964. Least Operators to Express Number

leastOpsExpressTarget.cpp

@@ -0,0 +1,45 @@
+class Solution {
+public:
+    int leastOpsExpressTarget(int x, int target) {
+        int r = target%x, c = x - r;
+        // Get number of x's used to express residual
+        int nr = min(2*r, 1 + 2*(x - r));
+        int nc = min(2*c, 1 + 2*(x-c));
+        return min(nr + dfs(target - r, x), nc + dfs(target + c, x)) - 1;
+    }
+private:
+    // Memorization
+    unordered_map<long, int> dp;
+    int dfs(long target, int x) {
+        if (target == 0)
+            return 0;
+        if (dp.find(target) != dp.end())
+            return dp[target];
+
+        long num = target;
+        int c = 0;
+        long lowestPower = 1;
+
+        // Get least significant x-git of target
+        while (num && (num%x == 0)) {
+            num /= x;
+            ++c;
+            lowestPower *= x;
+        }
+
+        int lowestPowerCoeff = (target/lowestPower)%x;
+        int distToHigherPower = lowestPower*(x - lowestPowerCoeff);
+
+        // If target only has one x-git, exit
+        if (lowestPowerCoeff*lowestPower == target) {
+            dp[target] = min(lowestPowerCoeff*c, (x - lowestPowerCoeff)*c + c + 1);
+            return dp[target];
+        }
+
+        int dp1 = lowestPowerCoeff*c + dfs(target - lowestPowerCoeff*lowestPower, x);
+        int dp2 = (x - lowestPowerCoeff)*c + dfs(target + distToHigherPower, x);
+
+        dp[target] = min(dp1, dp2); 
+        return dp[target];
+    }
+};