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day-90.cpp
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day-90.cpp
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/*
Unique Paths
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?
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
*/
// Bottom up simple DP solutions
// O(row * cols) both time & space complexity
class Solution {
public:
int uniquePaths(int m, int n) {
vector<vector<int>> dp(m, vector<int>(n));
for (int i = 0; i < n; i++) {
dp[m - 1][i] = 1;
}
for (int i = 0; i < m; i++) {
dp[i][n - 1] = 1;
}
for (int i = m - 2; i >= 0; i--) {
for (int j = n - 2; j >= 0; j--) {
dp[i][j] = dp[i + 1][j] + dp[i][j + 1];
}
}
return dp[0][0];
}
};