1578. Minimum Time To Make Rope Colorful - Explanation

Description

The string colors gives the colors of balloons along a rope, in order. Removing balloon i takes neededTime[i] seconds. After a removal, the balloons on either side become neighbors. Return the minimum total removal time needed so that no two remaining neighboring balloons have the same color. You may leave an already valid rope unchanged.

Diagram circles show colors as letters; the numbers underneath show removal times.

Example 1:

Minimum Time to Make Rope Colorful, example 1: illustration of the example

Input: colors = "aabbc"
neededTime = [4,1,2,7,3]

Output: 3

Explanation: Remove the second a for 1 second and the first b for 2 seconds. The remaining colors are abc, and the total time is 3 seconds. Choosing the cheaper removal within each repeated group is optimal.

Example 2:

Minimum Time to Make Rope Colorful, example 2: illustration of the example

Input: colors = "abc"
neededTime = [9,8,7]

Output: 0

Explanation: Every neighboring pair already has different colors. No balloons need to be removed, so the answer is 0.

Example 3:

Minimum Time to Make Rope Colorful, example 3: illustration of the example

Input: colors = "aaaa"
neededTime = [3,8,5,2]

Output: 10

Explanation: Only one a can remain. Keep the balloon that would cost 8 seconds to remove, and remove the others for 3 + 5 + 2 = 10 seconds.

Constraints:

1 <= colors.length == neededTime.length <= 100000
colors contains only lowercase English letters.
1 <= neededTime[i] <= 10000

Topics

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Prerequisites

Before attempting this problem, you should be comfortable with:

Two Pointers Technique - Using multiple indices to traverse arrays and identify groups of consecutive elements
Greedy Algorithms - Making locally optimal choices (keeping the most expensive balloon) to achieve a globally optimal solution
String Traversal - Iterating through characters while comparing adjacent elements

1. Two Pointers - I

Intuition

The goal is to remove consecutive balloons of the same color such that no two adjacent balloons share a color. When we find a group of consecutive same-colored balloons, we need to keep exactly one and remove the rest. To minimize the total removal time, we should keep the balloon with the highest removal cost and remove all others.

Algorithm

Initialize res = 0 and i = 0.
While i < n:
- Find all consecutive balloons with the same color starting at i.
- Track the sum of removal times (curr) and the maximum removal time (maxi) in this group.
- Add curr - maxi to res (we keep the most expensive one, remove the rest).
- Move i to the next group.
Return res as the result.

class Solution:
    def minCost(self, colors: str, neededTime: List[int]) -> int:
        n = len(neededTime)
        res = i = 0
        while i < n:
            j = i
            maxi = curr = 0
            while j < n and colors[j] == colors[i]:
                maxi = max(maxi, neededTime[j])
                curr += neededTime[j]
                j += 1
            res += curr - maxi
            i = j
        return res

public class Solution {
    public int minCost(String colors, int[] neededTime) {
        int n = neededTime.length;
        int res = 0, i = 0;
        while (i < n) {
            int j = i, maxi = 0, curr = 0;
            while (j < n && colors.charAt(j) == colors.charAt(i)) {
                maxi = Math.max(maxi, neededTime[j]);
                curr += neededTime[j];
                j++;
            }
            res += curr - maxi;
            i = j;
        }
        return res;
    }
}

class Solution {
public:
    int minCost(string colors, vector<int>& neededTime) {
        int n = neededTime.size();
        int res = 0, i = 0;
        while (i < n) {
            int j = i, maxi = 0, curr = 0;
            while (j < n && colors[j] == colors[i]) {
                maxi = max(maxi, neededTime[j]);
                curr += neededTime[j];
                j++;
            }
            res += curr - maxi;
            i = j;
        }
        return res;
    }
};

class Solution {
    /**
     * @param {string} colors
     * @param {number[]} neededTime
     * @return {number}
     */
    minCost(colors, neededTime) {
        const n = neededTime.length;
        let res = 0,
            i = 0;
        while (i < n) {
            let j = i,
                maxi = 0,
                curr = 0;
            while (j < n && colors[j] === colors[i]) {
                maxi = Math.max(maxi, neededTime[j]);
                curr += neededTime[j];
                j++;
            }
            res += curr - maxi;
            i = j;
        }
        return res;
    }
}

