Climbing Stairs

Miscellaneous Algorithms/Climbing stairs/README.md

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+
+# Climbing Stairs :
+
+## Description
+We will perform a programme in C language called climbing stairs
+
+### Problem Defination
+
+1. You are climbing a staircase.
+
+
+2. It takes n steps to reach the top.
+
+
+3. Each time you can either climb 1 or 2 steps
+
+4. In how many distinct ways can you climb to the top?
+
+
+
+### Examples : 
+
+Example 1:
+
+Input: n = 2
+Output: 2
+Explanation: There are two ways to climb to the top.
+1. 1 step + 1 step
+2. 2 steps
+
+
+
+Example 2:
+
+Input: n = 3
+Output: 3
+Explanation: There are three ways to climb to the top.
+1. 1 step + 1 step + 1 step
+2. 1 step + 2 steps
+3. 2 steps + 1 step
+
+
+
+
+
+### Time Complexity
+
+Time complexity: O(n)
+n is number of steps to reach the top.
+
+Space complexity: O(n)
+For dp list

Miscellaneous Algorithms/Climbing stairs/program.c

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+
+int climbStairs(int n) {
+        if(n<1){
+            return 0;
+        }
+        int dp[100];
+        dp[0] =1;
+        dp[1] = 2;
+        for(int i= 2; i<n ;i++) {
+            dp[i] = dp[i-1]+dp[i-2];
+        }
+        return dp[n-1];
+    }

Miscellaneous Algorithms/Maximum Products/README.md

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+# Maximum Products of two elements in an array
+
+
+
+## How Does It Work?
+
+Given the array of integers nums, you will choose two different indices i and j of that array. Return the maximum value of (nums[i]-1)*(nums[j]-1).
+
+
+## Example:
+### Example 1:
+
+Input: nums = [3,4,5,2]
+Output: 12 
+Explanation: If you choose the indices i=1 and j=2 (indexed from 0), you will get the maximum value, that is, (nums[1]-1)*(nums[2]-1) = (4-1)*(5-1) = 3*4 = 12. 
+
+### Example 2:
+Input: nums = [1,5,4,5]
+Output: 16
+Explanation: Choosing the indices i=1 and j=3 (indexed from 0), you will get the maximum value of (5-1)*(5-1) = 16.
+
+
+
+# Approach :
+1. Sort the Array : Begin by sorting the array nums in ascending order. This will arrange the numbers such that the largest numbers are at the end of the array.
+2. Identify the Two Largest Numbers : After sorting, the two largest numbers in the array will be at the last two indices. Specifically, the largest number will be at nums[nums.size() - 1] and the second largest will be at nums[nums.size() - 2].
+3. Calculate the Product : Subtract 1 from each of these two largest numbers and then calculate their product.
+
+# Complexity :
+Time complexity : O(n*log(n))
+The time complexity of this solution is O(n log n) due to the sorting operation, where n is the number of elements in the input vector.
+Space complexity : O(1)

Miscellaneous Algorithms/Maximum Products/programme.c

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+int cmp(const void *a, const void *b) {
+    return (*(int *)a - *(int *)b);
+}
+
+int maxProduct(int* nums, int numsSize) {
+    qsort(nums, numsSize, sizeof(int), cmp);
+    return (nums[numsSize - 2] - 1) * (nums[numsSize - 1] - 1);
+}