package algo

func DP(arr []int) int {
	n := len(arr) - 1
	if n <= 0 {
		return 0
	}

	const inf = int(^uint(0) >> 1)
	dp := make([][]int, n)
	for i := range dp {
		dp[i] = make([]int, n)
	}

	for length := 2; length <= n; length++ {
		for l := 0; l+length-1 < n; l++ {
			r := l + length - 1
			dp[l][r] = inf
			for k := l; k < r; k++ {
				cost := dp[l][k] + dp[k+1][r] + arr[l]*arr[k+1]*arr[r+1]
				if cost < dp[l][r] {
					dp[l][r] = cost
				}
			}
		}
	}

	return dp[0][n-1]
}

func Greedy(arr []int) int {
	if len(arr) <= 2 {
		return 0
	}

	dims := append([]int(nil), arr...)
	cost := 0

	for len(dims) > 2 {
		best := 1
		for i := 2; i < len(dims)-1; i++ {
			if dims[i] > dims[best] {
				best = i
			}
		}

		cost += dims[best-1] * dims[best] * dims[best+1]
		dims = append(dims[:best], dims[best+1:]...)
	}

	return cost
}