[Silver II] Title: 이항 계수 2, Time: 120 ms, Memory: 18284 KB -BaekjoonHub

Author: CheChe903

백준/Silver/11051. 이항 계수 2/README.md

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+# [Silver II] 이항 계수 2 - 11051 
+
+[문제 링크](https://www.acmicpc.net/problem/11051) 
+
+### 성능 요약
+
+메모리: 18284 KB, 시간: 120 ms
+
+### 분류
+
+조합론, 다이나믹 프로그래밍, 수학
+
+### 제출 일자
+
+2024년 12월 24일 14:50:50
+
+### 문제 설명
+
+<p>자연수 <mjx-container class="MathJax" jax="CHTML" style="font-size: 109%; position: relative;"><mjx-math class="MJX-TEX" aria-hidden="true"><mjx-mi class="mjx-i"><mjx-c class="mjx-c1D441 TEX-I"></mjx-c></mjx-mi></mjx-math><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>N</mi></math></mjx-assistive-mml><span aria-hidden="true" class="no-mathjax mjx-copytext">\(N\)</span></mjx-container>과 정수 <mjx-container class="MathJax" jax="CHTML" style="font-size: 109%; position: relative;"><mjx-math class="MJX-TEX" aria-hidden="true"><mjx-mi class="mjx-i"><mjx-c class="mjx-c1D43E TEX-I"></mjx-c></mjx-mi></mjx-math><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>K</mi></math></mjx-assistive-mml><span aria-hidden="true" class="no-mathjax mjx-copytext">\(K\)</span></mjx-container>가 주어졌을 때 이항 계수 <mjx-container class="MathJax" jax="CHTML" style="font-size: 109%; position: relative;"><mjx-math class="MJX-TEX" aria-hidden="true"><mjx-mrow><mjx-texatom texclass="OPEN"><mjx-mo class="mjx-sop"><mjx-c class="mjx-c28 TEX-S1"></mjx-c></mjx-mo></mjx-texatom><mjx-mfrac><mjx-frac atop="true" delims="true" style="vertical-align: -0.345em;"><mjx-num style="padding-bottom: 0.306em;"><mjx-mi class="mjx-i" size="s"><mjx-c class="mjx-c1D441 TEX-I"></mjx-c></mjx-mi></mjx-num><mjx-den><mjx-mi class="mjx-i" size="s"><mjx-c class="mjx-c1D43E TEX-I"></mjx-c></mjx-mi></mjx-den></mjx-frac></mjx-mfrac><mjx-texatom texclass="CLOSE"><mjx-mo class="mjx-sop"><mjx-c class="mjx-c29 TEX-S1"></mjx-c></mjx-mo></mjx-texatom></mjx-mrow></mjx-math><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="OPEN"><mo minsize="1.2em" maxsize="1.2em">(</mo></mrow><mfrac linethickness="0"><mi>N</mi><mi>K</mi></mfrac><mrow data-mjx-texclass="CLOSE"><mo minsize="1.2em" maxsize="1.2em">)</mo></mrow></mrow></math></mjx-assistive-mml><span aria-hidden="true" class="no-mathjax mjx-copytext">\(\binom{N}{K}\)</span></mjx-container>를 10,007로 나눈 나머지를 구하는 프로그램을 작성하시오.</p>
+
+### 입력 
+
+ <p>첫째 줄에 <mjx-container class="MathJax" jax="CHTML" style="font-size: 109%; position: relative;"><mjx-math class="MJX-TEX" aria-hidden="true"><mjx-mi class="mjx-i"><mjx-c class="mjx-c1D441 TEX-I"></mjx-c></mjx-mi></mjx-math><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>N</mi></math></mjx-assistive-mml><span aria-hidden="true" class="no-mathjax mjx-copytext">\(N\)</span></mjx-container>과 <mjx-container class="MathJax" jax="CHTML" style="font-size: 109%; position: relative;"><mjx-math class="MJX-TEX" aria-hidden="true"><mjx-mi class="mjx-i"><mjx-c class="mjx-c1D43E TEX-I"></mjx-c></mjx-mi></mjx-math><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>K</mi></math></mjx-assistive-mml><span aria-hidden="true" class="no-mathjax mjx-copytext">\(K\)</span></mjx-container>가 주어진다. (1 ≤ <mjx-container class="MathJax" jax="CHTML" style="font-size: 109%; position: relative;"><mjx-math class="MJX-TEX" aria-hidden="true"><mjx-mi class="mjx-i"><mjx-c class="mjx-c1D441 TEX-I"></mjx-c></mjx-mi></mjx-math><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>N</mi></math></mjx-assistive-mml><span aria-hidden="true" class="no-mathjax mjx-copytext">\(N\)</span></mjx-container> ≤ 1,000, 0 ≤ <mjx-container class="MathJax" jax="CHTML" style="font-size: 109%; position: relative;"><mjx-math class="MJX-TEX" aria-hidden="true"><mjx-mi class="mjx-i"><mjx-c class="mjx-c1D43E TEX-I"></mjx-c></mjx-mi></mjx-math><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>K</mi></math></mjx-assistive-mml><span aria-hidden="true" class="no-mathjax mjx-copytext">\(K\)</span></mjx-container> ≤ <mjx-container class="MathJax" jax="CHTML" style="font-size: 109%; position: relative;"><mjx-math class="MJX-TEX" aria-hidden="true"><mjx-mi class="mjx-i"><mjx-c class="mjx-c1D441 TEX-I"></mjx-c></mjx-mi></mjx-math><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>N</mi></math></mjx-assistive-mml><span aria-hidden="true" class="no-mathjax mjx-copytext">\(N\)</span></mjx-container>)</p>
+
+### 출력 
+
+ <p> <mjx-container class="MathJax" jax="CHTML" style="font-size: 109%; position: relative;"><mjx-math class="MJX-TEX" aria-hidden="true"><mjx-mrow><mjx-texatom texclass="OPEN"><mjx-mo class="mjx-sop"><mjx-c class="mjx-c28 TEX-S1"></mjx-c></mjx-mo></mjx-texatom><mjx-mfrac><mjx-frac atop="true" delims="true" style="vertical-align: -0.345em;"><mjx-num style="padding-bottom: 0.306em;"><mjx-mi class="mjx-i" size="s"><mjx-c class="mjx-c1D441 TEX-I"></mjx-c></mjx-mi></mjx-num><mjx-den><mjx-mi class="mjx-i" size="s"><mjx-c class="mjx-c1D43E TEX-I"></mjx-c></mjx-mi></mjx-den></mjx-frac></mjx-mfrac><mjx-texatom texclass="CLOSE"><mjx-mo class="mjx-sop"><mjx-c class="mjx-c29 TEX-S1"></mjx-c></mjx-mo></mjx-texatom></mjx-mrow></mjx-math><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="OPEN"><mo minsize="1.2em" maxsize="1.2em">(</mo></mrow><mfrac linethickness="0"><mi>N</mi><mi>K</mi></mfrac><mrow data-mjx-texclass="CLOSE"><mo minsize="1.2em" maxsize="1.2em">)</mo></mrow></mrow></math></mjx-assistive-mml><span aria-hidden="true" class="no-mathjax mjx-copytext">\(\binom{N}{K}\)</span></mjx-container>를 10,007로 나눈 나머지를 출력한다.</p>
+

백준/Silver/11051. 이항 계수 2/이항 계수 2.java

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+import java.io.*;
+import java.util.*;
+
+public class Main {
+    public static void main(String[] args) throws IOException {
+        BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
+    
+        StringTokenizer st = new StringTokenizer(br.readLine());
+
+        int N=  Integer.parseInt(st.nextToken());
+        int K = Integer.parseInt(st.nextToken());
+
+        int dp[][] = new int[1001][1001];
+
+        for(int i =0; i<=N; i++) {
+            dp[i][0] = 1;
+            dp[i][i] =1;
+        }
+
+        for(int i =1; i<=N; i++) {
+            for(int j =1; j<=K; j++) {
+                dp[i][j] = (dp[i-1][j] + dp[i-1][j-1])%10007;
+            }
+        }
+
+        System.out.println(dp[N][K]);
+    }
+}