Problem:
 Score : 1200 points    Problem Statement We have a weighted directed graph with N vertices numbered 0 to N-1 .  The graph initially has N-1 edges. The i -th edge ( 0 \leq i \leq N-2 ) is directed from Vertex i to Vertex i+1 and has a weight of 0 .  Snuke will now add a new edge (i → j) for every pair i, j ( 0 \leq i,j \leq N-1,\ i \neq j ).
The weight of the edge will be -1 if i < j , and 1 otherwise.  Ringo is a boy. A negative cycle (a cycle whose total weight is negative) in a graph makes him sad.
He will delete some of the edges added by Snuke so that the graph will no longer contain a negative cycle.
The cost of deleting the edge (i → j) is A_{i,j} . He cannot delete edges that have been present from the beginning.  Find the minimum total cost required to achieve Ringo's objective.      Constraints  3 \leq N \leq 500  1 \leq A_{i,j} \leq 10^9  All values in input are integers.         Input Input is given from Standard Input in the following format:  N  A_{0,1}  A_{0,2}  A_{0,3}  \cdots  A_{0,N-1}  A_{1,0}  A_{1,2}  A_{1,3}  \cdots  A_{1,N-1}  A_{2,0}  A_{2,1}  A_{2,3}  \cdots  A_{2,N-1}  \vdots  A_{N-1,0}  A_{N-1,1}  A_{N-1,2}  \cdots  A_{N-1,N-2}       Output Print the minimum total cost required to achieve Ringo's objective.        Sample Input 1 3
2 1
1 4
3 3      Sample Output 1 2  If we delete the edge (0 → 1) added by Snuke, the graph will no longer contain a negative cycle.
The cost will be 2 in this case, which is the minimum possible.       Sample Input 2 4
1 1 1
1 1 1
1 1 1
1 1 1      Sample Output 2 2  If we delete the edges (1 → 2) and (3 → 0) added by Snuke, the graph will no longer contain a negative cycle.
The cost will be 1+1=2 in this case, which is the minimum possible.       Sample Input 3 10
190587 2038070 142162180 88207341 215145790 38 2 5 20
32047998 21426 4177178 52 734621629 2596 102224223 5 1864
41 481241221 1518272 51 772 146 8805349 3243297 449
918151 126080576 5186563 46354 6646 491776 5750138 2897 161
3656 7551068 2919714 43035419 495 3408 26 3317 2698
455357 3 12 1857 5459 7870 4123856 2402 258
3 25700 16191 102120 971821039 52375 40449 20548149 16186673
2 16 130300357 18 6574485 29175 179 1693 2681
99 833 131 2 414045824 57357 56 302669472 95
8408 7 1266941 60620177 129747 41382505 38966 187 5151064      Sample Output 3 2280211

Solution (Python):
N = int(input())    

A = [[0] * N for _ in range(N)]
Al = [[0] * (N+1) for _ in range(N+1)]
Ar = [[0] * (N+1) for _ in range(N+1)]

for i in range(N) :
    a = [int(i) for i in input().split()]
    for j in range(N) :
        if i < j :
            A[i][j] = a[j-1]
        elif i > j :
            A[i][j] = a[j]

for i in range(N) :
    for j in range(i+1, N) :
        Al[j][i+1] = Al[j][i] + A[j][i]
        Ar[i][j] = Ar[i-1][j] + A[i][j]

dp = [[float('inf')] * (N+1) for _ in range(N+1)]
dp[0][0] = 0
        
for i in range(N+1) :
    for j in range(i, N+1) :
        if dp[i][j] == float('inf') :
            continue
        l, r = 0, 0
        for k in range(j+1, N+1) :
            l += Al[k-1][i]
            r += Ar[k-2][k-1] - Ar[j-1][k-1]
            dp[j][k] = min(dp[j][k], dp[i][j] + l + r)
print(min(dp[i][N] for i in range(N+1)))

Solution (Python):
N = int(input())    

A = [[0] * N for _ in range(N)]
Al = [[0] * (N+1) for _ in range(N+1)]
Ar = [[0] * (N+1) for _ in range(N+1)]

for i in range(N) :
    a = [int(i) for i in input().split()]
    for j in range(N) :
        if i < j :
            A[i][j] = a[j-1]
        elif i > j :
            A[i][j] = a[j]

for i in range(N) :
    for j in range(i+1, N) :
        Al[j][i+1] = Al[j][i] + A[j][i]
        Ar[i][j] = Ar[i-1][j] + A[i][j]


    


    

dp = [[float('inf')] * (N+1) for _ in range(N+1)]
dp[0][0] = 0
        
for i in range(N+1) :
    for j in range(i, N+1) :        
        l, r = 0, 0
        for k in range(j+1, N+1) :
            l += Al[k-1][i]
            r += Ar[k-2][k-1] - Ar[j-1][k-1]
            dp[j][k] = min(dp[j][k], dp[i][j] + l + r)
            

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