DynamicProgrammingStriver/UniquePathsLecture8.cpp at main · dhruvkej9/DynamicProgrammingStriver · GitHub

1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
#include "vector"
#include "iostream"
using namespace std;
int f(int i,int j,vector<vector<int>> dp)
{
    if(i == 0 && j == 0) return 1;
    if(i<0 || j<0) return 0;
    if(dp[i][j] != -1) return dp[i][j];
    int up = f(i-1,j,dp);
    int left = f(i,j-1,dp);
    return dp[i][j] = up + left;
}
int f2(int m, int n)
{
    vector<vector<int>> dp(m,vector<int>(n));
    for(int i = 0;i<m;i++)
    {
        for(int j = 0;j < n;j++)
        {
            if(i == 0 && j == 0) dp[i][j] = 1;
            else
            {
                int up = 0;
                int left = 0;
                if(i > 0) up = dp[i-1][j];
                if(j > 0) left = dp[i][j-1];
                dp[i][j] = up + left;
            }
        }
    }
    return dp[m-1][n-1];
}
int f3(int m, int n)
{
    vector<int> prev(n,0);
    for(int i = 0;i<m;i++)
    {
        vector<int> cur(n,0);
        for(int j = 0;j < n;j++)
        {
            if(i == 0 && j == 0) cur[j] = 1;
            else
            {
                int up = 0;
                int left = 0;
                if(i > 0) up = prev[j];
                if(j > 0) left = cur[j-1];
                cur[j] = up + left;
            }
        }
        prev = cur;
    }
    return prev[n-1];
}
int uniquePaths(int m, int n)
{
    vector<vector<int>> dp(m,vector<int>(n,-1));
	return f2(m,n);
}