//70、爬楼梯
func climbStairs(n int) int {
	//dp[i]爬i阶楼梯的方法数
	//dp[i]=dp[i-1]+dp[i-2]
	dp := make([]int, n+1)
	dp[0], dp[1] = 1, 1
	for i := 2; i <= n; i++ {
		dp[i] = dp[i-1] + dp[i-2]
	}
	return dp[n]

}

//62、不同路径
func uniquePaths(m int, n int) int {
	dp := make([][]int, m+1)
	for i := 0; i < m+1; i++ {
		dp[i] = make([]int, n+1)
	}
	for i := 0; i < m+1; i++ {
		dp[i][0] = 1
	}
	for j := 0; j < n+1; j++ {
		dp[0][j] = 1
	}
	for i := 1; i <= m; i++ {
		for j := 1; j <= n; j++ {
			dp[i][j] = dp[i][j-1] + dp[i-1][j]
		}
	}
	return dp[m-1][n-1]
}

//118.杨辉三角
func generate(numRows int) [][]int {
	dp := make([][]int, numRows)
	for i := 0; i < numRows; i++ {
		dp[i] = make([]int, i+1)
	}
	for i := 0; i < numRows; i++ {
		dp[i][0] = 1
		dp[i][i] = 1
	}
	for i := 2; i < numRows; i++ {
		for j := 1; j < i; j++ {
			dp[i][j] = dp[i-1][j] + dp[i-1][j-1]
		}
	}
	return dp
}

//198、打家劫舍
func rob(nums []int) int {
	dp := make([]int, len(nums))
	dp[0] = nums[0]
	dp[1] = max(nums[0], nums[1])
	for i := 2; i < len(nums); i++ {
		dp[i] = max(dp[i-1], dp[i-2]+nums[i])
	}
	return dp[len(nums)-1]
}

//279、完全平方数
func numSquares(n int) int {
	//完全背包
	dp := make([]int, n+1)
	dp[0] = 0
	for i := 1; i < n+1; i++ {
		dp[i] = math.MaxInt32
	}
	for i := 1; i*i <= n; i++ {
		for j := i * i; j <= n; j++ {
			dp[j] = min(dp[j-i*i]+1, dp[j])
		}
	}
	return dp[n]

}