Add fast problem 18 cpp solution

README.md

@@ -178,7 +178,7 @@ The following table summarizes the current project status. The speed of the fast
 |      15 |       -        |    -        |         -      |     -      |        -       |    + (0.00s)   |
 |      16 |    + (0.00s)   |    -        |         -      |     -      |        -       |    + (0.00s)   |
 |      17 |       -        |    -        |         -      |     -      |        -       |    + (0.01s)   |
-|      18 |       -        |    -        |         -      |     -      |        -       |    + (0.00s)   |
+|      18 |       -        |    -        |        TBD     |     -      |        -       |    + (0.00s)   |
 |      19 |    + (0.00s)   |    -        |    + (0.00s)   |     -      |        -       |        -       |
 |      20 |       -        |    -        |         -      |     -      |        -       |        -       |
 |      21 |       -        |    -        |         -      |     -      |        -       |        -       |

cpp_src/problem018.cpp

@@ -2,7 +2,7 @@
 //
 // Problem statement: By starting at the top of the triangle below and moving to adjacent numbers on the row below, the maximum total from top to bottom is 23.<p style="text-align:center;font-family:'courier new';font-size:12pt;"><span style="color:#ff0000;"><b>3</b></span><br /><span style="color:#ff0000;"><b>7</b></span> 4<br />2 <span style="color:#ff0000;"><b>4</b></span> 6<br />8 5 <span style="color:#ff0000;"><b>9</b></span> 3That is, 3 + 7 + 4 + 9 = 23.Find the maximum total from top to bottom of the triangle below:<p style="text-align:center;font-family:'courier new';">75<br />95 64<br />17 47 82<br />18 35 87 10<br />20 04 82 47 65<br />19 01 23 75 03 34<br />88 02 77 73 07 63 67<br />99 65 04 28 06 16 70 92<br />41 41 26 56 83 40 80 70 33<br />41 48 72 33 47 32 37 16 94 29<br />53 71 44 65 25 43 91 52 97 51 14<br />70 11 33 28 77 73 17 78 39 68 17 57<br />91 71 52 38 17 14 91 43 58 50 27 29 48<br />63 66 04 68 89 53 67 30 73 16 69 87 40 31<br />04 62 98 27 23 09 70 98 73 93 38 53 60 04 23<p class="note"><b>NOTE:</b> As there are only 16384 routes, it is possible to solve this problem by trying every route. However, Problem 67, is the same challenge with a triangle containing one-hundred rows; it cannot be solved by brute force, and requires a clever method! ;o)
 //
-// Solution description: Brute force, smart algorithm coming soon
+// Solution description: Brute force solution and a faster solution that will iterate over the rows and only keep the paths with the higher sum
 //
 // Author: Tom Praschan
 // 2019/03/18
@@ -14,40 +14,64 @@
 #include <fstream>
 #include <sstream>
 #include <iostream>
-#include <functional>
 
-Matrix getTriangle(const std::string &file) {
+Triangle getTriangle(const std::string &file) {
     std::ifstream ifs(file);
-    Matrix mat;
+    Triangle tri;
     std::string line;
     while (std::getline(ifs, line)) {
         std::istringstream iss(line);
-        mat.emplace_back(std::istream_iterator<unsigned>(iss), std::istream_iterator<unsigned>());
+        tri.emplace_back(std::istream_iterator<unsigned>(iss), std::istream_iterator<unsigned>());
     }
-    return mat;
+    return tri;
 }
 
-unsigned bruteforce_solution(const Matrix &mat, unsigned hor, unsigned ver, unsigned sum) {
+unsigned triangle_sum_bruteforce(const Triangle &tri, unsigned hor, unsigned ver, unsigned sum) {
     static std::vector<unsigned> finalSums;
-    sum += mat.at(ver).at(hor);
-    if (ver == mat.size() - 1) {
+    sum += tri.at(ver).at(hor);
+    if (ver == tri.size() - 1) {
         finalSums.emplace_back(sum);
         return 0;
     } else {
-        bruteforce_solution(mat, hor, ver + 1, sum);
-        bruteforce_solution(mat, hor + 1, ver + 1, sum);
+        triangle_sum_bruteforce(tri, hor, ver + 1, sum);
+        triangle_sum_bruteforce(tri, hor + 1, ver + 1, sum);
     }
     return *std::max_element(finalSums.begin(), finalSums.end());
 }
 
