PE 80, solved by digit-by-digit calculation

projecteuler/080/main.cpp

@@ -0,0 +1,95 @@
+#include <bits/stdc++.h>
+#include "../bigint.h"
+
+using namespace std;
+
+// This function should only work on positive integer n
+int rootDigitSum(unsigned int n, int decimals=99){
+
+    // Integer roots don't have decimals of course
+    int check = sqrt(n);
+    if(check * check == n){
+        return 0;
+    }
+
+    int result = check;
+    vector<int> digits;
+    
+    while(n > 0){
+        int last = n % 10;
+        n /= 10;
+
+        digits.push_back(last);
+    }
+
+    // Initialize method
+    InfInt remainder;
+    if(digits.size() % 2 == 0){
+        remainder = 10 * digits.back();
+        digits.pop_back();
+        remainder += digits.back();
+        digits.pop_back();
+    } else{
+        remainder = digits.back();
+        digits.pop_back();
+    }
+
+    InfInt minus = remainder.intSqrt();
+    InfInt root = minus;
+    remainder -= minus * minus;
+
+    while(decimals != 0){
+        // cout << remainder << " " << root << endl;
+        remainder *= 100;
+
+        bool decimalPart = true;
+        if(!digits.empty()){
+            decimalPart = false;
+
+            remainder += digits.back() * 10;
+            digits.pop_back();
+            remainder += digits.back();
+            digits.pop_back();
+        }
+
+        for(int guess = 0; guess < 10; ++guess){
+            InfInt lower = (root * 20 + guess) * guess;
+            InfInt upper = (root * 20 + guess + 1) * (guess + 1);
+            
+            if(lower <= remainder && remainder < upper){
+                remainder -= lower;
+                root = root * 10 + guess;
+
+                if(decimalPart) result += guess;
+
+                // cout << remainder << " " << root << " " << lower << " " << upper << endl;
+
+                break;
+            }
+        }
+
+        --decimals;
+    }
+    
+    return result;
+}
+
+int main(){
+
+    cout << "Hello this is Patrick" << endl;
+    auto start = chrono::high_resolution_clock::now();
+
+    int result = 0;
+
+    for(int i = 1; i <= 100; ++i){
+        result += rootDigitSum(i);
+    }
+
+    cout << result << endl;
+
+    // cout << rootDigitSum(2) << endl;
+
+    auto duration = chrono::duration_cast<chrono::milliseconds>(chrono::high_resolution_clock::now() - start);
+    cout << (float)duration.count()/1000 << endl;
+    return 0;
+}