From 6687050cdcb04cf24c4bc627004e8072bb059c86 Mon Sep 17 00:00:00 2001
From: magnes <magnes@aspire.(none)>
Date: Sun, 4 May 2014 13:06:17 +0400
Subject: [PATCH] 1

---
 magnes/combinations/allvectors.py   | 14 +++++++++
 magnes/combinations/choose.py       | 39 +++++++++++++++++++++++++
 magnes/combinations/nextchoose.py   | 33 ++++++++++++++++++++++
 magnes/combinations/nextperm.py     | 42 +++++++++++++++++++++++++++
 magnes/combinations/nextvector.py   | 44 +++++++++++++++++++++++++++++
 magnes/combinations/permutations.py | 15 ++++++++++
 magnes/combinations/subsets.py      | 28 ++++++++++++++++++
 magnes/combinations/vectors.py      | 26 +++++++++++++++++
 magnes/final homework/airplane.py   | 12 ++++++++
 magnes/final homework/harddrive.py  | 17 +++++++++++
 magnes/final homework/olympic.py    | 36 +++++++++++++++++++++++
 magnes/final homework/tower.py      | 30 ++++++++++++++++++++
 magnes/graphs/components.py         | 38 +++++++++++++++++++++++++
 magnes/graphs/pathbge1.py           | 34 ++++++++++++++++++++++
 14 files changed, 408 insertions(+)
 create mode 100644 magnes/combinations/allvectors.py
 create mode 100644 magnes/combinations/choose.py
 create mode 100644 magnes/combinations/nextchoose.py
 create mode 100644 magnes/combinations/nextperm.py
 create mode 100644 magnes/combinations/nextvector.py
 create mode 100644 magnes/combinations/permutations.py
 create mode 100644 magnes/combinations/subsets.py
 create mode 100644 magnes/combinations/vectors.py
 create mode 100644 magnes/final homework/airplane.py
 create mode 100644 magnes/final homework/harddrive.py
 create mode 100644 magnes/final homework/olympic.py
 create mode 100644 magnes/final homework/tower.py
 create mode 100644 magnes/graphs/components.py
 create mode 100644 magnes/graphs/pathbge1.py

diff --git a/magnes/combinations/allvectors.py b/magnes/combinations/allvectors.py
new file mode 100644
index 0000000..e5faec2
--- /dev/null
+++ b/magnes/combinations/allvectors.py
@@ -0,0 +1,14 @@
+def gen_perm(a, p):
+    if p < k:
+        a[p] = 0
+        gen_perm(a, p + 1)
+        a[p] = 1
+        gen_perm(a, p + 1)
+    else:
+        outfile.write(str(''.join([str(i) for i in a])) + '\n')
+
+with open('allvectors.in', 'r') as infile:
+    k = int(infile.readline().strip())
+
+with open('allvectors.out', 'w') as outfile:
+    gen_perm([2 for i in range(k)], 0)
diff --git a/magnes/combinations/choose.py b/magnes/combinations/choose.py
new file mode 100644
index 0000000..1431207
--- /dev/null
+++ b/magnes/combinations/choose.py
@@ -0,0 +1,39 @@
+
+def right(x):
+    if x[-1] == 0:
+        x = x[::-1]
+        for i in range(len(x)):
+            if x[i] == 1:
+                x[i], x[i - 1] = x[i - 1], x[i]
+                return x[::-1]
+    else:
+        x = x[::-1]
+        for i in range(len(x) - 1):
+            if x[i] == 0 and x[i + 1] == 1:
+                x[i], x[i + 1] = x[i + 1], x[i]
+                x = x[:i][::-1] + x[i:]
+                return x[::-1]
+
+
+def gen_all(array):
+    while array != end:
+        array = list(right(array))
+        yield ' '.join([str(i + 1) for i in range(len(array)) if array[i] == 1])
+
+
+with open('choose.in', 'r') as infile:
+
+    n, k = [int(i) for i in infile.readline().strip().split()]
+    array = [0 for x in range(n)]
+    for x in range(k):
+        array[x] = 1
+    end = [0 for x in range(n)]
+    for x in range(k):
+        end[-x - 1] = 1
+
+
+with open('choose.out', 'w') as outfile:
+    outfile.write(
+        ' '.join([str(i + 1) for i in range(len(array)) if array[i] == 1]) + '\n')
+    for x in gen_all(array):
+        outfile.write(x + '\n')
diff --git a/magnes/combinations/nextchoose.py b/magnes/combinations/nextchoose.py
