Add Paint House III.cpp file

This program solves issue Rohit0301#48
Question Link: https://leetcode.com/problems/paint-house-iii/

Leetcode/Paint_House_III.cpp

@@ -0,0 +1,70 @@
+/*
+Question Link: https://leetcode.com/problems/paint-house-iii/
+*/
+
+
+class Solution {
+public:
+
+    int dp[103][103][103];
+
+    int help(vector<int> &houses, vector<vector<int>> &cost, int m, int n, int target, int i, int prev) {
+
+        if (i == m) {
+            if (!target) return 0;
+            else return 1e9;
+        }
+
+        if (target < 0) return  1e9;
+
+        if (dp[i][prev][target] != -1) return dp[i][prev][target];
+
+
+        int mn = 1e9;
+
+        // case 1:
+        // no need to colorize
+        if (houses[i]) {
+            if (houses[i] != prev) // nbrs increase, hence target decreases
+                return dp[i][prev][target] = help(houses, cost, m, n, target - 1, i + 1, houses[i]);
+
+            else return dp[i][prev][target] = help(houses, cost, m, n, target, i + 1, houses[i]);
+        }
+
+        else {
+
+            // case 2: color them
+
+            // I need to paint with colors [1,n] such that the current color isn't the same as the prev
+            // if they are the same, nbrs remain the same (no change in target)
+            // else, nbrs increase, so target-1
+
+            // colors: 1 to n
+            // cost[i][j]: cost to paint ith building with color j+1
+
+
+            for (int c = 1; c <= n; c++) {
+                int cur = cost[i][c - 1];
+
+                if (prev == c) cur += help(houses, cost, m , n, target, i + 1, c);
+                else {
+
+                    // explore the rest (next rows)
+                    cur += help(houses, cost, m , n, target - 1, i + 1, c);
+                }
+                mn = min(mn, cur);
+            }
+
+            return dp[i][prev][target] = mn;
+        }
+
+
+    }
+
+    int minCost(vector<int>& houses, vector<vector<int>>& cost, int m, int n, int target) {
+
+        memset(dp, -1, sizeof(dp));
+        int mm =  help(houses, cost, m, n, target, 0, 0);
+        return (mm >= 1e9) ? -1 : mm;
+    }
+};