Given a number n (number of variables) and val (sum of the variables), find out how many such nonnegative integral solutions are possible.
Input : n = 5, val = 1 Output : 5 Explanation: x1 + x2 + x3 + x4 + x5 = 1 Number of possible solution are : (0 0 0 0 1), (0 0 0 1 0), (0 0 1 0 0), (0 1 0 0 0), (1 0 0 0 0) Total number of possible solutions are 5 Input : n = 5, val = 4 Output : 70 Explanation: x1 + x2 + x3 + x4 + x5 = 4 Number of possible solution are: (1 1 1 1 0), (1 0 1 1 1), (0 1 1 1 1), (2 1 0 0 1), (2 2 0 0 0)........ so on...... Total numbers of possible solutions are 70
Asked in: Microsoft Interview
1. Make a recursive function call to countSolutions(int n, int val)
2. Call this Solution function countSolutions(n-1, val-i) until n = 1 and val >=0 and then return 1.
Below is the implementation of above approach:
- Number of integral solutions of the equation x1 + x2 +.... + xN = k
- Number of integral solutions for equation x = b*(sumofdigits(x)^a)+c
- Number of non-negative integral solutions of a + b + c = n
- Number of solutions for the equation x + y + z <= n
- Find the number of solutions to the given equation
- Find number of solutions of a linear equation of n variables
- Program to find number of solutions in Quadratic Equation
- Number of solutions for x < y, where a <= x <= b and c <= y <= d and x, y are integers
- Number of solutions of n = x + n ⊕ x
- Count number of solutions of x^2 = 1 (mod p) in given range
- Number of solutions to Modular Equations
- Find 'N' number of solutions with the given inequality equations
- Number of sextuplets (or six values) that satisfy an equation
- Number of ordered points pair satisfying line equation
- Number of Integral Points between Two Points
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