Leetcode #1713: Minimum Operations to Make a Subsequence
In this guide, we solve Leetcode #1713 Minimum Operations to Make a Subsequence in Python and focus on the core idea that makes the solution efficient.
You will see the intuition, the step-by-step method, and a clean Python implementation you can use in interviews.
Problem Statement
You are given an array target that consists of distinct integers and another integer array arr that can have duplicates. In one operation, you can insert any integer at any position in arr.
Quick Facts
- Difficulty: Hard
- Premium: No
- Tags: Greedy, Array, Hash Table, Binary Search
Intuition
Fast membership checks and value lookups are the heart of this problem, which makes a hash map the natural choice.
By storing what we have already seen (or counts/indexes), we can answer the question in one pass without backtracking.
Approach
Scan the input once, using the map to detect when the condition is satisfied and to update state as you go.
This keeps the solution linear while remaining easy to explain in an interview setting.
Steps:
- Initialize a hash map for seen items or counts.
- Iterate through the input, querying/updating the map.
- Return the first valid result or the final computed value.
Example
Input: target = [5,1,3], arr = [9,4,2,3,4]
Output: 2
Explanation: You can add 5 and 1 in such a way that makes arr = [5,9,4,1,2,3,4], then target will be a subsequence of arr.
Python Solution
class BinaryIndexedTree:
__slots__ = "n", "c"
def __init__(self, n: int):
self.n = n
self.c = [0] * (n + 1)
def update(self, x: int, v: int):
while x <= self.n:
self.c[x] = max(self.c[x], v)
x += x & -x
def query(self, x: int) -> int:
res = 0
while x:
res = max(res, self.c[x])
x -= x & -x
return res
class Solution:
def minOperations(self, target: List[int], arr: List[int]) -> int:
d = {x: i for i, x in enumerate(target, 1)}
nums = [d[x] for x in arr if x in d]
m = len(target)
tree = BinaryIndexedTree(m)
ans = 0
for x in nums:
v = tree.query(x - 1) + 1
ans = max(ans, v)
tree.update(x, v)
return len(target) - ans
Complexity
The time complexity is , and the space complexity is . The space complexity is .
Edge Cases and Pitfalls
Watch for boundary values, empty inputs, and duplicate values where applicable. If the problem involves ordering or constraints, confirm the invariant is preserved at every step.
Summary
This Python solution focuses on the essential structure of the problem and keeps the implementation interview-friendly while meeting the constraints.