What is the brute force solution for Minimum Cost to Change the Final Value of Expression?

The brute force approach for Minimum Cost to Change the Final Value of Expression is Brute Force, with O(n²) time complexity and O(1) space complexity. The brute force approach evaluates all possible combinations of changing the bits and operators in the expression to see if the final value can be changed to 0. This method is straightforward but inefficient as it explores all possibilities. The optimal Optimal Solution approach improves this to O(n).

What algorithm or data structure is used to solve Minimum Cost to Change the Final Value of Expression?

Minimum Cost to Change the Final Value of Expression uses the following concepts: Math, String, Dynamic Programming, Stack. The recommended patterns to study are: Dynamic Programming, Stack.

What are the interview tips for Minimum Cost to Change the Final Value of Expression?

Clearly explain your thought process while coding. Break down the problem into smaller parts and solve each part individually. Practice evaluating expressions manually to understand how changes affect outcomes.

What are common mistakes when solving Minimum Cost to Change the Final Value of Expression?

Forgetting to handle operator precedence correctly. Not considering all possible states for each sub-expression.

#1896

Minimum Cost to Change the Final Value of Expression

Hard

MathStringDynamic ProgrammingStackDynamic ProgrammingStack

LeetCode ↗

Approaches

Brute ForceOptimal

Complexity Comparison

	Brute Force	Optimal Solution★
Time	O(n²)	O(n)
Space	O(1)	O(n)

💡

Intuition

Time O(n)Space O(n)

The optimal solution uses dynamic programming to minimize the cost of changing the expression by storing intermediate results for sub-expressions. This approach avoids redundant calculations and efficiently finds the minimum cost.

⚙️

Algorithm

3 steps

1Step 1: Use a stack to evaluate the expression and store the minimum cost to achieve both values (0 and 1) for each sub-expression.
2Step 2: For each operator, calculate the cost of changing the values based on the current operator and the values of the operands.
3Step 3: Return the minimum cost to change the final value to 0.

solution.py29 lines

1# Full working Python code
2from collections import defaultdict
3
4def min_cost_optimal(expression):
5    stack = []
6    cost_map = defaultdict(lambda: [float('inf'), float('inf')])
7    
8    for char in expression:
9        if char in '01':
10            cost_map[char] = [0, 0] if char == '1' else [1, 1]
11            stack.append(char)
12        elif char in '&|':
13            b = stack.pop()
14            a = stack.pop()
15            cost_a = cost_map[a]
16            cost_b = cost_map[b]
17            if char == '&':
18                cost_map[char] = [
19                    min(cost_a[0] + cost_b[0], cost_a[1] + cost_b[0] + 1, cost_a[0] + cost_b[1] + 1),
20                    min(cost_a[1] + cost_b[1], cost_a[1] + cost_b[0] + 1, cost_a[0] + cost_b[1] + 1)
21                ]
22            else:
23                cost_map[char] = [
24                    min(cost_a[0] + cost_b[0] + 1, cost_a[1] + cost_b[0], cost_a[0] + cost_b[1]),
25                    min(cost_a[1] + cost_b[1], cost_a[1] + cost_b[0] + 1, cost_a[0] + cost_b[1] + 1)
26                ]
27            stack.append(char)
28    return cost_map[stack[0]][0]
29

ℹ

Complexity note: The time complexity is O(n) because we process each character of the expression once, and the space complexity is O(n) due to the stack and cost map used to store intermediate results.

1Dynamic programming can significantly reduce redundant calculations.
2Understanding operator precedence and evaluation order is crucial.

Solutions and explanations are original Tejav content. Problem titles © LeetCode — use the LeetCode button above for the full problem statement.