new file mode 100644
index 0000000..38b9c28
--- /dev/null
+++ b/magnes/combinations/nextchoose.py
@@ -0,0 +1,33 @@
+
+def right(x):
+    if x[-1] == 0:
+        x = x[::-1]
+        for i in range(len(x)):
+            if x[i] == 1:
+                x[i], x[i - 1] = x[i - 1], x[i]
+                return x[::-1]
+    else:
+        x = x[::-1]
+        for i in range(len(x) - 1):
+            if x[i] == 0 and x[i + 1] == 1:
+                x[i], x[i + 1] = x[i + 1], x[i]
+                x = x[:i][::-1] + x[i:]
+                return x[::-1]
+
+
+with open('nextchoose.in', 'r') as infile:
+
+    n, k = [int(i) for i in infile.readline().strip().split()]
+    data = [int(i) for i in infile.readline().strip().split()]
+    array = [0 for i in range(n)]
+    for x in data:
+        array[x - 1] = 1
+
+
+with open('nextchoose.out', 'w') as outfile:
+    try:
+        array = right(array)
+        outfile.write(
+            ' '.join([str(i + 1) for i in range(n) if array[i] == 1]))
+    except TypeError:
+        outfile.write('-1')
diff --git a/magnes/combinations/nextperm.py b/magnes/combinations/nextperm.py
new file mode 100644
index 0000000..ebdaf69
--- /dev/null
+++ b/magnes/combinations/nextperm.py
@@ -0,0 +1,42 @@
+
+def right(x):
+    p = [int(i) for i in x[::-1]]
+
+    i = 1
+    while i < n and p[i - 1] < p[i]:
+        i += 1
+
+    if n == i:
+        return ' '.join(['0' for x in range(n)])
+
+    j = p.index(min([x for x in p[:i] if x > p[i]]))
+    p[i], p[j] = p[j], p[i]
+    p = p[:i][::-1] + p[i:]
+
+    return ' '.join(list([str(i) for i in p[::-1]]))
+
+
+def left(x):
+    p = [int(i) for i in x[::-1]]
+
+    i = 1
+    while i < n and p[i - 1] > p[i]:
+        i += 1
+
+    if n == i:
+        return ' '.join(['0' for x in range(n)])
+
+    j = p.index(max([x for x in p[:i] if x < p[i]]))
+    p[i], p[j] = p[j], p[i]
+    p = p[:i][::-1] + p[i:]
+
+    return ' '.join(list([str(i) for i in p[::-1]]))
+
+
+with open('nextperm.in', 'r') as infile:
+
+    n = int(infile.readline().strip())
+    p = infile.readline().strip().split(' ')
+
+with open('nextperm.out', 'w') as outfile:
+    outfile.write(left(p) + '\n' + right(p))
diff --git a/magnes/combinations/nextvector.py b/magnes/combinations/nextvector.py
new file mode 100644
index 0000000..e3b35fe
--- /dev/null
+++ b/magnes/combinations/nextvector.py
@@ -0,0 +1,44 @@
+
+def left(x):
+    x = list([int(i) for i in x])[::-1]
+    if x[0] == 1:
+        x[0] = 0
+    else:
+        for i in range(len(x)):
+            if x[i] == 1:
+                x[i] = 0
+                for z in range(len(x[:i])):
+                    x[z] = 1
+                break
+    return ''.join([str(i) for i in x[::-1]])
+
+
+def right(x):
+    x = list([int(i) for i in x])[::-1]
+    if x[0] == 0:
+        x[0] = 1
+    else:
+        for i in range(len(x)):
+            if x[i] == 0:
+                x[i] = 1
+                for z in range(len(x[:i])):
+                    x[z] = 0
+                break
+    return ''.join([str(i) for i in x[::-1]])
+
+
+with open('nextvector.in', 'r') as infile:
+
+    x = infile.readline().strip()
+
+    a = '-'
+    b = '-'
+
+    if set(list(x)) != set(['0']):
+        a = left(x)
+
+    if set(list(x)) != set(['1']):
+        b = right(x)
+
+with open('nextvector.out', 'w') as outfile:
+    outfile.write(a + '\n' + b)
diff --git a/magnes/combinations/permutations.py b/magnes/combinations/permutations.py
new file mode 100644
index 0000000..977754f
--- /dev/null
+++ b/magnes/combinations/permutations.py
@@ -0,0 +1,15 @@
+def gen_perm(a, p):
+    if p < k:
+        for i in range(1, k + 1):
+            if i not in a:
