Syntax error Program to find number of strictly increasing colorful candle sequences are there in Python

Program to find number of strictly increasing colorful candle sequences are there in Python

Suppose there are n candles which are aligned from left to right. The i-th candle from the left side has the height h[i] and the color c[i]. We also have an integer k, represents there are colors in range 1 to k. We have to find how many strictly increasing colorful sequences of candies are there? The increasing sequence is checked based on heights, and a sequence is said to be colorful if there are at least one candle of each color in range 1 to K are available. If the answer is too large, then return result mod 10^9 + 7.

So, if the input is like K = 3 h = [1,3,2,4] c = [1,2,2,3], then the output will be 2 because it has sequences [1,2,4] and [1,3,4].

To solve this, we will follow these steps −

  • Define a function read() . This will take T, i
  • s := 0
  • while i > 0, do
    • s := s + T[i]
    • s := s mod 10^9+7
    • i := i -(i AND -i)
  • return s
  • Define a function update() . This will take T, i, v
  • while i <= 50010, do
    • T[i] := T[i] + v
    • T[i] := T[i] mod 10^9+7
    • i := i +(i AND -i)
  • return v
  • From the main method, do the following −
  • L := 2^k, R := 0, N := size of h
  • for i in range 0 to L - 1, do
    • T := an array of size 50009 and fill with 0
    • t := 0
    • for j in range 0 to N - 1, do
      • if (i after shifting bits (c[j] - 1) times to the right) is odd, then
        • t := t + update(T, h[j], read(T, h[j] - 1) + 1)
        • t := t mod 10^9+7
    • if (number of bits in i) mod 2 is same as k mod 2, then
      • R := R + t
      • R := R mod 10^9+7
    • otherwise,
      • R := (R + 10^9+7) - t
      • R := R mod 10^9+7
  • return R

Example

Let us see the following implementation to get better understanding −

def solve(k, h, c):
   def read(T, i):
      s = 0
      while i > 0:
         s += T[i]
         s %= 1000000007
         i -= (i & -i)
      return s

   def update(T, i, v):
      while i <= 50010:
         T[i] += v
         T[i] %= 1000000007
         i += (i & -i)
      return v

   def number_of_bits(b):
      c = 0
      while b:
         b &= b - 1
         c += 1
      return c

   L = 2 ** k
   R = 0
   N = len(h)

   for i in range(L):
      T = [0 for _ in range(50010)]
      t = 0

      for j in range(N):
         if (i >> (c[j] - 1)) & 1:
            t += update(T, h[j], read(T, h[j] - 1) + 1)
            t %= 1000000007

      if number_of_bits(i) % 2 == k % 2:
         R += t
         R %= 1000000007
      else:
         R += 1000000007 - t
         R %= 1000000007
   return R

k = 3
h = [1,3,2,4]
c = [1,2,2,3]

print(solve(k, h, c))

Input

3, [1,3,2,4], [1,2,2,3]

Output

2
Updated on: 2021-10-23T07:19:41+05:30

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