public class Solution {
    public int MinCost(string colors, int[] neededTime) {
        int n = neededTime.Length;
        int res = 0, i = 0;
        while (i < n) {
            int j = i, maxi = 0, curr = 0;
            while (j < n && colors[j] == colors[i]) {
                maxi = Math.Max(maxi, neededTime[j]);
                curr += neededTime[j];
                j++;
            }
            res += curr - maxi;
            i = j;
        }
        return res;
    }
}

func minCost(colors string, neededTime []int) int {
    n := len(neededTime)
    res, i := 0, 0
    for i < n {
        j := i
        maxi, curr := 0, 0
        for j < n && colors[j] == colors[i] {
            if neededTime[j] > maxi {
                maxi = neededTime[j]
            }
            curr += neededTime[j]
            j++
        }
        res += curr - maxi
        i = j
    }
    return res
}

class Solution {
    fun minCost(colors: String, neededTime: IntArray): Int {
        val n = neededTime.size
        var res = 0
        var i = 0
        while (i < n) {
            var j = i
            var maxi = 0
            var curr = 0
            while (j < n && colors[j] == colors[i]) {
                maxi = maxOf(maxi, neededTime[j])
                curr += neededTime[j]
                j++
            }
            res += curr - maxi
            i = j
        }
        return res
    }
}

class Solution {
    func minCost(_ colors: String, _ neededTime: [Int]) -> Int {
        let n = neededTime.count
        let chars = Array(colors)
        var res = 0
        var i = 0
        while i < n {
            var j = i
            var maxi = 0
            var curr = 0
            while j < n && chars[j] == chars[i] {
                maxi = max(maxi, neededTime[j])
                curr += neededTime[j]
                j += 1
            }
            res += curr - maxi
            i = j
        }
        return res
    }
}

impl Solution {
    pub fn min_cost(colors: String, needed_time: Vec<i32>) -> i32 {
        let n = needed_time.len();
        let colors = colors.as_bytes();
        let mut res = 0;
        let mut i = 0;
        while i < n {
            let mut j = i;
            let mut maxi = 0;
            let mut curr = 0;
            while j < n && colors[j] == colors[i] {
                maxi = maxi.max(needed_time[j]);
                curr += needed_time[j];
                j += 1;
            }
            res += curr - maxi;
            i = j;
        }
        res
    }
}

Time & Space Complexity

Time complexity: $O(n)$
Space complexity: $O(1)$ extra space.

2. Two Pointers - II

Intuition

Instead of finding entire groups at once, we can process pairs of adjacent balloons. When two adjacent balloons have the same color, we remove the one with smaller removal time. We keep a pointer l to track the balloon we're keeping, and compare it with each new balloon at position r.

Algorithm

Initialize l = 0 and res = 0.
For each r from 1 to n-1:
- If colors[l] == colors[r] (same color):
  - If neededTime[l] < neededTime[r]: add neededTime[l] to res and update l = r.
  - Otherwise: add neededTime[r] to res (keep l unchanged).
- If different colors: update l = r.
Return res.

class Solution:
    def minCost(self, colors: str, neededTime: List[int]) -> int:
        l, res = 0, 0
        for r in range(1, len(colors)):
            if colors[l] == colors[r]:
                if neededTime[l] < neededTime[r]:
                    res += neededTime[l]
                    l = r
                else:
                    res += neededTime[r]
            else:
                l = r
        return res

public class Solution {
    public int minCost(String colors, int[] neededTime) {
        int l = 0, res = 0;
        for (int r = 1; r < colors.length(); r++) {
            if (colors.charAt(l) == colors.charAt(r)) {
                if (neededTime[l] < neededTime[r]) {
                    res += neededTime[l];
                    l = r;
                } else {
                    res += neededTime[r];
                }
            } else {
                l = r;
            }
        }
        return res;
    }
}

