p062.js

/**
 * A robot is located at the top-left corner of a m x n grid (marked 'Start' in the diagram below).

The robot can only move either down or right at any point in time. The robot is trying to reach the bottom-right corner of the grid (marked 'Finish' in the diagram below).

How many possible unique paths are there?


Above is a 7 x 3 grid. How many possible unique paths are there?

Note: m and n will be at most 100.

Example 1:

Input: m = 3, n = 2
Output: 3
Explanation:
From the top-left corner, there are a total of 3 ways to reach the bottom-right corner:
1. Right -> Right -> Down
2. Right -> Down -> Right
3. Down -> Right -> Right
Example 2:

Input: m = 7, n = 3
Output: 28
 */

/**
 * @param {number} m
 * @param {number} n
 * @return {number}
 */

var uniquePaths = function (m, n) {
  function factorial(x) {
    if (typeof x !== 'number' || x !== x) throw TypeError();
    if (x < 0) throw RangeError();
    if (x == 0) return 1;
    return x * factorial(x - 1);
  }
  return factorial(m + n - 2) / factorial(m - 1) / factorial(n - 1);
};

/**
 * 动态规划
 */

var uniquePaths2 = function (m, n) {
  var res = []
  for (let i = 0; i < m; i++) {
    res[i] = []
    for (let j = 0; j < n; j++) {
      res[i][j] = 1
    }
  }
  for (let i = 1; i < m; i++) {
    for (let j = 1; j < n; j++) {
      res[i][j] = res[i - 1][j] + res[i][j - 1]
    }
  }
  console.log(res)
  return res[m - 1][n - 1]
};


/**
 * 递归求解
 */

var uniquePaths3 = function (m, n) {
  findPath(1, 1, m, n)
  return road
};

var road = 0

var findPath = function (i, j, m, n) {
  if (m === 0 || n === 0) {
    return
  }
  if (i === m && j === n) {
    road = road + 1
    return
  }
  if (i === m) {
    findPath(i, j + 1, m, n)
  } else if (j === n) {
    findPath(i + 1, j, m, n)
  } else {
    findPath(i, j + 1, m, n)
    findPath(i + 1, j, m, n)
  }
}

console.log(uniquePaths2(7, 3))