Add: Solutions 19, 20, 21

euler019.py

@@ -0,0 +1,90 @@
+_days_in_month = [31, 28, 31, 30, 31, 30, 31, 31, 30, 31, 30, 31]
+
+def is_leap(year):
+    return (year%4 ==0 and year%100 != 0) or (year%400 == 0)
+
+
+def days_in_month(month, year):
+    if month == 1:
+        return _days_in_month[1] + (1 if is_leap(year) else 0)
+    else:
+        return _days_in_month[month]
+
+def days_in_year(year):
+    return 365 + (1 if is_leap(year) else 0)
+
+def days_from_1900_to_2000():
+    num_days = 0
+    for year in xrange(1900, 2000):
+        num_days += days_in_year(year)
+    return num_days
+
+def sundays_from_2000_to_2400():
+    day = 5 #Saturday
+    num_sundays = 0
+    for year in xrange(2000, 2400):
+        for month in xrange(12):
+            day = (day + days_in_month(month, year)) % 7
+            if day == 6: #if day is sunday
+                num_sundays += 1
+    return num_sundays #688
+
+
+sundays_per_400_years = 688
+
+def solve(to_year, to_month):
+    # Returns the number of sundays from 1.1.1900 to day.month.year
+    if to_year < 1900:
+        return 0
+    to_month -= 1
+    result = 0
+    day_of_week = 0 #monday
+
+    year = 1900
+
+    #simulate until 1.1.2000
+    if to_year>2000:
+        while year < 2000:
+            for month in xrange(12):
+                if day_of_week == 6:
+                    result += 1
+                day_of_week = (day_of_week + days_in_month(month, year)) % 7
+            year += 1
+
+        num_400_years = (to_year - 2000) / 400
+        result += num_400_years * sundays_per_400_years
+        year += num_400_years * 400
+
+    #simulate until current year
+    while year < to_year:
+        for month in xrange(12):
+            if day_of_week == 6:
+                result += 1
+            day_of_week = (day_of_week + days_in_month(month, year)) % 7
+        year += 1
+
+    #simulate until current month
+    month = 0 #starting on january
+    while month <= to_month:
+        if day_of_week == 6:
+            result += 1
+        day_of_week = (day_of_week + days_in_month(month, year)) % 7
+        month += 1
+    return result    
+
+
+
+T = int(raw_input())
+for i in xrange(T):
+    y1, m1, d1 = map(int, raw_input().split())
+    y2, m2, d2 = map(int, raw_input().split())
+
+
+    d1 -= 1
+    if d1 == 0:
+        m1 -= 1
+        if m1 == 0:
+            y1 -= 1
+            m1 = 12
+
+    print solve(y2, m2)-solve(y1, m1)

euler020.py

@@ -0,0 +1,24 @@
+def fact(n):
+    factorials = [0]*1001
+    factorials[0] = 1
+
+    for i in range(1, n + 1):
+        factorials[i] = i*factorials[i-1]
+
+    if n == 0:
+        return factorials[0]
+    else:
+        return factorials[n]
+
+def digitSum(n):
+    sum = 0
+    while n > 0:
+        sum += n%10
+        n = n/10
+    return sum
+
+T = int(raw_input())
+for tc in xrange(T):
+    N = int(raw_input())
+
+    print digitSum(fact(N))

euler021.py

@@ -0,0 +1,38 @@
+import math
+def sumDiv(n):
+    sum = 1
+    i = 2
+    while i*i < n:
+        if n % i == 0:
+            sum += i + n/i
+        i += 1
+    if(i*i == n):
+        sum += i
+
+    return sum
+
+
+Max = 100007
+is_amicable = [-1]*Max
+
+
+is_amicable[0] = 0
+for i in xrange(1, Max):
+    if is_amicable[i] != -1:
+        continue
+    j = sumDiv(i)
+    if(i!=j and sumDiv(j) == i):
+        is_amicable[i] = is_amicable[j] = 1
+    else:
+        is_amicable[i] = 0
+
+
+for i in xrange(1, Max):
+    is_amicable[i] = is_amicable[i-1] + (i if is_amicable[i]==1 else 0)
+
+
+T = int(raw_input())
+for tc in xrange(T):
+    N = int(raw_input())
+    print sumDiv(N)
+    print is_amicable[N]