minFallingPathSumTriangle.cpp created

Dynamic Programming/minFallingPathSumTriangle.cpp

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+// Problem : Given a triangle array, return the minimum path sum from top to bottom. For each step, you may move to an
+// adjacent number of the row below.More formally, if you are on index i on the current row, you may move to either
+// index i or index i + 1 on the next row.
+
+#include <bits/stdc++.h>
+using namespace std;
+
+int minimumTotal(vector<vector<int>> &triangle)
+{
+    int n = triangle.size();
+    vector<vector<int>> dp(n);
+    for (int i = 0; i < n; i++)
+    {
+        for (int j = 0; j < triangle[i].size(); j++)
+        {
+            if (i == 0 and j == 0)
+            {
+                // very first cell
+                dp[i].push_back(triangle[i][j]);
+            }
+            else if (j == 0)
+            {
+                // we can jump to this cell by one way(⬇️)
+                dp[i].push_back(dp[i - 1][j] + triangle[i][j]);
+            }
+            else if (j == (triangle[i].size() - 1))
+            {
+                // we can jump to this cell by one way(↘️)
+                dp[i].push_back(dp[i - 1][j - 1] + triangle[i][j]);
+            }
+            else
+            {
+                // we can jump to this cell by two ways(⬇️ and ↘️)
+                dp[i].push_back(min(dp[i - 1][j], dp[i - 1][j - 1]) + triangle[i][j]);
+            }
+        }
+    }
+    // returning the minimum out of all calculated sums
+    return *min_element(dp[n - 1].begin(), dp[n - 1].end());
+}
+int main()
+{
+    int n;
+    cin >> n;
+    vector<vector<int>> triangle(n);
+    for (int i = 0; i < n; i++)
+    {
+        for (int j = 0; j <= i; j++)
+        {
+            int x;
+            cin >> x;
+            triangle[i].push_back(x);
+        }
+    }
+    cout << minimumTotal(triangle);
+}
+
+// Sample Inputs
+
+// Sample Inputs
+
+// Sample Inputs
+
+// 4
+// 2
+// 3 4
+// 6 5 7
+// 4 1 8 3
+
+// 1
+// -10
+
+// Corresponding Outputs
+
+// 11
+
+// -10