From dd9eaefbd22083857654cd41af04d686b88a87e8 Mon Sep 17 00:00:00 2001
From: EdouardParis <mail@edouard.paris>
Date: Wed, 1 Jun 2016 15:08:14 +0200
Subject: [PATCH] Question_13.cpp
---
src/Makefile | 5 ++-
src/question_13.cpp | 74 +++++++++++++++++++++++++++++++++++++++++++++
2 files changed, 78 insertions(+), 1 deletion(-)
create mode 100644 src/question_13.cpp
diff --git a/src/Makefile b/src/Makefile
index 75887c5..96ab7f5 100644
--- a/src/Makefile
+++ b/src/Makefile
@@ -1,4 +1,4 @@
-all: question_3 question_5 question_9 question_11
+all: question_3 question_5 question_9 question_11 question_13
question_3: question_3.cpp
g++ -o ./bin/question_3 question_3.cpp -Wall -Wextra -lgmp -lgmpxx
@@ -12,6 +12,9 @@ question_9: question_9.cpp
question_11: question_11.cpp
g++ -o ./bin/question_11 question_11.cpp -Wall -Wextra -lgmp -lgmpxx
+question_13: question_13.cpp
+ g++ -o ./bin/question_13 question_13.cpp -Wall -Wextra -lgmp -lgmpxx
+
test:
./test.sh
diff --git a/src/question_13.cpp b/src/question_13.cpp
new file mode 100644
index 0000000..aa4de48
--- /dev/null
+++ b/src/question_13.cpp
@@ -0,0 +1,74 @@
+/*Projet Edouard Paris 2016 - Arithmetique entière
+ *
+ * Question 13
+ * */
+
+#include <iostream>
+#include <cstdlib>
+#include <gmpxx.h>
+#include <cassert>
+
+void algo_k_root(mpz_class const& a, long const k, mpz_class & res)
+{
+ mpz_class r1 = a + 1;
+ mpz_class r2 = a;
+ mpz_class r3 = a;
+
+ while (r2 < r1 && r2 != 0) {
+ r1 = r2;
+ mpz_pow_ui(r3.get_mpz_t(), r1.get_mpz_t(), (k-1));
+ r2 = (r1*(k - 1) + (a / r3))/k;
+ }
+
+ mpz_pow_ui(r3.get_mpz_t(), r2.get_mpz_t(), k);
+
+ if ((a - r3) != 0) {
+ res = 0;
+ } else {
+ res = r2;
+ }
+};
+
+long fact_perf_pow(mpz_class const& a, mpz_class * res)
+{
+ long l;
+ long k = 0;
+ long n = 1;
+ mpz_class b(0);
+ mpz_class p(2);
+
+ while (b == 0 && p < a) {
+ n = n+1;
+ algo_k_root(a, n, b);
+ p = p*2;
+ }
+
+ if (b == 0) {
+ *res = a;
+ }
+ else {
+ l = fact_perf_pow(b, res);
+ k = n + l;
+ }
+
+ return k;
+};
+
+int main(int argc, char** argv) {
+ long k;
+
+ assert(argc == 2);
+ long n = strtol(argv[1], NULL, 10);
+
+ mpz_class a(n);
+ mpz_class res(0);
+
+ k = fact_perf_pow(a, &res);
+
+ if (a == res) {
+ k = 1;
+ }
+
+ std::cout << res << "\t" << k << std::endl;
+ return 0;
+}
--
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