# number solitair

February 9, 2023

## Problem

## Solution

package mainimport ( "fmt" "math")func main() { fmt.Println(Solution([]int{1, -2, -0, 9, -1, -2})) // it should be 8}func Solution(A []int) int { n := len(A) dp := make([]int, n) dp[0] = A[0] for i := 1; i < n; i++ { maxVal := math.MinInt for j := 1; j <= 6; j++ { if i-j >= 0 { maxVal = max(maxVal, dp[i-j]+A[i]) } } dp[i] = maxVal } return dp[n-1]}func max(a, b int) int { if a > b { return a } return b}

The code above implements a dynamic programming algorithm to find the maximum sum of an array `A`

of integers. The array `A`

represents a sequence of numbers, and the goal is to find the maximum sum of a sub-sequence of `A`

with the restriction that the sub-sequence can only have a maximum length of 6.

The algorithm starts by initializing an array `dp`

with the same length as `A`

. The first element of `dp`

is set to the first element of `A`

, which is `A[0]`

.

Next, the code loops through each element of `A`

starting from index 1 to the end of the array `A`

. For each element, the code calculates the maximum value that can be achieved by adding the current element to the sum of one of the previous 6 elements. It does this by looping through the previous 6 elements and checking if the current index minus `j`

(where `j`

is the loop variable) is greater than or equal to zero. If this is the case, the maximum value is updated by taking the maximum of the current `maxVal`

and the sum of the current element of `A`

and the corresponding element in `dp`

(which represents the maximum sum of a sub-sequence ending at that element).

The calculated maximum value is then stored in the current element of `dp`

. This process continues until the end of the loop, after which the last element of `dp`

is returned, which represents the maximum sum of a sub-sequence of `A`

with the restriction that the sub-sequence can only have a maximum length of 6.

The `max`

function is a helper function that returns the maximum of two integers.