Minimum Operations to Make Binary Array Elements Equal to One II

Minimum Operations to Make Binary Array Elements Equal to One II

1. What is this problem about?

This problem is a variation of the binary array flipping challenge. You are given an array of 0s and 1s. In one operation, you can choose an index i and flip all elements from index i to the end of the array (suffix flip). The objective is to find the minimum number of such suffix flips required to make every element in the array equal to 1.

2. Why is this asked in interviews?

Uber and other technology-driven companies ask this to test a candidate's ability to optimize a process that seems to involve a lot of repetitive work. A naive simulation of flipping the entire suffix for every operation would result in an O(N^2) complexity, which is inefficient. The problem tests if you can maintain the "current state" of the elements using a single variable, effectively reducing the complexity to O(N).

3. Algorithmic pattern used

The algorithmic pattern used is Greedy with State Tracking. Instead of actually flipping the array elements, you keep track of how many flips have been performed so far. If the number of flips is even, the current element's value is its original value. If the number of flips is odd, its value is flipped (0 becomes 1, 1 becomes 0). You traverse the array from left to right, and whenever the current effective value of an element is 0, you perform a flip and increment your flip counter.

4. Example explanation

Array: [0, 1, 0, 1]

• Index 0: Value is 0. Flips = 0 (even). Effective value = 0. We must flip. Flips = 1.
• Index 1: Value is 1. Flips = 1 (odd). Effective value = 0. We must flip. Flips = 2.
• Index 2: Value is 0. Flips = 2 (even). Effective value = 0. We must flip. Flips = 3.
• Index 3: Value is 1. Flips = 3 (odd). Effective value = 0. We must flip. Flips = 4. Total operations = 4.

5. Common mistakes candidates make

The most frequent mistake is implementing the actual flipping of the subarray, which leads to a Time Limit Exceeded (TLE) error on large inputs. Candidates also sometimes get confused about how an even or odd number of flips affects the current bit, leading to incorrect "if" conditions. Another common error is starting the traversal from the right instead of the left, which doesn't work for suffix flips.

6. Interview preparation tip

Whenever a problem involves "flipping a range to the end," always think about how you can track the "global state" of flips instead of updating individual elements. This "state-tracking" pattern is a very common optimization in string and array problems. Practice identifying whether a change at one index affects all subsequent indices.