{"id":35047,"date":"2022-06-22T12:42:41","date_gmt":"2022-06-22T07:12:41","guid":{"rendered":"https:\/\/btechgeeks.com\/?p=35047"},"modified":"2022-07-01T08:41:30","modified_gmt":"2022-07-01T03:11:30","slug":"java-program-to-find-number-of-ways-to-express-a-number-as-sum-of-powers-using-recursion","status":"publish","type":"post","link":"https:\/\/btechgeeks.com\/java-program-to-find-number-of-ways-to-express-a-number-as-sum-of-powers-using-recursion\/","title":{"rendered":"Java Program to Find Number of Ways to Express a Number as Sum of Powers Using Recursion"},"content":{"rendered":"<p>In the previous article, we have discussed about <a href=\"https:\/\/btechgeeks.com\/java-program-to-find-the-sum-of-all-perfect-divisors-of-a-number-using-recursion\/\">Java Program to Find Sum of Proper Divisors of a Number by Using Recursion<\/a><\/p>\n<p>In this article we are going to see how we can find the number of ways so that a number can be expressed as sum of powers by using recursion.<\/p>\n<h2>Java Program to Find Number of Ways to Express a Number as Sum of Powers Using Recursion<\/h2>\n<p>As per the problem statement you have to find the number of ways so that a number can be expressed as sum of powers.<\/p>\n<p><strong>For example:\u00a0<\/strong><\/p>\n<pre>Number = 100 and Power = 2\r\nThen 100 can be expressed as sum of powers as follows\r\n10^2 OR \r\n6^2+8^2 OR \r\n1^2 + 3^2 + 4^2 + 5^2 + 7^2 \r\nSo there are total 3 ways.<\/pre>\n<p>Let&#8217;s see the program to understand it more clearly.<\/p>\n<ul>\n<li><a href=\"#Java_Program_to_Find_Number_of_Ways_to_Express_a_Number_as_Sum_of_Powers_By_Using_Recursion_&amp;_Static_Input_Value\">Java Program to Find Number of Ways to Express a Number as Sum of Powers By Using Recursion &amp; Static Input Value<\/a><\/li>\n<li><a href=\"#Java_Program_to_Find_Number_of_Ways_to_Express_a_Number_as_Sum_of_Powers_By_Using_Recursion_&amp;_User_Input_Value\">Java Program to Find Number of Ways to Express a Number as Sum of Powers By Using Recursion &amp; User Input Value<\/a><\/li>\n<\/ul>\n<h3><a id=\"Java_Program_to_Find_Number_of_Ways_to_Express_a_Number_as_Sum_of_Powers_By_Using_Recursion_&amp;_Static_Input_Value\"><\/a>Method-1: Java Program to Find Number of Ways to Express a Number as Sum of Powers By Using Recursion &amp; Static Input Value<\/h3>\n<p><strong>Approach:<\/strong><\/p>\n<ul>\n<li>Declare and initialize two integer variables say &#8216;<code>num<\/code>&#8216; and &#8216;<code>power<\/code>&#8216;\u00a0 respectively.<\/li>\n<li>Pass both of them to the user defined method <code>countWays( )<\/code>\u00a0 that calls <code>countWaysUtil( )<\/code> function which is a recursive function. It calculates the ways we can represent the number as a sum of numbers raised to the specific power.<\/li>\n<li>Print the result.<\/li>\n<\/ul>\n<p><strong>Program:<\/strong><\/p>\n<pre class=\"EnlighterJSRAW\" data-enlighter-language=\"java\">import java.util.*;\r\n\/\/ Main class\r\npublic class Main\r\n{\r\n    \/\/ Recursive method that finds ways to represent number as a sum of power\r\n    static int countWaysUtil(int x, int power, int num)\r\n    {\r\n        \/\/ Base cases\r\n        int val = (int) (x - Math.pow(num, power));\r\n        if (val == 0)\r\n            return 1;\r\n        if (val &lt; 0)\r\n            return 0;\r\n        \/\/ Breaks into two cases one with num included and the other one without num\r\n        return countWaysUtil(val, power, num + 1) +\r\n                countWaysUtil(x, power, num + 1);\r\n    }\r\n\r\n    \/\/ Returns number of ways to express\r\n    \/\/ x as sum of numbers raised to the specified power\r\n    static int countWays(int x, int power)\r\n    {\r\n        return countWaysUtil(x, power, 1);\r\n    }\r\n    \r\n    public static void main(String[] args)\r\n    {\r\n        int num = 100, power =2;\r\n        \/\/ call the method and store the ways\r\n        int ways = countWays(num,power);\r\n        System.out.println(num+\" can be represented with power \"+power+\" in \"+ways+\" ways.\");\r\n    }\r\n}\r\n<\/pre>\n<pre>Output:\r\n\r\n100 can be represented with power 2 in 3 ways.<\/pre>\n<h3><a id=\"Java_Program_to_Find_Number_of_Ways_to_Express_a_Number_as_Sum_of_Powers_By_Using_Recursion_&amp;_User_Input_Value\"><\/a>Method-2: Java Program to Find Number of Ways to Express a Number as Sum of Powers By Using Recursion &amp; User Input Value<\/h3>\n<p><strong>Approach:<\/strong><\/p>\n<ul>\n<li>Ask the user to enter a &#8216;num&#8217; and &#8216;power&#8217;.