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construct edit matrix for Levenshtein distance

To calculate Levenshtein distance, we always choose to use dynamic programming. For this, we will create an edit distance matrix as shown below:
enter image description here
Here is the code:
while True:
try:
a = input()
b = input()
board = [[0 for j in range(len(b)+1)] for i in range(len(a)+1)]
for i in range(len(a)+1):
board[i][0] = i
for j in range(len(b)+1):
board[0][j] = j
for i in range(1, len(a)+1):
for j in range(1, len(b)+1):
if a[i-1] == b[j-1]:
d = 0
else:
d = 1
board[i][j] = min(board[i-1][j]+1,
board[i][j-1]+1,
board[i-1][j-1]+d)
print(board[-1][-1])
except:
break
So my question is when we construct the matrix, why we need to add 1 to len(a) and len(b). Because as shown in the picture before, only the red part is the valid part in the matrix. So I modified my code:
while True:
try:
a = input()
b = input()
board = [[0 for j in range(len(b))] for i in range(len(a))]
for i in range(len(a)):
board[i][0] = i
for j in range(len(b)):
board[0][j] = j
for i in range(1, len(a)):
for j in range(1, len(b)):
if a[i] == b[j]:
d = 0
else:
d = 1
board[i][j] = min(board[i-1][j]+1,
board[i][j-1]+1,
board[i-1][j-1]+d)
print(board[-1][-1])
except:
break
I test this modified code and it still gives the correct answer in most tests. But when both strings are very long, the result will be 1 less. I am very confused about this. Maybe this question is stupid, but I still hope to be answered, thank you. 🙏

The problem with your solution is that you skip a[0] and b[0] case and you have to handle that case first. The original solution handles it with a[i-1] == b[j-1] when i = 1 and j = 1 but you don't

Why this Merge Sort does not work properly?

I need to implement Merge Sort using Python 3. I coded it. But It doesn't give proper output. Can anybody check it please?
Here my code is,
def mergeSort(A, p, r):
if p < r:
q = (p + r) // 2
mergeSort(A, p, q)
mergeSort(A, q+1, r)
Merge(A, p, q, r)
def Merge(A, p, q, r):
i = 1
j = q+1
k = 0
TEMP = [0] * (r+1)
while i <= q and j <= r:
if A[i] <= A[j]:
TEMP[k] = A[i]
k += 1
i += 1
else:
TEMP[k] = A[j]
k += 1
j += 1
if (j > r) :
for t in range(0, q-1):
A[r-t] = A[q-t]
for t in range(0, k-1):
A[p+t] = TEMP[t+1]
A = [15, 16, 13, 10, 19, 18]
mergeSort(A, 0, len(A)-1)
print(A)
Thank you

The way you perform merge looks weird (to me), but I will correct on what you have so far.
1- Initialization value of i is wrong, it should be:
i = p
because i is the first element you will look in array A.
2- Initialization value of size of TEMP array is wrong, it should be:
(r - p + 1)
3- There seems a mistake in filling in TEMP array and/or replacing A array elements, here is the fixed code. I wrote a comment about the part after first while loop to indicate what needs to be done at that point.
def mergeSort(A,p,r):
if p < r:
q = (p+r)//2
mergeSort(A,p,q)
mergeSort(A,q+1,r)
Merge(A,p,q,r)
def Merge(A,p,q,r):
i = p
j = q+1
k=0
TEMP = [0]*(r - p + 1)
while i <= q and j <= r:
if A[i] <= A[j]:
TEMP[k] = A[i]
k += 1
i += 1
else:
TEMP[k] = A[j]
k += 1
j += 1
"""
There are currently 2 cases
1- i > q, means we exhausted left but there are elements in the right
2- j > r, means we exhausted right but there are elements in the left
"""
if (j > r):
# copy elements at the left side to temp
while (i <= q):
TEMP[k] = A[i]
i += 1
k += 1
else:
# copy elements at the right side to temp
while (j <= r):
TEMP[k] = A[j]
j += 1
k += 1
# replace elements in A with elements in TEMP
for t in range(k):
A[p+t] = TEMP[t]
A = [15,16,13,10,19,18]
mergeSort(A,0,len(A)-1)
print(A)

The error lies in the Merge() function.
Initialisation of i=p and not i=1
After the while loop terminates, there's a chance that either i<q or j<r. We need to accommodate those cases as well.
Size of array TEMP was incorrect.
Corrected Merge Function:
def Merge(A,p,q,r):
i = p
j = q+1
k=0
TEMP = [0]*(r-p+1)
while i <= q and j <= r:
if A[i] <= A[j]:
TEMP[k] = A[i]
k += 1
i += 1
else:
TEMP[k] = A[j]
k += 1
j += 1
while i<=q:
TEMP[k] = A[i]
k+=1
i += 1
while j<=r:
TEMP[k] = A[j]
k+=1
j += 1
for t in range (p,r+1):
A[t] = TEMP[t-p]
Note: Please try using more meaningful variable names.

Python: What is wrong with the indexing logic in my code?

"You are given an array of n integers and an integer k. Find and print the number of (i,j) pairs where i<j and a[i] + a[j] is evenly divisible by k."
Sample input would be:
6 3
1 3 2 6 1 2
where 6 is n, 3 is k and the second line is the array of integers. The output for this input would be 5.
Here is my code, but i am not passing the test cases and am almost positive it has to do with how i am indexing it.
import sys
n,k = input().strip().split(' ')
n,k = [int(n),int(k)]
a = [int(a_temp) for a_temp in input().strip().split(' ')]
count=0;
for i in range(n):
curr = n-i
for j in range(curr):
if i < i + j:
if k % (a[i] + a[i+j]) ==0:
count = count + 1
print(count)
Also, followup question: Is this method i am approaching an efficient way of going about it?

you can try this ...
import sys
n,k = input().strip().split(' ')
n,k = [int(n),int(k)]
a = [int(a_temp) for a_temp in input().strip().split(' ')]
print(sum([1 for i in range(n) for j in range(i) if (a[i]+a[j])%k==0]))

k % ... means "k is divisible by ...", not "... is divisible by k".
if i < i + j is not very useful; you're better off doing what furas recommends in comments.

