Leetcode #1187: Make Array Strictly Increasing
In this guide, we solve Leetcode #1187 Make Array Strictly Increasing 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
Given two integer arrays arr1 and arr2, return the minimum number of operations (possibly zero) needed to make arr1 strictly increasing. In one operation, you can choose two indices 0 <= i < arr1.length and 0 <= j < arr2.length and do the assignment arr1[i] = arr2[j].
Quick Facts
- Difficulty: Hard
- Premium: No
- Tags: Array, Binary Search, Dynamic Programming, Sorting
Intuition
The problem structure suggests a monotonic decision, which makes binary search a natural fit.
By halving the search space each step, we reach the answer efficiently.
Approach
Search either directly on a sorted array or on the answer space using a check function.
Each check is fast, and the logarithmic search keeps the overall runtime low.
Steps:
- Define the search bounds.
- Check the mid point condition.
- Narrow the bounds until convergence.
Example
Input: arr1 = [1,5,3,6,7], arr2 = [1,3,2,4]
Output: 1
Explanation: Replace 5 with 2, then arr1 = [1, 2, 3, 6, 7].
Python Solution
class Solution:
def makeArrayIncreasing(self, arr1: List[int], arr2: List[int]) -> int:
arr2.sort()
m = 0
for x in arr2:
if m == 0 or x != arr2[m - 1]:
arr2[m] = x
m += 1
arr2 = arr2[:m]
arr = [-inf] + arr1 + [inf]
n = len(arr)
f = [inf] * n
f[0] = 0
for i in range(1, n):
if arr[i - 1] < arr[i]:
f[i] = f[i - 1]
j = bisect_left(arr2, arr[i])
for k in range(1, min(i - 1, j) + 1):
if arr[i - k - 1] < arr2[j - k]:
f[i] = min(f[i], f[i - k - 1] + k)
return -1 if f[n - 1] >= inf else f[n - 1]
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.