算法学习记录（五十七）

问：

1. 剑指 Offer 10- II. 青蛙跳台阶问题
2. 剑指 Offer 12. 矩阵中的路径
3. 剑指 Offer 13. 机器人的运动范围
4. 剑指 Offer 14- I. 剪绳子

解： 1.

const numWays = function(n) {
    const dp = []
    const mod = 1000000007
    dp[n] = 1
    for (let i = n - 1; i >= 0; i--) {
        dp[i] = (dp[i + 1] + (dp[i + 2] ?? 0)) % mod
    }
    return dp[0]
};

const exist = function(board, word) {
     for (let i = 0; i < board.length; i++) {
        for (let j = 0; j < board[0].length; j++) {
            if (getRes(i, j, 0)) return true
        }
    }
    return false
    function getRes(x, y, len) {
        if (x < 0 || y < 0 || x > board.length - 1 || y > board[0].length - 1 || board[x][y] !== word[len]) return false
        if (len === word.length - 1) return true
        board[x][y] = ''
        const res = getRes(x + 1, y, len + 1) || getRes(x - 1, y, len + 1) || getRes(x, y + 1, len + 1) || getRes(x, y - 1, len + 1);
        board[x][y] = word[len]
        return res
    }
};

const movingCount = function(m, n, k) {
    const isActive = []
    for (let i = 0; i < m; i++) {
        isActive[i] = []
    }
    function getRes(i, j) {
        if (i < 0 || j < 0 || i >= m || j >= n || sum(i, j) > k || isActive[i][j]) return 0
        isActive[i][j] = true
        return getRes(i, j + 1) + getRes(i, j - 1) + getRes(i + 1, j) + getRes(i - 1, j) + 1
    }
    return getRes(0, 0, false)
    function sum(i, j) {
        i = i.toString()
        j = j.toString()
        const arr = i.split('').concat(j.split(''))
        return arr.reduce((pre, item) => {
            return pre + +item
        }, 0)
    }
};

const cuttingRope = function(n) {
    const dp = []
    dp[0] = 1
    dp[1] = 1
    dp[2] = 1
    for (let i = 3; i <= n; i++) {
        dp[i] = 0
        for (let j = 2; j < i; j++) {
            dp[i] = Math.max(Math.max(dp[i - j] * j, j * (i - j)), dp[i])
        }
    }
    return dp[n]
};