<\/li>\n<li>Pass both of them to the countWays( ) function that calls countWaysUtil( ) function which is a recursive function. It calculates the ways we can represent the number as a sumof numbers raised to the specific power.<\/li>\n<li>Print the result.<\/li>\n<\/ul>\n<p><strong>Program:<\/strong><\/p>\n<pre class=\"EnlighterJSRAW\" data-enlighter-language=\"java\">import java.util.*;\r\n\/\/ Main class\r\npublic class Main\r\n{\r\n    \/\/ recursive method that finds ways to represent number as a sum of power\r\n    static int countWaysUtil(int x, int power, int num)\r\n    {\r\n        \/\/ Base cases\r\n        int val = (int) (x - Math.pow(num, power));\r\n        if (val == 0)\r\n            return 1;\r\n        if (val &lt; 0)\r\n            return 0;\r\n        \/\/ Breaks into two cases\r\n        \/\/ one with num included and the other one without num\r\n        return countWaysUtil(val, power, num + 1) +\r\n                countWaysUtil(x, power, num + 1);\r\n    }\r\n\r\n    \/\/ Returns number of ways to express\r\n    \/\/ x as sum of numbers raised to the specified power\r\n    static int countWays(int x, int power)\r\n    {\r\n        return countWaysUtil(x, power, 1);\r\n    }\r\n\r\n    public static void main(String[] args)\r\n    {\r\n        \/\/ Asking the user for input\r\n        Scanner sc = new Scanner(System.in);\r\n        System.out.println(\"Enter the number and power\");\r\n        int num = sc.nextInt(), power =sc.nextInt();\r\n        \/\/ call the method and store the ways\r\n        int ways = countWays(num,power);\r\n        System.out.println(num+\" can be represented with power \"+power+\" in \"+ways+\" ways.\");\r\n    }\r\n}\r\n<\/pre>\n<pre>Output:\r\n\r\nEnter the number and power\r\n100 3\r\n100 can be represented with power 3 in 1 ways.<\/pre>\n<p>Access the <a href=\"https:\/\/btechgeeks.com\/java-programming-examples\/\">Simple Java program for Interview<\/a> examples with output from our page and impress your interviewer panel with your coding skills.<\/p>\n<p><strong>Related Java Programs:<\/strong><\/p>\n<ul>\n<li><a href=\"https:\/\/btechgeeks.com\/java-program-to-print-the-sum-of-all-subsets-of-a-given-set-of-numbers-using-recursion\/\">Java Program to Find Sum of All Subsets of a Given Set by Using recursion<\/a><\/li>\n<li><a href=\"https:\/\/btechgeeks.com\/java-program-to-find-the-product-of-all-perfect-divisors-of-a-number-using-recursion\/\">Java Program to Find the Product of All Perfect Divisors of a Number Using Recursion<\/a><\/li>\n<li><a href=\"https:\/\/btechgeeks.com\/java-program-to-test-divisibility-of-a-number-by-11-and-9-using-recursion\/\">Java Program to Test Divisibility by 11 and 9 Using Recursion<\/a><\/li>\n<li><a href=\"https:\/\/btechgeeks.com\/java-program-to-find-string-permutation-using-recursion\/\">Java Program to Find String Permutation by Using Recursion<\/a><\/li>\n<\/ul>\n","protected":false},"excerpt":{"rendered":"<p>In the previous article, we have discussed about Java Program to Find Sum of Proper Divisors of a Number by Using Recursion In this article we are going to see how we can find the number of ways so that a number can be expressed as sum of powers by using recursion. Java Program to &#8230; <a title=\"Java Program to Find Number of Ways to Express a Number as Sum of Powers Using Recursion\" class=\"read-more\" href=\"https:\/\/btechgeeks.com\/java-program-to-find-number-of-ways-to-express-a-number-as-sum-of-powers-using-recursion\/\" aria-label=\"More on Java Program to Find Number of Ways to Express a Number as Sum of Powers Using Recursion\">Read more<\/a><\/p>\n","protected":false},"author":9,"featured_media":35465,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"spay_email":""},"categories":[15],"tags":[],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v17.2 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>Java Program to Find Number of Ways to Express a Number as Sum of Powers Using Recursion - BTech Geeks<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/btechgeeks.com\/java-program-to-find-number-of-ways-to-express-a-number-as-sum-of-powers-using-recursion\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Java Program to Find Number of Ways to Express a Number as Sum of Powers Using Recursion - BTech Geeks\" \/>\n<meta property=\"og:description\" content=\"In the previous article, we have discussed about Java Program to Find Sum of Proper Divisors of a Number by Using Recursion In this article we are going to see how we can find the number of ways so that a number can be expressed as sum of powers by using recursion. 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