+                a[p] = i
+                gen_perm(a, p + 1)
+                a[p] = 0
+    else:
+        outfile.write(str(' '.join([str(i) for i in a])) + '\n')
+
+with open('permutations.in', 'r') as infile:
+    k = int(infile.readline().strip())
+
+with open('permutations.out', 'w') as outfile:
+    gen_perm([0 for i in range(k)], 0)
diff --git a/magnes/combinations/subsets.py b/magnes/combinations/subsets.py
new file mode 100644
index 0000000..f7c2294
--- /dev/null
+++ b/magnes/combinations/subsets.py
@@ -0,0 +1,28 @@
+from operator import itemgetter
+
+
+def bar(a, p, i):
+    if i < n:
+        a[i] = ''
+        bar(a, p[1:], i + 1)
+
+        for x in p:
+            if x not in a:
+                a[i] = x
+                bar(a, p[1:], i + 1)
+
+    else:
+        answer.append([x for x in a])
+
+with open('subsets.in', 'r') as infile:
+    n = int(infile.readline().strip())
+
+with open('subsets.out', 'w') as outfile:
+    a = [0 for x in range(n)]
+    p = [x for x in range(1, n + 1)]
+
+    answer = []
+    bar(a, p, 0)
+    answer = [filter(None, x) for x in answer]
+    for x in sorted(answer):
+        outfile.write(' '.join([str(z) for z in x]) + '\n')
diff --git a/magnes/combinations/vectors.py b/magnes/combinations/vectors.py
new file mode 100644
index 0000000..f81a0d8
--- /dev/null
+++ b/magnes/combinations/vectors.py
@@ -0,0 +1,26 @@
+def gen_perm(a, p):
+    if k == 0:
+        return 0
+    if p < k:
+        a[p] = 0
+        gen_perm(a, p + 1)
+
+        if a[p - 1] != 1:
+            a[p] = 1
+            gen_perm(a, p + 1)
+
+    else:
+        output.append(str(''.join([str(i) for i in a])) + '\n')
+
+with open('vectors.in', 'r') as infile:
+    k = int(infile.readline().strip())
+
+with open('vectors.out', 'w') as outfile:
+    output = []
+    gen_perm([0 for i in range(k)], 0)
+    gen_perm([1 for i in range(k)], 1)
+
+    output = sorted(list(set(output)))
+    outfile.write(str(len(output)) + '\n')
+    for x in output:
+        outfile.write(x)
diff --git a/magnes/final homework/airplane.py b/magnes/final homework/airplane.py
new file mode 100644
index 0000000..7a9d2fd
--- /dev/null
+++ b/magnes/final homework/airplane.py	
@@ -0,0 +1,12 @@
+with open('airplane.in', 'r') as infile:
+    s, n, a = [int(x) for x in infile.readline().strip().split()]
+    p = sum([int(x) for x in infile.readline().strip().split()])
+
+    if a >= 1000:
+        x = 'Impossible'
+    else:
+        x = (s + p) * a / (1000 - a)
+
+
+with open('airplane.out', 'w') as outfile:
+    outfile.write(str(x))
diff --git a/magnes/final homework/harddrive.py b/magnes/final homework/harddrive.py
new file mode 100644
index 0000000..550999a
--- /dev/null
+++ b/magnes/final homework/harddrive.py	
@@ -0,0 +1,17 @@
+from collections import defaultdict
+
+with open('harddrive.in', 'r') as infile:
+    n = int(infile.readline().strip())
+    data = [int(x) for x in infile.readline().strip().split()]
+
+    starts = defaultdict(int)
+
+    for x in data:
+        if x - 1 not in starts:
+            starts[x] = 1
+        if x - 1 in starts:
+            starts[x - 1] = 0
+            starts[x] = 1
+
+with open('harddrive.out', 'w') as outfile:
+    outfile.write(str(len([x for x in starts if starts[x]]) - 1))
diff --git a/magnes/final homework/olympic.py b/magnes/final homework/olympic.py
new file mode 100644
index 0000000..ff61cc6
--- /dev/null
+++ b/magnes/final homework/olympic.py	
@@ -0,0 +1,36 @@
+from collections import defaultdict
+
+with open('olympic.in', 'r') as infile:
+
+    n = int(infile.readline().strip())
+
+    data = []
+    for x in infile:
+        data.append(x.strip().split())
+
