Published Jan 19, 2022
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There is a robot on an m x n grid. The robot is initially located at the
top-left corner (i.e., grid[0][0]). The robot tries to move to the
bottom-right corner (i.e., grid[m - 1][n - 1]). The robot can only move either
down or right at any point in time.
Given the two integers m and n, return the number of possible unique paths that the robot can take to reach the bottom-right corner.
The test cases are generated so that the answer will be less than or equal to 2 * 10^9.
Input: m = 3, n = 7
Output: 28
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 -> Down -> Down
2. Down -> Down -> Right
3. Down -> Right -> Down
1 <= m, n <= 100
function uniquePaths(m: number, n: number): number {
// entry i, j represents number of ways to move to i, j
const table: number[][] = Array(m + 1).fill(null).map(x => Array(n + 1).fill(0));
table[1][1] = 1;
for(let i = 1; i <= m; i++){
for(let j = 1; j <= n; j++){
if(i === 1 && j === 1) continue;
// update i, j from sum of left & top
table[i][j] = table[i - 1][j] + table[i][j - 1]
}
}
return table[m][n];
};