What you need is to make use of itertools.combinations:
from itertools import combinations
count = 0
for i, j in combinations(range(n), 2):
if i < j and (a[i] + a[j]) % k == 0:
print i, j
count += 1
Discussion
range(n) returns a list of indices 0 .. n-1
combinations(range(n), 2) will yield a list of two indices (without duplications)
(a[i] + a[j]) % k == 0 is the test that your asked
Note that combinations will yield pairs of i, j where i is always less than j, but the test i < j is there as a paranoid measure

Solution to splitting array into equal subarrays too slow

I'm having trouble with a dynamic programming problem. I have tested my solution against test cases, and it is correct. However, it is too slow. This leads me to believe that I may not be caching the solutions to subproblems effectively. Here is the problem statement:
There is an array A that contains N numbers. Given an array, a player can split the array into two non-empty subarrays only if the elements in each subarray sum to the same value. After a split is made, the player discards one subarray and is allowed to continue splitting on the remaining subarray. This continues until a split is no longer possible. What is the maximum number of splits possible on the given array A?
Here is my (slow) solution, which calls topSplit(A) on the given array:
def topSplitAux(A, C, i, j):
if -1 != C[i][j]:
return C[i][j]
if i == j:
return 0
s = float('-inf')
for k in range(i + 1, j):
if sum(A[i:k]) == sum(A[k:j]):
p1 = 1 + topSplitAux(A, C, i, k)
p2 = 1 + topSplitAux(A, C, k, j)
s = max(s, p1, p2)
C[i][j] = s
if s == float('-inf'): # we couldn't split, game over
C[i][j] = 0
return C[i][j]
def topSplit(A):
# initialize a cache to store solutions already solved
n = len(A)
# the subproblem we are interested in will be in C[0][n]
C = [[-1 for _ in range(n + 1)] for _ in range(n + 1)]
return topSplitAux(A, C, 0, n)
if __name__ == '__main__':
T = int(raw_input())
for t in range(T):
N = int(raw_input())
A = map(int, raw_input().split())
n = len(A)
print topSplit(A)
Here's a simple test case:
3
3
3 3 3
4
2 2 2 2
7
4 1 0 1 1 0 1
with expected result:
0
2
3
Any help on making this solution faster would be greatly appreciated. Thanks!

Python: TypeError: list indices must be integers, not str

I'm going to do Matrix Addition on Python.(Not finish). But it shows an error.
m, n = (int(i) for i in raw_input().split())
a = [[0 for i in range(m)] for j in range(n)]
b = [[0 for i in range(m)] for j in range(n)]
c = []
total = []
for i in range(m):
x = raw_input()
for j in range(n):
value = [int(i) for i in x.split()]
c[i][j] = a[i][j]
#c.append(value)
print a
for i in c:
print i
I want to input
3 3 <-- matrix dimensional m*n
1 2 3 >
3 2 1 > matrix A
1 3 2 >
1 1 1 >
1 1 1 > matrix B
1 1 1 >
and shows as
2 3 4 >
4 3 2 > matrix A + B
2 4 3 >

You are using i in your outer for loop, and it is an int. Then in the loop you have:
value = [int(i) for i in x.split()]
which makes i a string (which is what split returns). Maybe you think there is some sort of scoping inside [ ]? There isn't. You have a name collision, change one of them.

You are using same variable in inner for loop.
for i in range(m):
x = raw_input()
for j in range(n):
# variable i is refering to outer loop
value = [int(p) for p in x.split()]
c[i][j] = a[i][j]
#c.append(value)
print a
for i in c:
print i

Beyond the first two answers you'll have a problem with this statement:
c[i][j] = a[i][j]
When the loop starts i will be 0 and that's so far OK, but c is an empty list and has no iterable at the first position so c[0][0] will return an error.
Get rid of it and uncomment the following line:
#c.append(value)
EDIT:
Your code won't return what you want. You'd better make something like this to create a matrix with the given sides:
for i in range(m):
d = []
for j in range(n):
x = raw_input()
d.append(int(x))
c.append(d)
If you have 3 for both m and n, then you will create matrix with sides 3 x 3 saved in the variable c.
In this way you don't have to split the user input. The user can give a number at a time. And you could even change the following line:
x = raw_input()
to:
x = raw_input("{0}. row, {1}. column: ".format(i+1, j+1))
Try it out!

import time
m, n = (int(i) for i in raw_input().split())
a = []
b = []
total = [[0 for i in range(n)] for j in range(m)]
for i in range(m):
x = raw_input()
for j in range(n):
value = [int(i) for i in x.split()]
a.append(value)
#print a
for i in range(m):
x = raw_input()
for j in range(n):
value = [int(i) for i in x.split()]
b.append(value)
#print b
for i in range(m):
for j in range(n):
total[i][j] = a[i][j] + b[i][j]
for i in total:
print ' '.join(map(str, i))
time.sleep(2)
OK! I just figured it out! Thank you

you can also hit this error if you declare an int and treat it like a dict
>>> a = []
>>> a['foo'] = 'bar'
Traceback (most recent call last):
File "<stdin>", line 1, in <module>
TypeError: list indices must be integers, not str