Problem Analysis

Given a target string of '0's and '1's representing the desired state of bulbs, the goal is to determine the minimum number of flips required to transform an initial state of all '0's to the target state. Each flip operation selects a bulb at position i and flips all bulbs from i to the end of the array.

Key Insight

The problem can be simplified by recognizing that each flip operation affects all subsequent bulbs. Therefore, the state of each bulb is influenced by the cumulative number of flips applied starting at or before its position.

Approach

1. Problem Transformation: Instead of simulating each flip, observe that the state of each bulb depends on the number of times it has been flipped. Since flipping twice is equivalent to no flip, we only care about the parity (odd or even) of flips.

2. State Tracking: Maintain a variable currentFlip representing the cumulative effect of flips up to the current bulb. This variable starts at 0 (no flips) and toggles between 0 and 1 each time a flip is initiated.

3. Comparison with Target: For each bulb in the target state:

   • If the bulb's target state differs from currentFlip, a flip operation must be initiated at this position. This increments the flip count and toggles currentFlip.
   • Otherwise, no flip is needed.

4. Complexity: This approach processes each bulb exactly once, resulting in O(n) time complexity and O(1) space compelxity.

Solution Code

var minFlips = function(target) {
    let flips = 0;
    let currentState = 0;
    for (let i = 0; i < target.length; i++) {
        const targetState = parseInt(target[i]);
        if (targetState !== currentState) {
            flips++;
            currentState = 1 - currentState;
        }
    }
    return flips;
};

Explanation

• Initialization: Start with flips = 0 and currentState = 0 (indicating no flips have been applied).
• Iterate through each bulb: For each bulb at index i:
  • If the target state of the bulb (target[i]) does not match currentState, initiate a flip. This increments flips and toggles currentState (from 0 to 1 or vice versa).
  • The togggle of currentState affects all subsequent bulbs, simulating the flip operation.
• Result: The total count of flips (flips) is returned, representing the minimum operations needed to achieve the target state.

This approach efficiently tracks the necessary flips without explicitly modifying the bulb array, leveraging the cumulative effect of flip operations.