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Find sub-arrays from given two arrays such that they have equal sum in Python
Suppose we have two arrays P and Q whose size are N, they are holding numbers 1 to N. We have to find sub-arrays from the given arrays so that they have equal sum. Finally return the indices of such sub-arrays. If there is no solution, then return -1.
So, if the input is like P = [2, 3, 4, 5, 6], Q = [9, 3, 2, 6, 5], then the output will be Indices in first array : 0, 1, 2 and indices in second array: 0, so P[0..2] = 2 + 3 + 4 = 9 and Q[0] = 9.
To solve this, we will follow these steps −
Define a function get_subarray() . This will take P, Q, swap
N := size of P
index := a new map
difference := 0, j := 0
index[0] := a pair like (-1, -1)
for i in range 0 to N, do
while Q[j] < P[i], do
j := j + 1
difference := Q[j] - P[i]
if difference present in index, then
if swap is ture, then
idx := index[Q[j] - P[i]]
display all values from idx[1] + 1 to j for P
display all values from idx[0] + 1 to i for Q
otherwise,
idx := index[Q[j] - P[i]]
display all values from idx[0] + 1 to i for P
display all values from idx[1] + 1 to j for Q
return
index[difference] := (i, j)
display -1
From the main methood, do the following −
Update P and Q using their cumulative sums
N := size of P
if Q[N - 1] > P[N - 1], then
get_subarray(P, Q, False)
otherwise,
get_subarray(Q, P, True)
Example
Let us see the following implementation to get better understanding −
def show_res(x, y, num):
print("Indices of array", num, ":", end = " ")
for i in range(x, y):
print(i, end = ", ")
print(y)
def get_subarray(P, Q, swap):
N = len(P)
index = {}
difference, j = 0, 0
index[0] = (-1, -1)
for i in range(0, N):
while Q[j] < P[i]:
j += 1
difference = Q[j] - P[i]
if difference in index:
if swap:
idx = index[Q[j] - P[i]]
show_res(idx[1] + 1, j, 1)
show_res(idx[0] + 1, i, 2)
else:
idx = index[Q[j] - P[i]]
show_res(idx[0] + 1, i, 1)
show_res(idx[1] + 1, j, 2)
return
index[difference] = (i, j)
print(-1)
def cumsum(arr):
n = len(arr)
for i in range(1, n):
arr[i] += arr[i - 1]
P = [2, 3, 4, 5, 6]
Q = [9, 3, 2, 6, 5]
cumsum(P)
cumsum(Q)
N = len(P)
if Q[N - 1] > P[N - 1]:
get_subarray(P, Q, False)
else:
get_subarray(Q, P, True)Input
[2, 3, 4, 5, 6],[9, 3, 2, 6, 5]
Output
Indices of array 1 : 0, 1, 2 Indices of array 2 : 0
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