+    prizes = defaultdict(lambda: defaultdict(lambda: 0))
+
+    for a, b, c in data:
+        prizes[a][0] += 1
+        prizes[b][1] += 1
+        prizes[c][2] += 1
+
+    data = defaultdict(list)
+    for x in prizes.items():
+        for z in range(3):
+            data[x[0]].append((x[1][z]))
+
+    for i in range(3):
+        out = []
+        best = max([x[1][i] for x in data.items()])
+        for x in data.items():
+            if x[1][i] < best:
+                out.append(x[0])
+        for x in out:
+            del data[x]
+
+    data = [x for x in data]
+
+
+with open('olympic.out', 'w') as outfile:
+    outfile.write((sorted(data)[0]))
diff --git a/magnes/final homework/tower.py b/magnes/final homework/tower.py
new file mode 100644
index 0000000..fd2038c
--- /dev/null
+++ b/magnes/final homework/tower.py	
@@ -0,0 +1,30 @@
+from collections import defaultdict
+
+with open('tower.in', 'r') as infile:
+
+    n = int(infile.readline().strip())
+    data = []
+    for x in infile:
+        data.append(set([int(z) for z in x.strip().split()[1:]]))
+
+    g = defaultdict(set)
+    for i in range(len(data)):
+        for j in range(len(data)):
+            if data[i] & data[j] and i != j:
+                g[i].add(j)
+                g[j].add(i)
+
+    seen = set()
+    que = [0]
+
+    while que:
+        for x in que:
+            seen.add(x)
+            for y in g[que[0]]:
+                seen.add(y)
+                que.extend([z for z in g[y] if z not in que and z not in seen])
+            del que[0]
+
+
+with open('tower.out', 'w') as outfile:
+    outfile.write(str(len(seen)))
diff --git a/magnes/graphs/components.py b/magnes/graphs/components.py
new file mode 100644
index 0000000..61335ce
--- /dev/null
+++ b/magnes/graphs/components.py
@@ -0,0 +1,38 @@
+from collections import defaultdict
+
+
+def bfs():
+    num_ks = 0
+    ks = {}
+    for x in range(1, n + 1):
+        if x not in ks:
+            num_ks += 1
+            ks[x] = num_ks
+            que = [x]
+            while len(que) != 0:
+                for x in g[que[0]]:
+                    if x not in ks:
+                        ks[x] = num_ks
+                        que.append(x)
+                del que[0]
+    return str(num_ks) + '\n' + ' '.join([str(x) for x in ks.values()])
+
+with open('components.in', 'r') as infile:
+
+    g = defaultdict(list)
+    edges = []
+
+    n, m = [int(x) for x in infile.readline().strip().split()]
+
+    for x in range(m):
+        e = infile.readline().strip().split()
+        if e[0] != e[1]:
+            edges.append(e)
+
+    for x, y in edges:
+        g[int(x)].append(int(y))
+        g[int(y)].append(int(x))
+
+
+with open('components.out', 'w') as outfile:
+    outfile.write(dfs())
diff --git a/magnes/graphs/pathbge1.py b/magnes/graphs/pathbge1.py
new file mode 100644
index 0000000..1eb55c7
--- /dev/null
+++ b/magnes/graphs/pathbge1.py
@@ -0,0 +1,34 @@
+from collections import defaultdict
+
+
+def bfs():
+    ks = defaultdict(int)
+    ks[1] = 0
+    que = [1]
+    while len(que) != 0:
+        for x in g[que[0]]:
+            if x not in ks:
+                ks[x] = ks[que[0]] + 1
+                que.append(x)
+        del que[0]
+    return(' '.join([str(x) for x in ks.values()]))
+
+with open('pathbge1.in', 'r') as infile:
+
+    g = defaultdict(list)
+    edges = []
+
+    n, m = [int(x) for x in infile.readline().strip().split()]
+
+    for x in range(m):
+        e = infile.readline().strip().split()
+        if e[0] != e[1]:
+            edges.append(e)
+
+    for x, y in edges:
+        g[int(x)].append(int(y))
+        g[int(y)].append(int(x))
+
+
+with open('pathbge1.out', 'w') as outfile:
+    outfile.write(str(bfs()))