Problem Description
Alice has n balloons arranged on a rope. You are given a 0-indexed string colors where colors[i] is the color of the i-th balloon. Alice wants the rope to be colorful. She does not want two consecutive balloons to be of the same color, so she asks Bob for help. Bob can remove some balloons from the rope to make it colorful. You are given a 0-indexed integer array neededTime where neededTime[i] is the time (in seconds) that Bob needs to remove the i-th balloon from the rope. Return the minimum time Bob needs to make the rope colorful.
Key Insights
- The problem requires ensuring that no two consecutive balloons are of the same color.
- When consecutive balloons are of the same color, we must remove some to minimize the removal time.
- To minimize the time, we should always keep the balloon with the highest removal time in a group of consecutive balloons of the same color.
- The total time spent removing balloons is the sum of the removal times of the balloons we choose to delete in each group.
Space and Time Complexity
Time Complexity: O(n)
Space Complexity: O(1)
Solution
To solve this problem, we can iterate through the colors string while keeping track of the current balloon color and its corresponding removal times. When we encounter a balloon of the same color as the previous one, we compare their removal times and add the smaller one to our total time, ensuring we only remove the necessary balloons. The algorithm proceeds through the entire string, ensuring that at the end, all consecutive balloons of the same color have been handled appropriately.
The primary data structure used is a simple counter for the total time needed, along with a few variables to track the current balloon color and its removal time.