Project Euler problem 86 taking a long time
$begingroup$
I'm trying to solve problem 86 in Project Euler. After some tinkering, I managed to unroll the DP solution into a loop. But still the solution takes >150s to complete. What can I do to improve the performance of this algorithm?
(defn- square [n]
(* n n))
(defn- is-perfect-square? [n]
(let [sq (int (Math/sqrt n))]
(= n (* sq sq))))
;; See: https://math.stackexchange.com/a/1189884/7078 (Second case)
;; So lengths = [sqrt(l^2 + b^2 + h^2 + 2bh), sqrt(l^2 + b^2 + h^2 + 2lb), sqrt(l^2 + b^2 + h^2 + 2lh)]
;; Shortest length is the smallest of the above. == sqrt(l^2 + b^2 + h^2 + min(2bh, 2lb, 2lh))
(defn- shortest-cuboid-dist-has-int-length?
([a b c]
(->> (min (* a b) (* b c) (* c a))
(* 2)
(+ (square a) (square b) (square c))
(is-perfect-square?)))
([[a b c]]
(shortest-cuboid-dist-has-int-length? a b c)))
;; if F(n) denotes number of integer shortest lengths for cuboids with dimensions equal to or less than (n,n,n),
;; F(i+1) = F(i) + int_lengths(cuboids with at least one side dimension of i+1)
(defn- get-int-dist-above [lim]
(loop [dim 0 c 0 i 1 j 1]
(cond (> c lim) dim
(= i (inc dim)) (recur (inc dim) c 1 1)
(= j (inc i)) (recur dim c (inc i) 1)
:else (recur dim (if (shortest-cuboid-dist-has-int-length? dim i j) (inc c) c) i (inc j)))))
(defn problem-86
(get-int-dist-above 1000000))
(time (problem-86)) ;; Takes 150s
performance programming-challenge clojure
edited 1 hour ago
AJNeufeld
4,497318
asked 3 hours ago
nakiyanakiya
1215
$endgroup$
add a comment |
$begingroup$
I'm trying to solve problem 86 in Project Euler. After some tinkering, I managed to unroll the DP solution into a loop. But still the solution takes >150s to complete. What can I do to improve the performance of this algorithm?
(defn- square [n]
(* n n))
(defn- is-perfect-square? [n]
(let [sq (int (Math/sqrt n))]
(= n (* sq sq))))
;; See: https://math.stackexchange.com/a/1189884/7078 (Second case)
;; So lengths = [sqrt(l^2 + b^2 + h^2 + 2bh), sqrt(l^2 + b^2 + h^2 + 2lb), sqrt(l^2 + b^2 + h^2 + 2lh)]
;; Shortest length is the smallest of the above. == sqrt(l^2 + b^2 + h^2 + min(2bh, 2lb, 2lh))
(defn- shortest-cuboid-dist-has-int-length?
([a b c]
(->> (min (* a b) (* b c) (* c a))
(* 2)
(+ (square a) (square b) (square c))
(is-perfect-square?)))
([[a b c]]
(shortest-cuboid-dist-has-int-length? a b c)))
;; if F(n) denotes number of integer shortest lengths for cuboids with dimensions equal to or less than (n,n,n),
;; F(i+1) = F(i) + int_lengths(cuboids with at least one side dimension of i+1)
(defn- get-int-dist-above [lim]
(loop [dim 0 c 0 i 1 j 1]
(cond (> c lim) dim
(= i (inc dim)) (recur (inc dim) c 1 1)
(= j (inc i)) (recur dim c (inc i) 1)
:else (recur dim (if (shortest-cuboid-dist-has-int-length? dim i j) (inc c) c) i (inc j)))))
(defn problem-86
(get-int-dist-above 1000000))
(time (problem-86)) ;; Takes 150s
performance programming-challenge clojure
edited 1 hour ago
AJNeufeld
4,497318
asked 3 hours ago
nakiyanakiya
1215
$endgroup$
add a comment |
$begingroup$
I'm trying to solve problem 86 in Project Euler. After some tinkering, I managed to unroll the DP solution into a loop. But still the solution takes >150s to complete. What can I do to improve the performance of this algorithm?
(defn- square [n]
(* n n))
(defn- is-perfect-square? [n]
(let [sq (int (Math/sqrt n))]
(= n (* sq sq))))
;; See: https://math.stackexchange.com/a/1189884/7078 (Second case)
;; So lengths = [sqrt(l^2 + b^2 + h^2 + 2bh), sqrt(l^2 + b^2 + h^2 + 2lb), sqrt(l^2 + b^2 + h^2 + 2lh)]
;; Shortest length is the smallest of the above. == sqrt(l^2 + b^2 + h^2 + min(2bh, 2lb, 2lh))
(defn- shortest-cuboid-dist-has-int-length?
([a b c]
(->> (min (* a b) (* b c) (* c a))
(* 2)
(+ (square a) (square b) (square c))
(is-perfect-square?)))