class Solution {
public:
    int minCost(string colors, vector<int>& neededTime) {
        int l = 0, res = 0;
        for (int r = 1; r < colors.size(); r++) {
            if (colors[l] == colors[r]) {
                if (neededTime[l] < neededTime[r]) {
                    res += neededTime[l];
                    l = r;
                } else {
                    res += neededTime[r];
                }
            } else {
                l = r;
            }
        }
        return res;
    }
};

class Solution {
    /**
     * @param {string} colors
     * @param {number[]} neededTime
     * @return {number}
     */
    minCost(colors, neededTime) {
        let l = 0,
            res = 0;
        for (let r = 1; r < colors.length; r++) {
            if (colors[l] === colors[r]) {
                if (neededTime[l] < neededTime[r]) {
                    res += neededTime[l];
                    l = r;
                } else {
                    res += neededTime[r];
                }
            } else {
                l = r;
            }
        }
        return res;
    }
}

public class Solution {
    public int MinCost(string colors, int[] neededTime) {
        int l = 0, res = 0;
        for (int r = 1; r < colors.Length; r++) {
            if (colors[l] == colors[r]) {
                if (neededTime[l] < neededTime[r]) {
                    res += neededTime[l];
                    l = r;
                } else {
                    res += neededTime[r];
                }
            } else {
                l = r;
            }
        }
        return res;
    }
}

func minCost(colors string, neededTime []int) int {
    l, res := 0, 0
    for r := 1; r < len(colors); r++ {
        if colors[l] == colors[r] {
            if neededTime[l] < neededTime[r] {
                res += neededTime[l]
                l = r
            } else {
                res += neededTime[r]
            }
        } else {
            l = r
        }
    }
    return res
}

class Solution {
    fun minCost(colors: String, neededTime: IntArray): Int {
        var l = 0
        var res = 0
        for (r in 1 until colors.length) {
            if (colors[l] == colors[r]) {
                if (neededTime[l] < neededTime[r]) {
                    res += neededTime[l]
                    l = r
                } else {
                    res += neededTime[r]
                }
            } else {
                l = r
            }
        }
        return res
    }
}

class Solution {
    func minCost(_ colors: String, _ neededTime: [Int]) -> Int {
        let chars = Array(colors)
        var l = 0
        var res = 0
        for r in 1..<chars.count {
            if chars[l] == chars[r] {
                if neededTime[l] < neededTime[r] {
                    res += neededTime[l]
                    l = r
                } else {
                    res += neededTime[r]
                }
            } else {
                l = r
            }
        }
        return res
    }
}

impl Solution {
    pub fn min_cost(colors: String, needed_time: Vec<i32>) -> i32 {
        let colors = colors.as_bytes();
        let mut l = 0;
        let mut res = 0;
        for r in 1..colors.len() {
            if colors[l] == colors[r] {
                if needed_time[l] < needed_time[r] {
                    res += needed_time[l];
                    l = r;
                } else {
                    res += needed_time[r];
                }
            } else {
                l = r;
            }
        }
        res
    }
}

Time & Space Complexity

Time complexity: $O(n)$
Space complexity: $O(1)$ extra space.

3. Two Pointers - III

Intuition

We can simplify the logic further by tracking the maximum removal time seen so far in the current group of same-colored balloons. For each balloon, we add the minimum of the current maximum and the current balloon's time to the result, then update the maximum. When we encounter a different color, we reset the maximum to 0.

Algorithm

Initialize res = 0 and maxi = 0.
For each index i:
- If i > 0 and colors[i] != colors[i-1], reset maxi = 0.
- Add min(maxi, neededTime[i]) to res.
- Update maxi = max(maxi, neededTime[i]).
Return res.

