1+ // Problem : Given a triangle array, return the minimum path sum from top to bottom. For each step, you may move to an
2+ // adjacent number of the row below.More formally, if you are on index i on the current row, you may move to either
3+ // index i or index i + 1 on the next row.
4+ 5+ #include < bits/stdc++.h>
6+ using namespace std ;
7+ 8+ int minimumTotal (vector<vector<int >> &triangle)
9+ {
10+ int n = triangle.size ();
11+ vector<vector<int >> dp (n);
12+ for (int i = 0 ; i < n; i++)
13+ {
14+ for (int j = 0 ; j < triangle[i].size (); j++)
15+ {
16+ if (i == 0 and j == 0 )
17+ {
18+ // very first cell
19+ dp[i].push_back (triangle[i][j]);
20+ }
21+ else if (j == 0 )
22+ {
23+ // we can jump to this cell by one way(⬇️)
24+ dp[i].push_back (dp[i - 1 ][j] + triangle[i][j]);
25+ }
26+ else if (j == (triangle[i].size () - 1 ))
27+ {
28+ // we can jump to this cell by one way(↘️)
29+ dp[i].push_back (dp[i - 1 ][j - 1 ] + triangle[i][j]);
30+ }
31+ else
32+ {
33+ // we can jump to this cell by two ways(⬇️ and ↘️)
34+ dp[i].push_back (min (dp[i - 1 ][j], dp[i - 1 ][j - 1 ]) + triangle[i][j]);
35+ }
36+ }
37+ }
38+ // returning the minimum out of all calculated sums
39+ return *min_element (dp[n - 1 ].begin (), dp[n - 1 ].end ());
40+ }
41+ int main ()
42+ {
43+ int n;
44+ cin >> n;
45+ vector<vector<int >> triangle (n);
46+ for (int i = 0 ; i < n; i++)
47+ {
48+ for (int j = 0 ; j <= i; j++)
49+ {
50+ int x;
51+ cin >> x;
52+ triangle[i].push_back (x);
53+ }
54+ }
55+ cout << minimumTotal (triangle);
56+ }
57+ 58+ // Sample Inputs
59+ 60+ // Sample Inputs
61+ 62+ // Sample Inputs
63+ 64+ // 4
65+ // 2
66+ // 3 4
67+ // 6 5 7
68+ // 4 1 8 3
69+ 70+ // 1
71+ // -10
72+ 73+ // Corresponding Outputs
74+ 75+ // 11
76+ 77+ // -10
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