+unsigned triangle_sum_fast(const Triangle &tri) {
+    Triangle partialSum(tri.size());
+
+    for (unsigned i = 0; i < tri.size(); i++)
+        partialSum.at(i).reserve(tri.at(i).size());
+    partialSum.at(0).push_back(tri.at(0).at(0));
+
+    for (unsigned ver = 1; ver < tri.size(); ver++) {
+        partialSum.at(ver).push_back(tri.at(ver).at(0) + partialSum.at(ver-1).at(0));
+        unsigned horSize = tri.at(ver).size();
+        for (unsigned hor = 1; hor < horSize - 1; hor++) {
+            partialSum.at(ver).push_back(tri.at(ver).at(hor)
+                    + std::max(partialSum.at(ver-1).at(hor-1), partialSum.at(ver-1).at(hor)));
+        }
+        partialSum.at(ver).push_back(tri.at(ver).at(horSize - 1) + partialSum.at(ver-1).at(horSize - 2));
+    }
+    return *std::max_element(partialSum.back().begin(),partialSum.back().end());
+}
+
 #ifndef TESTING
 int main(int argc, char **argv) {
     auto start = omp_get_wtime();
-    auto mat = getTriangle("../input_files/problem018.txt");
-    auto solution = bruteforce_solution(mat);
+    auto solution = triangle_sum_bruteforce(getTriangle("../input_files/problem018.txt"));
     auto end = omp_get_wtime();
 
-    fmt::print("Solution: {} \n", solution);
+    fmt::print("Bruteforce Solution: {} \n", solution);
+    fmt::print("Elapsed time: {}s \n", end - start);
+
+    start = omp_get_wtime();
+    solution = triangle_sum_fast(getTriangle("../input_files/problem018.txt"));
+    end = omp_get_wtime();
+
+    fmt::print("Fast Solution: {} \n", solution);
     fmt::print("Elapsed time: {}s \n", end - start);
 }
 #endif

cpp_src/problem018.hpp

@@ -2,8 +2,10 @@
 #include <vector>
 #include <string>
 
-typedef std::vector<std::vector<unsigned>> Matrix;
+typedef std::vector<std::vector<unsigned>> Triangle;
 
-Matrix getTriangle(const std::string &file);
+Triangle getTriangle(const std::string &file);
 
-unsigned bruteforce_solution(const Matrix &mat, unsigned hor = 0, unsigned ver = 0, unsigned sum = 0);
+unsigned triangle_sum_bruteforce(const Triangle &tri, unsigned hor = 0, unsigned ver = 0, unsigned sum = 0);
+
+unsigned triangle_sum_fast(const Triangle &tri);

cpp_src/tests.cpp

@@ -93,8 +93,10 @@ TEST_CASE( "Testing collatz_len (Problem 14)") {
     REQUIRE(collatz_len(13) == 10);
 }
 
-TEST_CASE( "Testing Problem 18 brute_force_solution") {
-    REQUIRE(bruteforce_solution(getTriangle("../input_files/test018.txt")) == 23);
-    REQUIRE(bruteforce_solution(getTriangle("../input_files/problem018.txt")) == 1074);
+TEST_CASE( "Testing Problem 18/67 fst and bruteforce solution") {
+    REQUIRE(triangle_sum_bruteforce(getTriangle("../input_files/test018.txt")) == 23);
+    REQUIRE(triangle_sum_bruteforce(getTriangle("../input_files/problem018.txt")) == 1074);
+    REQUIRE(triangle_sum_fast(getTriangle("../input_files/test018.txt")) == 23);
+    REQUIRE(triangle_sum_fast(getTriangle("../input_files/problem018.txt")) == 1074);
 }