class Solution:
    def minCost(self, colors: str, neededTime: List[int]) -> int:
        res = maxi = 0
        for i in range(len(colors)):
            if i and colors[i] != colors[i - 1]:
                maxi = 0
            res += min(maxi, neededTime[i])
            maxi = max(maxi, neededTime[i])
        return res

public class Solution {
    public int minCost(String colors, int[] neededTime) {
        int res = 0, maxi = 0;
        for (int i = 0; i < colors.length(); i++) {
            if (i > 0 && colors.charAt(i) != colors.charAt(i - 1)) {
                maxi = 0;
            }
            res += Math.min(maxi, neededTime[i]);
            maxi = Math.max(maxi, neededTime[i]);
        }
        return res;
    }
}

class Solution {
public:
    int minCost(string colors, vector<int>& neededTime) {
        int res = 0, maxi = 0;
        for (int i = 0; i < colors.size(); i++) {
            if (i > 0 && colors[i] != colors[i - 1]) {
                maxi = 0;
            }
            res += min(maxi, neededTime[i]);
            maxi = max(maxi, neededTime[i]);
        }
        return res;
    }
};

class Solution {
    /**
     * @param {string} colors
     * @param {number[]} neededTime
     * @return {number}
     */
    minCost(colors, neededTime) {
        let res = 0,
            maxi = 0;
        for (let i = 0; i < colors.length; i++) {
            if (i > 0 && colors[i] !== colors[i - 1]) {
                maxi = 0;
            }
            res += Math.min(maxi, neededTime[i]);
            maxi = Math.max(maxi, neededTime[i]);
        }
        return res;
    }
}

public class Solution {
    public int MinCost(string colors, int[] neededTime) {
        int res = 0, maxi = 0;
        for (int i = 0; i < colors.Length; i++) {
            if (i > 0 && colors[i] != colors[i - 1]) {
                maxi = 0;
            }
            res += Math.Min(maxi, neededTime[i]);
            maxi = Math.Max(maxi, neededTime[i]);
        }
        return res;
    }
}

func minCost(colors string, neededTime []int) int {
    res, maxi := 0, 0
    for i := 0; i < len(colors); i++ {
        if i > 0 && colors[i] != colors[i-1] {
            maxi = 0
        }
        if maxi < neededTime[i] {
            res += maxi
            maxi = neededTime[i]
        } else {
            res += neededTime[i]
        }
    }
    return res
}

class Solution {
    fun minCost(colors: String, neededTime: IntArray): Int {
        var res = 0
        var maxi = 0
        for (i in colors.indices) {
            if (i > 0 && colors[i] != colors[i - 1]) {
                maxi = 0
            }
            res += minOf(maxi, neededTime[i])
            maxi = maxOf(maxi, neededTime[i])
        }
        return res
    }
}

class Solution {
    func minCost(_ colors: String, _ neededTime: [Int]) -> Int {
        let chars = Array(colors)
        var res = 0
        var maxi = 0
        for i in 0..<chars.count {
            if i > 0 && chars[i] != chars[i - 1] {
                maxi = 0
            }
            res += min(maxi, neededTime[i])
            maxi = max(maxi, neededTime[i])
        }
        return res
    }
}

impl Solution {
    pub fn min_cost(colors: String, needed_time: Vec<i32>) -> i32 {
        let colors = colors.as_bytes();
        let mut res = 0;
        let mut maxi = 0;
        for i in 0..colors.len() {
            if i > 0 && colors[i] != colors[i - 1] {
                maxi = 0;
            }
            res += maxi.min(needed_time[i]);
            maxi = maxi.max(needed_time[i]);
        }
        res
    }
}

Time & Space Complexity

Time complexity: $O(n)$
Space complexity: $O(1)$ extra space.

Common Pitfalls

Removing the Wrong Balloon

When encountering consecutive same-colored balloons, some may instinctively remove the first balloon encountered or remove all of them. The correct strategy is to keep the balloon with the maximum removal time and remove all others, minimizing total cost.

Forgetting to Reset State Between Groups

When processing groups of consecutive same-colored balloons, failing to reset the maximum or sum tracking variables when transitioning to a new color group leads to incorrect calculations. Each group must be processed independently.

Off-by-One Errors in Group Boundaries

When using two pointers to identify groups of consecutive balloons, it is easy to mishandle the boundary conditions, either including an extra balloon from the next group or missing the last balloon in the current group. Carefully ensure the inner loop condition correctly identifies when colors change.