library/heapq.html
    from copy import deepcopy, copy # https://docs.python.org/ja/3/library/copy.html
    import operator
    from operator import itemgetter #sort 
    # ex1: List.sort(key=itemgetter(1))
    # ex2: sorted(tuples, key=itemgetter(1,2))
    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 # Deprecated since version 3.5: Use math.gcd() instead.
    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)
    
    # first create factorial_list
    # fac_list = mod_factorial_list(n)
    INF = 10 ** 18
    MOD = 10 ** 9 + 7
    modpow = lambda a, n, p = MOD: pow(a, n, p) # Recursive function in python is slow!
    def modinv(a, p = MOD):
        # evaluate reciprocal using Fermat's little theorem:
        # a**(p-1) is identical to 1 (mod p) when a and p is coprime
        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):
        # fac_list = modfactorial_list(100)
        # print(modcomb(100, 5, modfactorial_list(100)))
        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]

    # Graph: https://en.wikipedia.org/wiki/Directed_graph
    # Bellman-Ford: O(|V||E|). Use this if there exists an edge with negative length in the graph
    # After N steps, the shortest path has converded if there doesn't exist an cycle of edges with negative
    # Watch out: d[N] == d[2*N] doesn't necessarily mean the graph doesn't have negative cycle
    # ref: https://www.youtube.com/watch?v=1Z6ofKN03_Y

    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
    # initialize variables
        # to initialize list, use [0] * n
        # to initialize two dimentional array:
            # ex) [[0] * N for _ in range(N)]
            # ex2) dp = [[0] * (N+1) for _ in range(W*2)]
    # set inputs
        # put inputs between specific values (almost as quickly)
        # ex) S = [-INF] + [int(r()) for _ in range(A)] + [INF]
        # open(0).read() is sometimes useful:
        # ex) n, m, *x = map(int, open(0).read().split())
        #     min(x[::2]) - max(x[1::2])
        # ex2) *x, = map(int, open(0).read().split())
        #     don't forget to add comma after *x if only one variable is used
    # preprocessing
        # transpose = [x for x in zip(*data)]
        # ex) [[1, 2, 3], [4, 5, 6], [7, 8, 9]] => [(1, 4, 7), (2, 5, 8), (3, 6, 9)]
        # flat = [flatten for inner in data for flatten in inner]
        # ex) [[1, 2, 3], [4, 5, 6], [7, 8, 9]] => [1, 2, 3, 4, 5, 6, 7, 8, 9]
    # calculate and output
        # output pattern
        # ex1) print(*l) => when l = [2, 5, 6], printed 2 5 6
    """

    # functions to read input
    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
    # single int: int(r())
    # single string: r()
    # single float: float(r())
    # line int: R()
    # line string: r().split()
    # line (str, int, int): [j if i == 0 else int(j) for i, j in enumerate(r().split())]
    # lines int: [R() for _ in range(n)]
    """

    # for test
    if sample_file:
        sys.stdin = open(sample_file)
        
    # ----------------------------------
    # main

    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])


    # to finish code, use return instead of exit()
    # end of main
    # ----------------------------------

    """memo: how to use defaultdict of list
    # initialize
    Dic = defaultdict(list)
    # append / extend
    Dic[x].append(y)
    # three methods for loop: keys(), values(), items()
    for k, v in Dic.items():
    """
    
    """memo: how to solve binary problems
    # to make binary digits text
    >>> a = 5
    >>> bin_str_a = format(a, '#06b')
    >>> print(bin_str_a)
    0b0101 # first 2 strings (='0b') indicates it is binary
    """
    
    """memo: how to solve the problem
    creating simple test/answer
    greed
    simple dp
    graph
    """

if __name__ == '__main__':
    main()

Submission status: Accepted

Solution code:
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])

Submission status: Accepted

Solution code:
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])

Submission status: Accepted

Solution code:
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])

Submission status: Accepted

Solution code:
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])

Submission status: Accepted

Solution code:
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(s)
print(solve(0,n-1))
# print(c)

Submission status: Accepted

Solution code:
n = int(input())
a = list(map(int, input().split()))
# dp[i][j] - the minimum total cost of combining interval [i,j] into one vertex
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])

Submission status: Accepted

Solution code:
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()

Submission status: Accepted

Solution code:
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])

Submission status: Accepted

Solution code:
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))

Submission status: Accepted

Solution code:
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])

Submission status: Accepted

Solution code:
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())

Submission status: Accepted

Solution code:
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()

Submission status: Accepted

Solution code:
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))

Submission status: Accepted

Solution code:
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])

Submission status: Accepted

Solution code:
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

# 左端ごとに、個数 -> 大きさ
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)

Submission status: Accepted

Solution code:
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()

Submission status: Accepted

Solution code:
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)]
#print(a_data)
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)

Submission status: Accepted

Solution code:
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]
#print(CSUM)
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])
#print(dp)

Submission status: Accepted

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

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]
#            print(i,j,dpcandi)

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

ans = dp[0][N-1]

print(ans)

Submission status: Accepted

Solution code:
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()

Submission status: Accepted

Solution code:
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()

Submission status: Accepted

Solution code:
# AT DP N
#
# n items
# n-1 choices, each choice costs A[n] + A[n+1]

#    10 20 30 40

#     0  1  2  3
# 0  10 30 40      # A[0:2] = A[0:1] + A[2] or A[0] + A[1:2]
# 1     20 50
# 2        30
# 3           40
#

#    10 10 10 10 10
#
#     0  1  2  3  4
#  0 10 20       50
#  1    10
#  2       10 20 30
#  3          10
#  4             10

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):
                # 1-2: 1-1 + 2-2
                # 0-3: 0-0 + 1-3
                # 0-3: 0-1 + 2-3
                # 0-3: 0-2 + 3-3
                left, lv = dp[v][j]
                right, rv = dp[j + 1][h]
                sum_ = left + right
#                print(v, h, "<-", v, j, " + ", j + 1, h, "L", dp[v][j], "R", dp[j + 1][h])
                cost = lv + rv + sum_
                if cost < dp[v][h][1]:
#                    print("* SET")
                    dp[v][h] = (sum_, lv + rv + sum_)
#    for d in dp:
#        print(d)
    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)