Commit explanation of optimized approach

Author: SartHak-0-Sach

209-27th_July-Min_cost_to_convert/approach-explanation.txt

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+Intuition
+step 1: make graph
+step 2: Floyd-Warshall algorithm to find the minimum transformation costs between all pairs of characters
+
+Approach
+The goal is to transform the string source into the string target using the minimal cost specified in the cost array. The transformation rules are defined by the original and changed arrays, where original[i] can be changed to changed[i] at a cost of cost[i].
+
+Complexity
+Time complexity:
+O(m+n^3)
+
+Space complexity:
+O(n^2)

209-27th_July-Min_cost_to_convert/code.cpp

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+class Solution
+{
+public:
+    long long minimumCost(string source, string target, vector<char> &original, vector<char> &changed, vector<int> &cost)
+    {
+        int n = 26;
+        vector<vector<int>> grid(n, vector<int>(n, INT_MAX));
+        for (int i = 0; i < n; i++)
+        {
+            grid[i][i] = 0;
+        }
+
+        for (int i = 0; i < original.size(); i++)
+        {
+            int from = original[i] - 'a';
+            int to = changed[i] - 'a';
+            grid[from][to] = min(grid[from][to], cost[i]);
+        }
+
+        for (int via = 0; via < n; via++)
+        {
+            for (int i = 0; i < n; i++)
+            {
+                for (int j = 0; j < n; j++)
+                {
+                    if (grid[i][via] != INT_MAX && grid[via][j] != INT_MAX)
+                    {
+                        grid[i][j] = min(grid[i][j], grid[i][via] + grid[via][j]);
+                    }
+                }
+            }
+        }
+
+        long long ans = 0;
+        for (int i = 0; i < source.size(); i++)
+        {
+            if (source[i] != target[i])
+            {
+                int cost = grid[source[i] - 'a'][target[i] - 'a'];
+                if (cost == INT_MAX)
+                    return -1;
+                ans += cost;
+            }
+        }
+        return ans;
+    }
+};