([[a b c]]
(shortest-cuboid-dist-has-int-length? a b c)))
;; if F(n) denotes number of integer shortest lengths for cuboids with dimensions equal to or less than (n,n,n),
;; F(i+1) = F(i) + int_lengths(cuboids with at least one side dimension of i+1)
(defn- get-int-dist-above [lim]
(loop [dim 0 c 0 i 1 j 1]
(cond (> c lim) dim
(= i (inc dim)) (recur (inc dim) c 1 1)
(= j (inc i)) (recur dim c (inc i) 1)
:else (recur dim (if (shortest-cuboid-dist-has-int-length? dim i j) (inc c) c) i (inc j)))))
(defn problem-86
(get-int-dist-above 1000000))
(time (problem-86)) ;; Takes 150s
performance programming-challenge clojure
edited 1 hour ago
AJNeufeld
4,497318
asked 3 hours ago
nakiyanakiya
1215
$endgroup$
I'm trying to solve problem 86 in Project Euler. After some tinkering, I managed to unroll the DP solution into a loop. But still the solution takes >150s to complete. What can I do to improve the performance of this algorithm?
(defn- square [n]
(* n n))
(defn- is-perfect-square? [n]
(let [sq (int (Math/sqrt n))]
(= n (* sq sq))))
;; See: https://math.stackexchange.com/a/1189884/7078 (Second case)
;; So lengths = [sqrt(l^2 + b^2 + h^2 + 2bh), sqrt(l^2 + b^2 + h^2 + 2lb), sqrt(l^2 + b^2 + h^2 + 2lh)]
;; Shortest length is the smallest of the above. == sqrt(l^2 + b^2 + h^2 + min(2bh, 2lb, 2lh))
(defn- shortest-cuboid-dist-has-int-length?
([a b c]
(->> (min (* a b) (* b c) (* c a))
(* 2)
(+ (square a) (square b) (square c))
(is-perfect-square?)))
([[a b c]]
(shortest-cuboid-dist-has-int-length? a b c)))
;; if F(n) denotes number of integer shortest lengths for cuboids with dimensions equal to or less than (n,n,n),
;; F(i+1) = F(i) + int_lengths(cuboids with at least one side dimension of i+1)
(defn- get-int-dist-above [lim]
(loop [dim 0 c 0 i 1 j 1]
(cond (> c lim) dim
(= i (inc dim)) (recur (inc dim) c 1 1)
(= j (inc i)) (recur dim c (inc i) 1)
:else (recur dim (if (shortest-cuboid-dist-has-int-length? dim i j) (inc c) c) i (inc j)))))
(defn problem-86
(get-int-dist-above 1000000))
(time (problem-86)) ;; Takes 150s
performance programming-challenge clojure
performance programming-challenge clojure
edited 1 hour ago
AJNeufeld
4,497318
asked 3 hours ago
nakiyanakiya
1215
edited 1 hour ago
AJNeufeld
4,497318
asked 3 hours ago
nakiyanakiya
1215
edited 1 hour ago
AJNeufeld
4,497318
edited 1 hour ago
AJNeufeld
4,497318
edited 1 hour ago
AJNeufeld
4,497318
4,497318
asked 3 hours ago
nakiyanakiya
1215
asked 3 hours ago
nakiyanakiya
1215
asked 3 hours ago
nakiyanakiya
1215
1215
add a comment |
add a comment |
1 Answer
1
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oldest
votes
$begingroup$
Given: 1 ≤ a ≤ b ≤ c = M,
then, min(a*b, b*c, a*c) == a*b
This means, you can remove 2 multiplications and the min operation from shortest-cuboid-dist-has-int-length? as long as you pass your room’s length, width, and height in the proper order.
answered 1 hour ago
AJNeufeldAJNeufeld
4,497318
$endgroup$
add a comment |
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1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
$begingroup$
Given: 1 ≤ a ≤ b ≤ c = M,
then, min(a*b, b*c, a*c) == a*b
This means, you can remove 2 multiplications and the min operation from shortest-cuboid-dist-has-int-length? as long as you pass your room’s length, width, and height in the proper order.
answered 1 hour ago
AJNeufeldAJNeufeld
4,497318
$endgroup$
add a comment |
$begingroup$
Given: 1 ≤ a ≤ b ≤ c = M,
then, min(a*b, b*c, a*c) == a*b
This means, you can remove 2 multiplications and the min operation from shortest-cuboid-dist-has-int-length? as long as you pass your room’s length, width, and height in the proper order.
answered 1 hour ago
AJNeufeldAJNeufeld
4,497318
$endgroup$
add a comment |
$begingroup$
Given: 1 ≤ a ≤ b ≤ c = M,
then, min(a*b, b*c, a*c) == a*b
This means, you can remove 2 multiplications and the min operation from shortest-cuboid-dist-has-int-length? as long as you pass your room’s length, width, and height in the proper order.
answered 1 hour ago
AJNeufeldAJNeufeld
4,497318
$endgroup$
Given: 1 ≤ a ≤ b ≤ c = M,
then, min(a*b, b*c, a*c) == a*b
This means, you can remove 2 multiplications and the min operation from shortest-cuboid-dist-has-int-length? as long as you pass your room’s length, width, and height in the proper order.
answered 1 hour ago
AJNeufeldAJNeufeld
4,497318
answered 1 hour ago
AJNeufeldAJNeufeld
4,497318
answered 1 hour ago
AJNeufeldAJNeufeld
4,497318
answered 1 hour ago
AJNeufeldAJNeufeld
4,497318
4,497318
add a comment |
add a comment |
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