[Golang] DP and Prefix Sums easy to understand.
Intuition\n Describe your first thoughts on how to solve this problem. \n### 1. Dynamic Programming Arrays:\ndp and dp2 arrays are used to keep track of the num
# Intuition\n<!-- Describe your first thoughts on how to solve this problem. -->\n### 1. Dynamic Programming Arrays:\ndp and dp2 arrays are used to keep track of the number of valid sequences up to the current element.\n\n### 2. Prefix Sums:\nThe dp array is updated with prefix sums to allow efficient computation of valid sequences.\n\n### 3. Transition Logic:\nThe transition between dp and dp2 handles the constraints given by x and y values in the input array v.\n\n### 4. Final Summation:\nThe result is calculated by summing up all values in the dp array after processing all elements in the input array.\n\n# Complexity\n- Time complexity: O(N\u2217S)\n<!-- Add your time complexity here, e.g. $$O(n)$$ -->\n\n- Space complexity: O(S)\n<!-- Add your space complexity here, e.g. $$O(n)$$ -->\n\n# Code\n```\nconst (\n\tS   = 1001\n\tMOD = 1000000007\n)\n\nfunc countOfPairs(nums []int) int {\n\tdp := make([]int, S)\n\tdp2 := make([]int, S)\n\tfor i := 0; i <= nums[0]; i++ {\n\t\tdp[i] = 1\n\t}\n\tfor i := 1; i < len(nums); i++ {\n\t\tx := nums[i-1]\n\t\ty := nums[i]\n\t\tfor j := 1; j < S; j++ {\n\t\t\tdp[j] += dp[j-1]\n\t\t\tif dp[j] >= MOD {\n\t\t\t\tdp[j] -= MOD\n\t\t\t}\n\t\t}\n\t\tfor j := 0; j <= y; j++ {\n\t\t\tp := min(j, x+j-y)\n\t\t\tdp2[j] = 0\n\t\t\tif p >= 0 {\n\t\t\t\tdp2[j] = dp[p]\n\t\t\t}\n\t\t}\n\t\tfor j := y + 1; j < S; j++ {\n\t\t\tdp2[j] = 0\n\t\t}\n\t\tdp, dp2 = dp2, dp\n\t}\n\tvar rs int\n\tfor i := 0; i < S; i++ {\n\t\trs += dp[i]\n\t\tif rs >= MOD {\n\t\t\trs -= MOD\n\t\t}\n\t}\n\treturn rs\n}\n\nfunc min(a, b int) int {\n\tif a < b {\n\t\treturn a\n\t}\n\treturn b\n}\n```
['Go']