# Program to find number of minimum steps to reach last index in Python

PythonServer Side ProgrammingProgramming

Suppose we have a list of numbers called nums and we are placed currently at nums. On each step, we can either jump from the current index i to i + 1 or i - 1 or j where nums[i] == nums[j]. We have to find the minimum number of steps required to reach the final index.

So, if the input is like nums = [4, 8, 8, 5, 4, 6, 5], then the output will be 3, as we can jump from index 0 to index 4 as their values are both 4. And then we jump back to index 3. Finally, we can jump from index 3 to 6 since both of their values are 5.

To solve this, we will follow these steps −

• pos := an empty map
• for each index i, and value n in nums, do
• insert i at the end of pos[n]
• n := size of nums
• visited := make a list of size n, and fill this with False
• visited := True
• while q is not empty, do
• (u, d) := left element of q, and delete left element
• if u is same as n - 1, then
• return d
• for each v in the lists pos[nums[u]] and [u - 1, u + 1], do
• if 0 <= v < n and visited[v] is false, then
• visited[v] := True
• insert pair (v, d + 1) at the end of q
• remove pos[nums[u]]

Let us see the following implementation to get better understanding −

## Example

Live Demo

class Solution:
def solve(self, nums):
from collections import defaultdict, deque
pos = defaultdict(list)
for i, n in enumerate(nums):
pos[n].append(i)
q = deque([(0, 0)])
n = len(nums)
visited = [False] * n
visited = True
while q:
u, d = q.popleft()
if u == n - 1:
return d
for v in pos[nums[u]] + [u - 1, u + 1]:
if 0 <= v < n and not visited[v]:
visited[v] = True
q.append((v, d + 1))
del pos[nums[u]]
ob = Solution()
nums = [4, 8, 8, 5, 4, 6, 5]
print(ob.solve(nums))

## Input

[4, 8, 8, 5, 4, 6, 5]

## Output

3