> For the complete documentation index, see [llms.txt](https://mayanktyagi3111.gitbook.io/interview-prep/llms.txt). Markdown versions of documentation pages are available by appending `.md` to page URLs; this page is available as [Markdown](https://mayanktyagi3111.gitbook.io/interview-prep/dynamic-programming/minimum-and-maximum-values-of-an-expression-with-and-+.md).

# Minimum and Maximum values of an expression with \* and +

Given an expression which contains numbers and two operators ‘+’ and ‘\*’, we need to find maximum and minimum value which can be obtained by evaluating this expression by different parenthesization.\
Examples:

```
Input  : expr = “1+2*3+4*5” 
Output : Minimum Value = 27, Maximum Value = 105 
Explanation:
Minimum evaluated value = 1 + (2*3) + (4*5) = 27
Maximum evaluated value = (1 + 2)*(3 + 4)*5 = 105
```

```java
class Solution {
    public static void minMaxValues(String exp) {
        // Converting String into array of Strings
        ArrayList<StringBuilder> list = new ArrayList<>();
        for (int i = 0; i < exp.length(); i++) {
            StringBuilder str = new StringBuilder();
            if (exp.charAt(i) == '+' || exp.charAt(i) == '*')
                str.append(exp.charAt(i));
            else {
                while (i < exp.length() && exp.charAt(i) >= '0' && exp.charAt(i) <= '9')
                    str.append(exp.charAt(i++));
                i--;
            }
            list.add(str);
        }
        String[] str = new String[list.size()];
        for (int i = 0; i < list.size(); i++)
            str[i] = list.get(i).toString();
        int n = str.length;
        // DP[i][j] -> Min/Max ans between [i,j]
        int[][] minDP = new int[n][n], maxDP = new int[n][n];
        // Diagonal base case
        for (int i = 0; i < n; i += 2)
            minDP[i][i] = maxDP[i][i] = Integer.parseInt(str[i]);
        // Remember i,j stays at numerical values
        for (int i = n - 1; i >= 0; i -= 2) {
            for (int j = i + 2; j < n; j += 2) {
                minDP[i][j] = Integer.MAX_VALUE;
                maxDP[i][j] = Integer.MIN_VALUE;
                // Consider all the symbols one be one for first execution
                // K runs at symbol values
                for (int k = i + 1; k <= j - 1; k += 2) {
                    int leftAnsMin = minDP[i][k - 1], rightAnsMin = minDP[k + 1][j];
                    int leftAnsMax = maxDP[i][k - 1], rightAnsMax = maxDP[k + 1][j];
                    int minAns, maxAns;
                    if (str[k].equals("+")) {
                        minAns = leftAnsMin + rightAnsMin;
                        maxAns = leftAnsMax + rightAnsMax;
                    } else {
                        minAns = leftAnsMin * rightAnsMin;
                        maxAns = leftAnsMax * rightAnsMax;
                    }
                    minDP[i][j] = Math.min(minDP[i][j], minAns);
                    maxDP[i][j] = Math.max(maxDP[i][j], maxAns);
                }
            }
        }
        System.out.println("Max Result : " + maxDP[0][n - 1]);
        System.out.println("Min Result : " + minDP[0][n - 1]);
    }
}
```


---

# Agent Instructions
This documentation is published with GitBook. GitBook is the documentation platform designed so that both humans and AI agents can read, navigate, and reason over technical content effectively. Learn more at gitbook.com.

## Querying This Documentation
If you need additional information that is not directly available in this page, you can query the documentation dynamically by asking a question.

Perform an HTTP GET request on the current page URL with the `ask` query parameter:

```
GET https://mayanktyagi3111.gitbook.io/interview-prep/dynamic-programming/minimum-and-maximum-values-of-an-expression-with-and-+.md?ask=<question>
```

The question should be specific, self-contained, and written in natural language.
The response will contain a direct answer to the question and relevant excerpts and sources from the documentation.

Use this mechanism when the answer is not explicitly present in the current page, you need clarification or additional context, or you want to retrieve related documentation sections.